From 5a33edf56f97e1be05e2fb9d333a2fb3d2297b04 Mon Sep 17 00:00:00 2001 From: odunbar Date: Mon, 26 Sep 2022 15:32:27 -0700 Subject: [PATCH] added RF emulator update project toml examples for RF shuffle data update example example to produce comparable figs updates for compatability with CES 0.2.0 and RF 0.1.0 vector random feature support added fixes to ensure CES pipeline runs regularization and lorenz example format allows training with fewer features than data VRFI with SVD, and cholesky options feature num dep on n GCM example replace data multithreading and rng add ProgressBars remove high-level threading for now (takes place within LinAlg solvers) sbatch script truth at some points increased number optimization features default bugfix reg matrix argument initial tik-reg for EKI working TEKI 0 default eki, small tweaks add logdet complexity more consistent adding of definiteness chol/svd add logdet to scalar learning shape bug logdetI unite common functions in Random Feature, expand Scalar feature learning extend reverse svd for covs add diag terms to MatrixNormal description, default to diagonal regularizations rather than pos-def add diagonal option trimmed, and added const hp for diag cov compat with svd truncation, and more standard posdef corrections added scaling to complexity data change scalar interface lorenz 2d statsplot combine all MLT examples into this improved interfacing, unification and initial unit testing condensed into emulate_sample simplify scalar interface bug improved vector interface reg should be multiplicative! fixed small edits update ess.jl MSE on next ensemble, add input-diag case inflation optimizer defaults and cov representation inflation vec inflation utility for ensembles test pass with new defaults and cov structure format format add RF tests GP test fails resolved scalar_optimize_and_plot_RF.jl with new RF accel removed some abstract types, compatible with RandomFeatures 0.2.5 format typo another typo compatible with v0.3 RandomFeatures dispatching over RandomFeatures v0.3.1 multthread options typo more flexible priors compataility for SRF and RF v0.3.1 updates to GCM example scripts docstrings docstring API and format rm duplicate API docs format API docs work locally rename test pass format better messages, bugfix priors for diagonalized options emulation test scenarios for scalar and vector RF multithread supp for lorenz example added cov samples user option, added opt-option for threading in prediction test format Lorenz example config verbose flag tests pass format test for tullio threading format comment api docs until github docs bug fixed --- Project.toml | 6 +- docs/Project.toml | 1 - docs/make.jl | 6 +- docs/src/API/GaussianProcess.md | 3 +- docs/src/API/RandomFeatures.md | 39 ++ examples/Emulator/GaussianProcess/plot_GP.jl | 12 +- examples/Emulator/RandomFeature/Project.toml | 15 + .../scalar_optimize_and_plot_RF.jl | 259 +++++++ .../vector_optimize_and_plot_RF.jl | 286 ++++++++ examples/GCM/Project.toml | 16 + .../GCM/data_from_eki_inflateyonly_100.jld2 | Bin 0 -> 859553 bytes examples/GCM/emulate_sample_script.jl | 227 ++++++ examples/GCM/priors.jld2 | Bin 0 -> 11146 bytes examples/GCM/sbatch_emulate_sample_jl | 36 + examples/GCM/truthobj_meanparam.jld2 | Bin 0 -> 587846 bytes examples/GCM/truthobj_physparam.jld2 | Bin 0 -> 587846 bytes examples/GCM/truthobj_randparam.jld2 | Bin 0 -> 586730 bytes examples/Lorenz/GModel.jl | 9 +- examples/Lorenz/calibrate.jl | 13 +- examples/Lorenz/emulate_sample.jl | 364 +++++----- src/CalibrateEmulateSample.jl | 7 +- src/Emulator.jl | 191 +++-- src/MarkovChainMonteCarlo.jl | 5 +- src/RandomFeature.jl | 661 ++++++++++++++++++ src/ScalarRandomFeature.jl | 437 ++++++++++++ src/Utilities.jl | 45 +- src/VectorRandomFeature.jl | 567 +++++++++++++++ test/GaussianProcess/runtests.jl | 2 +- test/RandomFeature/runtests.jl | 306 ++++++++ test/Utilities/runtests.jl | 13 + test/runtests.jl | 2 +- 31 files changed, 3282 insertions(+), 246 deletions(-) create mode 100644 docs/src/API/RandomFeatures.md create mode 100644 examples/Emulator/RandomFeature/Project.toml create mode 100644 examples/Emulator/RandomFeature/scalar_optimize_and_plot_RF.jl create mode 100644 examples/Emulator/RandomFeature/vector_optimize_and_plot_RF.jl create mode 100644 examples/GCM/Project.toml create mode 100644 examples/GCM/data_from_eki_inflateyonly_100.jld2 create mode 100644 examples/GCM/emulate_sample_script.jl create mode 100644 examples/GCM/priors.jld2 create mode 100644 examples/GCM/sbatch_emulate_sample_jl create mode 100644 examples/GCM/truthobj_meanparam.jld2 create mode 100644 examples/GCM/truthobj_physparam.jld2 create mode 100644 examples/GCM/truthobj_randparam.jld2 create mode 100644 src/RandomFeature.jl create mode 100644 src/ScalarRandomFeature.jl create mode 100644 src/VectorRandomFeature.jl create mode 100644 test/RandomFeature/runtests.jl diff --git a/Project.toml b/Project.toml index 6b4d02b54..a2c6f4132 100644 --- a/Project.toml +++ b/Project.toml @@ -15,9 +15,12 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" MCMCChains = "c7f686f2-ff18-58e9-bc7b-31028e88f75d" Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" +ProgressBars = "49802e3a-d2f1-5c88-81d8-b72133a6f568" PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +RandomFeatures = "36c3bae2-c0c3-419d-b3b4-eebadd35c5e5" ScikitLearn = "3646fa90-6ef7-5e7e-9f22-8aca16db6324" +StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3" Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" @@ -32,8 +35,9 @@ GaussianProcesses = "0.12" MCMCChains = "4.14, 5, 6" PyCall = "1.93" ScikitLearn = "0.6, 0.7" +RandomFeatures = "0.3" StatsBase = "0.33" -julia = "1.6" +julia = "1.6, 1.7, 1.8" [extras] Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" diff --git a/docs/Project.toml b/docs/Project.toml index a500ef4a7..51a4903c7 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,4 +1,3 @@ [deps] CalibrateEmulateSample = "95e48a1f-0bec-4818-9538-3db4340308e3" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" - diff --git a/docs/make.jl b/docs/make.jl index 9e20907e5..cbbe22da9 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -12,7 +12,11 @@ design = ["AbstractMCMC sampling API" => "API/AbstractMCMC.md"] api = [ "CalibrateEmulateSample" => [ - "Emulators" => ["General Emulator" => "API/Emulators.md", "Gaussian Process" => "API/GaussianProcess.md"], + "Emulators" => [ + "General Interface" => "API/Emulators.md", + "Gaussian Process" => "API/GaussianProcess.md", +# "Random Features" => "API/RandomFeatures.md", + ], "MarkovChainMonteCarlo" => "API/MarkovChainMonteCarlo.md", "Utilities" => "API/Utilities.md", ], diff --git a/docs/src/API/GaussianProcess.md b/docs/src/API/GaussianProcess.md index 79be9e7c0..3b1058352 100644 --- a/docs/src/API/GaussianProcess.md +++ b/docs/src/API/GaussianProcess.md @@ -8,6 +8,7 @@ CurrentModule = CalibrateEmulateSample.Emulators GaussianProcessesPackage PredictionType GaussianProcess -build_models! +build_models!(::GaussianProcess{GPJL}, ::PairedDataContainer{FT}) where {FT <: AbstractFloat} optimize_hyperparameters!(::GaussianProcess{GPJL}) +predict(::GaussianProcess{GPJL}, ::AbstractMatrix{FT}) where {FT <: AbstractFloat} ``` \ No newline at end of file diff --git a/docs/src/API/RandomFeatures.md b/docs/src/API/RandomFeatures.md new file mode 100644 index 000000000..b5f5956bc --- /dev/null +++ b/docs/src/API/RandomFeatures.md @@ -0,0 +1,39 @@ +# RandomFeatures + +```@meta +CurrentModule = CalibrateEmulateSample.Emulators +``` + +## Scalar interface + +```@docs +ScalarRandomFeatureInterface +ScalarRandomFeatureInterface(::Int,::Int) +build_models!(::ScalarRandomFeatureInterface, ::PairedDataContainer{FT}) where {FT <: AbstractFloat} +predict(::ScalarRandomFeatureInterface, ::M) where {M <: AbstractMatrix} +``` + +## Vector Interface + +```@docs +VectorRandomFeatureInterface +VectorRandomFeatureInterface(::Int, ::Int, ::Int) +build_models!(::VectorRandomFeatureInterface, ::PairedDataContainer{FT}) where {FT <: AbstractFloat} +predict(::VectorRandomFeatureInterface, ::M) where {M <: AbstractMatrix} +``` + +## Other utilities +```@docs +get_rfms +get_fitted_features +get_batch_sizes +get_n_features +get_input_dim +get_output_dim +get_rng +get_diagonalize_input +get_feature_decomposition +get_optimizer_options +optimize_hyperparameters!(::ScalarRandomFeatureInterface) +optimize_hyperparameters!(::VectorRandomFeatureInterface) +``` diff --git a/examples/Emulator/GaussianProcess/plot_GP.jl b/examples/Emulator/GaussianProcess/plot_GP.jl index 5a815969c..a0ee9751f 100644 --- a/examples/Emulator/GaussianProcess/plot_GP.jl +++ b/examples/Emulator/GaussianProcess/plot_GP.jl @@ -68,9 +68,9 @@ if !isdir(output_directory) end #create the machine learning tools: Gaussian Process -gppackage = GPJL() +gppackage = SKLJL() pred_type = YType() -gaussian_process = GaussianProcess(gppackage, noise_learn = true) +gaussian_process = GaussianProcess(gppackage, noise_learn = false) # Generate training data (x-y pairs, where x ∈ ℝ ᵖ, y ∈ ℝ ᵈ) # x = [x1, x2]: inputs/predictors/features/parameters @@ -92,7 +92,7 @@ gx[2, :] = g2x # Add noise η μ = zeros(d) -Σ = 0.1 * [[0.8, 0.0] [0.0, 0.5]] # d x d +Σ = 0.1 * [[0.8, 0.1] [0.1, 0.5]] # d x d noise_samples = rand(MvNormal(μ, Σ), n) # y = G(x) + η Y = gx .+ noise_samples @@ -182,9 +182,9 @@ println("GP trained") # Plot mean and variance of the predicted observables y1 and y2 # For this, we generate test points on a x1-x2 grid. -n_pts = 50 -x1 = range(0.0, stop = 2 * π, length = n_pts) -x2 = range(0.0, stop = 2 * π, length = n_pts) +n_pts = 200 +x1 = range(0.0, stop = (4.0 / 5.0) * 2 * π, length = n_pts) +x2 = range(0.0, stop = (4.0 / 5.0) * 2 * π, length = n_pts) X1, X2 = meshgrid(x1, x2) # Input for predict has to be of size N_samples x input_dim inputs = permutedims(hcat(X1[:], X2[:]), (2, 1)) diff --git a/examples/Emulator/RandomFeature/Project.toml b/examples/Emulator/RandomFeature/Project.toml new file mode 100644 index 000000000..9d41c3993 --- /dev/null +++ b/examples/Emulator/RandomFeature/Project.toml @@ -0,0 +1,15 @@ +[deps] +CalibrateEmulateSample = "95e48a1f-0bec-4818-9538-3db4340308e3" +Conda = "8f4d0f93-b110-5947-807f-2305c1781a2d" +Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" + +[compat] +FiniteDiff = "~2.10" +julia = "~1.6" diff --git a/examples/Emulator/RandomFeature/scalar_optimize_and_plot_RF.jl b/examples/Emulator/RandomFeature/scalar_optimize_and_plot_RF.jl new file mode 100644 index 000000000..d202f0391 --- /dev/null +++ b/examples/Emulator/RandomFeature/scalar_optimize_and_plot_RF.jl @@ -0,0 +1,259 @@ +# Reference the in-tree version of CalibrateEmulateSample on Julias load path +include(joinpath(@__DIR__, "..", "..", "ci", "linkfig.jl")) + +# Import modules +using Random +using StableRNGs +using Distributions +using Statistics +using LinearAlgebra +using CalibrateEmulateSample.Emulators +using CalibrateEmulateSample.DataContainers +using CalibrateEmulateSample.ParameterDistributions + +case = "scalar" +println("running case $case") + +diagonalize_input = true + +plot_flag = true +if plot_flag + using Plots + gr(size = (1500, 700)) + Plots.scalefontsizes(1.3) + font = Plots.font("Helvetica", 18) + fontdict = Dict(:guidefont => font, :xtickfont => font, :ytickfont => font, :legendfont => font) + +end + +function meshgrid(vx::AbstractVector{T}, vy::AbstractVector{T}) where {T} + m, n = length(vy), length(vx) + gx = reshape(repeat(vx, inner = m, outer = 1), m, n) + gy = reshape(repeat(vy, inner = 1, outer = n), m, n) + + return gx, gy +end +rng_seed = 41 +Random.seed!(rng_seed) +output_directory = joinpath(@__DIR__, "output") +if !isdir(output_directory) + mkdir(output_directory) +end + +#problem +n = 100 # number of training points +p = 2 # input dim +d = 2 # output dim +X = 2.0 * π * rand(p, n) +# G(x1, x2) +g1x = sin.(X[1, :]) .+ cos.(X[2, :]) +g2x = sin.(X[1, :]) .- cos.(X[2, :]) +gx = zeros(2, n) +gx[1, :] = g1x +gx[2, :] = g2x + +# Add noise η +μ = zeros(d) +Σ = 0.1 * [[0.8, 0.1] [0.1, 0.5]] # d x d +noise_samples = rand(MvNormal(μ, Σ), n) +# y = G(x) + η +Y = gx .+ noise_samples + +iopairs = PairedDataContainer(X, Y, data_are_columns = true) +@assert get_inputs(iopairs) == X +@assert get_outputs(iopairs) == Y + +#plot training data with and without noise +if plot_flag + p1 = plot( + X[1, :], + X[2, :], + g1x, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + + figpath = joinpath(output_directory, "RF_observed_y1nonoise.png") + savefig(figpath) + + p2 = plot( + X[1, :], + X[2, :], + g2x, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + figpath = joinpath(output_directory, "RF_observed_y2nonoise.png") + savefig(figpath) + + p3 = plot( + X[1, :], + X[2, :], + Y[1, :], + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + figpath = joinpath(output_directory, "RF_observed_y1.png") + savefig(figpath) + + p4 = plot( + X[1, :], + X[2, :], + Y[2, :], + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + figpath = joinpath(output_directory, "RF_observed_y2.png") + savefig(figpath) + +end + +# setup random features +n_features = 180 + +srfi = ScalarRandomFeatureInterface(n_features, p, diagonalize_input = diagonalize_input) +emulator = Emulator(srfi, iopairs, obs_noise_cov = Σ, normalize_inputs = true) +println("build RF with $n training points and $(n_features) random features.") + +optimize_hyperparameters!(emulator) # although RF already optimized + +# Plot mean and variance of the predicted observables y1 and y2 +# For this, we generate test points on a x1-x2 grid. +n_pts = 200 +x1 = range(0.0, stop = 4.0 / 5.0 * 2 * π, length = n_pts) +x2 = range(0.0, stop = 4.0 / 5.0 * 2 * π, length = n_pts) +X1, X2 = meshgrid(x1, x2) +# Input for predict has to be of size N_samples x input_dim +inputs = permutedims(hcat(X1[:], X2[:]), (2, 1)) + +rf_mean, rf_cov = predict(emulator, inputs, transform_to_real = true) +println("end predictions at ", n_pts * n_pts, " points") + + +#plot predictions +for y_i in 1:d + rf_var_temp = [diag(rf_cov[j]) for j in 1:length(rf_cov)] # (40000,) + rf_var = permutedims(vcat([x' for x in rf_var_temp]...), (2, 1)) # 2 x 40000 + + mean_grid = reshape(rf_mean[y_i, :], n_pts, n_pts) # 2 x 40000 + if plot_flag + p5 = plot( + x1, + x2, + mean_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "mean of y" * string(y_i), + zguidefontrotation = 90, + ) + end + var_grid = reshape(rf_var[y_i, :], n_pts, n_pts) + if plot_flag + p6 = plot( + x1, + x2, + var_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "var of y" * string(y_i), + zguidefontrotation = 90, + ) + + plot(p5, p6, layout = (1, 2), legend = false) + + savefig(joinpath(output_directory, "RF_" * case * "_y" * string(y_i) * "_predictions.png")) + end +end + +# Plot the true components of G(x1, x2) +g1_true = sin.(inputs[1, :]) .+ cos.(inputs[2, :]) +g1_true_grid = reshape(g1_true, n_pts, n_pts) +if plot_flag + p7 = plot( + x1, + x2, + g1_true_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "sin(x1) + cos(x2)", + zguidefontrotation = 90, + ) + savefig(joinpath(output_directory, "RF_" * case * "_true_g1.png")) +end + +g2_true = sin.(inputs[1, :]) .- cos.(inputs[2, :]) +g2_true_grid = reshape(g2_true, n_pts, n_pts) +if plot_flag + p8 = plot( + x1, + x2, + g2_true_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "sin(x1) - cos(x2)", + zguidefontrotation = 90, + ) + g_true_grids = [g1_true_grid, g2_true_grid] + + savefig(joinpath(output_directory, "RF_" * case * "_true_g2.png")) + +end + +# Plot the difference between the truth and the mean of the predictions +for y_i in 1:d + + # Reshape rf_cov to size N_samples x output_dim + rf_var_temp = [diag(rf_cov[j]) for j in 1:length(rf_cov)] # (40000,) + rf_var = permutedims(vcat([x' for x in rf_var_temp]...), (2, 1)) # 40000 x 2 + + mean_grid = reshape(rf_mean[y_i, :], n_pts, n_pts) + var_grid = reshape(rf_var[y_i, :], n_pts, n_pts) + # Compute and plot 1/variance * (truth - prediction)^2 + + if plot_flag + zlabel = "1/var * (true_y" * string(y_i) * " - predicted_y" * string(y_i) * ")^2" + + p9 = plot( + x1, + x2, + sqrt.(1.0 ./ var_grid .* (g_true_grids[y_i] .- mean_grid) .^ 2), + st = :surface, + camera = (30, 60), + c = :magma, + zlabel = zlabel, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + + savefig(joinpath(output_directory, "RF_" * case * "_y" * string(y_i) * "_difference_truth_prediction.png")) + end +end diff --git a/examples/Emulator/RandomFeature/vector_optimize_and_plot_RF.jl b/examples/Emulator/RandomFeature/vector_optimize_and_plot_RF.jl new file mode 100644 index 000000000..05e4f348f --- /dev/null +++ b/examples/Emulator/RandomFeature/vector_optimize_and_plot_RF.jl @@ -0,0 +1,286 @@ +# Reference the in-tree version of CalibrateEmulateSample on Julias load path +include(joinpath(@__DIR__, "..", "..", "ci", "linkfig.jl")) + +# Import modules +using Random +using StableRNGs +using Distributions +using Statistics +using LinearAlgebra +using CalibrateEmulateSample.Emulators +using CalibrateEmulateSample.DataContainers +using CalibrateEmulateSample.ParameterDistributions +plot_flag = true +if plot_flag + using Plots + gr(size = (1500, 700)) + Plots.scalefontsizes(1.3) + font = Plots.font("Helvetica", 18) + fontdict = Dict(:guidefont => font, :xtickfont => font, :ytickfont => font, :legendfont => font) + +end + + +function meshgrid(vx::AbstractVector{T}, vy::AbstractVector{T}) where {T} + m, n = length(vy), length(vx) + gx = reshape(repeat(vx, inner = m, outer = 1), m, n) + gy = reshape(repeat(vy, inner = 1, outer = n), m, n) + + return gx, gy +end + +function main() + + rng_seed = 41 + Random.seed!(rng_seed) + output_directory = joinpath(@__DIR__, "output") + if !isdir(output_directory) + mkdir(output_directory) + end + + cases = ["svd-diag", "svd-nondiag", "nosvd-diag", "nosvd-nondiag"] + case_mask = 1:4 # which cases to do + + #problem + n = 150 # number of training points + p = 2 # input dim + d = 2 # output dim + X = 2.0 * π * rand(p, n) + # G(x1, x2) + g1x = sin.(X[1, :]) .+ cos.(X[2, :]) + g2x = sin.(X[1, :]) .- cos.(X[2, :]) + gx = zeros(2, n) + gx[1, :] = g1x + gx[2, :] = g2x + + # Add noise η + μ = zeros(d) + Σ = 0.1 * [[0.8, 0.1] [0.1, 0.5]] # d x d + noise_samples = rand(MvNormal(μ, Σ), n) + # y = G(x) + η + Y = gx .+ noise_samples + + iopairs = PairedDataContainer(X, Y, data_are_columns = true) + @assert get_inputs(iopairs) == X + @assert get_outputs(iopairs) == Y + + #plot training data with and without noise + if plot_flag + p1 = plot( + X[1, :], + X[2, :], + g1x, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + + figpath = joinpath(output_directory, "RF_observed_y1nonoise.png") + savefig(figpath) + + p2 = plot( + X[1, :], + X[2, :], + g2x, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + figpath = joinpath(output_directory, "RF_observed_y2nonoise.png") + savefig(figpath) + + p3 = plot( + X[1, :], + X[2, :], + Y[1, :], + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + figpath = joinpath(output_directory, "RF_observed_y1.png") + savefig(figpath) + + p4 = plot( + X[1, :], + X[2, :], + Y[2, :], + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + figpath = joinpath(output_directory, "RF_observed_y2.png") + savefig(figpath) + + end + + for case in cases[case_mask] + println("running case $case") + + + + + # setup random features + n_features = 200 + + if case == "svd-diag" + vrfi = VectorRandomFeatureInterface(n_features, p, d, diagonalize_output = true) + emulator = Emulator(vrfi, iopairs, obs_noise_cov = Σ, normalize_inputs = true) + elseif case == "svd-nondiag" + vrfi = VectorRandomFeatureInterface(n_features, p, d) + emulator = Emulator(vrfi, iopairs, obs_noise_cov = Σ, normalize_inputs = true) + elseif case == "nosvd-diag" + vrfi = VectorRandomFeatureInterface(n_features, p, d, diagonalize_output = true) + emulator = Emulator(vrfi, iopairs, obs_noise_cov = Σ, normalize_inputs = true, decorrelate = false) + elseif case == "nosvd-nondiag" + vrfi = VectorRandomFeatureInterface(n_features, p, d) + emulator = Emulator(vrfi, iopairs, obs_noise_cov = Σ, normalize_inputs = true, decorrelate = false) + end + println("build RF with $n training points and $(n_features) random features.") + + optimize_hyperparameters!(emulator) # although RF already optimized + + # Plot mean and variance of the predicted observables y1 and y2 + # For this, we generate test points on a x1-x2 grid. + n_pts = 200 + x1 = range(0.0, stop = 4.0 / 5.0 * 2 * π, length = n_pts) + x2 = range(0.0, stop = 4.0 / 5.0 * 2 * π, length = n_pts) + X1, X2 = meshgrid(x1, x2) + # Input for predict has to be of size input_dim x N_samples + inputs = permutedims(hcat(X1[:], X2[:]), (2, 1)) + + rf_mean, rf_cov = predict(emulator, inputs, transform_to_real = true) + println("end predictions at ", n_pts * n_pts, " points") + + + #plot predictions + for y_i in 1:d + + rf_var_temp = [diag(rf_cov[j]) for j in 1:length(rf_cov)] # (40000,) + rf_var = permutedims(vcat([x' for x in rf_var_temp]...), (2, 1)) # 2 x 40000 + + mean_grid = reshape(rf_mean[y_i, :], n_pts, n_pts) # 2 x 40000 + if plot_flag + p5 = plot( + x1, + x2, + mean_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "mean of y" * string(y_i), + zguidefontrotation = 90, + ) + end + var_grid = reshape(rf_var[y_i, :], n_pts, n_pts) + if plot_flag + p6 = plot( + x1, + x2, + var_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "var of y" * string(y_i), + zguidefontrotation = 90, + ) + + plot(p5, p6, layout = (1, 2), legend = false) + + savefig(joinpath(output_directory, "RF_" * case * "_y" * string(y_i) * "_predictions.png")) + end + end + + # Plot the true components of G(x1, x2) + g1_true = sin.(inputs[1, :]) .+ cos.(inputs[2, :]) + g1_true_grid = reshape(g1_true, n_pts, n_pts) + if plot_flag + p7 = plot( + x1, + x2, + g1_true_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "sin(x1) + cos(x2)", + zguidefontrotation = 90, + ) + savefig(joinpath(output_directory, "RF_" * case * "_true_g1.png")) + end + + g2_true = sin.(inputs[1, :]) .- cos.(inputs[2, :]) + g2_true_grid = reshape(g2_true, n_pts, n_pts) + if plot_flag + p8 = plot( + x1, + x2, + g2_true_grid, + st = :surface, + camera = (30, 60), + c = :cividis, + xlabel = "x1", + ylabel = "x2", + zlabel = "sin(x1) - cos(x2)", + zguidefontrotation = 90, + ) + g_true_grids = [g1_true_grid, g2_true_grid] + + savefig(joinpath(output_directory, "RF_" * case * "_true_g2.png")) + + end + MSE = 1 / size(rf_mean, 2) * sqrt(sum((rf_mean[1, :] - g1_true) .^ 2 + (rf_mean[2, :] - g2_true) .^ 2)) + println("L^2 error of mean and latent truth:", MSE) + + # Plot the difference between the truth and the mean of the predictions + for y_i in 1:d + + # Reshape rf_cov to size N_samples x output_dim + rf_var_temp = [diag(rf_cov[j]) for j in 1:length(rf_cov)] # (40000,) + rf_var = permutedims(vcat([x' for x in rf_var_temp]...), (2, 1)) # 40000 x 2 + + mean_grid = reshape(rf_mean[y_i, :], n_pts, n_pts) + var_grid = reshape(rf_var[y_i, :], n_pts, n_pts) + # Compute and plot 1/variance * (truth - prediction)^2 + + if plot_flag + zlabel = "1/var * (true_y" * string(y_i) * " - predicted_y" * string(y_i) * ")^2" + + p9 = plot( + x1, + x2, + sqrt.(1.0 ./ var_grid .* (g_true_grids[y_i] .- mean_grid) .^ 2), + st = :surface, + camera = (30, 60), + c = :magma, + zlabel = zlabel, + xlabel = "x1", + ylabel = "x2", + zguidefontrotation = 90, + ) + + savefig( + joinpath(output_directory, "RF_" * case * "_y" * string(y_i) * "_difference_truth_prediction.png"), + ) + end + end + end +end + +main() diff --git a/examples/GCM/Project.toml b/examples/GCM/Project.toml new file mode 100644 index 000000000..aba51ad3c --- /dev/null +++ b/examples/GCM/Project.toml @@ -0,0 +1,16 @@ +[deps] +CalibrateEmulateSample = "95e48a1f-0bec-4818-9538-3db4340308e3" +Conda = "8f4d0f93-b110-5947-807f-2305c1781a2d" +Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41" +JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PyPlot = "d330b81b-6aea-500a-939a-2ce795aea3ee" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" + +[compat] +FiniteDiff = "~2.10" +julia = "~1.6" diff --git a/examples/GCM/data_from_eki_inflateyonly_100.jld2 b/examples/GCM/data_from_eki_inflateyonly_100.jld2 new file mode 100644 index 0000000000000000000000000000000000000000..1eae5106d00cdeb1123e895bb4fbc5c96f9200e1 GIT binary patch literal 859553 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println("build RF with $(N_ens*N_iter) training points and $(n_features) random features.") + + + mlt = VectorRandomFeatureInterface(n_features, input_dim, output_dim, optimizer_options = eki_options_override) + + elseif emulator_type == "VectorRFR-svd-diag" + + println("Running Vector RF model - using SVD and assuming diagonal variance") + n_features = 20 * Int(floor(5 * sqrt(N_ens * N_iter))) + println("build RF with $(N_ens*N_iter) training points and $(n_features) random features.") + + mlt = VectorRandomFeatureInterface( + n_features, + input_dim, + output_dim, + diagonalize_output = true, + optimizer_options = eki_options_override, + ) + + elseif emulator_type == "ScalarRFR" + println("Running Scalar RF model") + n_features = 5 * Int(floor(5 * sqrt(N_ens * N_iter))) + mlt = ScalarRandomFeatureInterface(n_features, input_dim, optimizer_options = eki_options_override) + + else + emulator_type == "GPR" + println("Running Gaussian Process model") + gppackage = SKLJL() + mlt = GaussianProcess(gppackage, noise_learn = false) + + end + + if emulator_type == "VectorRFR-nondiag" + emulator = Emulator( + mlt, + input_output_pairs; + obs_noise_cov = obs_noise_cov, + normalize_inputs = normalized, + decorrelate = false, + ) + else + emulator = Emulator(mlt, input_output_pairs; obs_noise_cov = obs_noise_cov, normalize_inputs = normalized) + + end + optimize_hyperparameters!(emulator) + + # + # save the emulator! + # + @save joinpath(data_save_directory, "emulator_" * expname * ".jld2") emulator + + # + # predict at some validation points + # + validate_id = ["phys", "mean", "rand"] + + for vid in validate_id + if vid == "phys" + new_input = [log(0.7 / 0.3) log(7200)]' # physical parameter value (at truth) + elseif vid == "mean" + new_input = [log(0.5 / (1 - 0.5)) log(43200)]' # mean-of-prior parameter value ("near-ish" truth) + elseif vid == "rand" + new_input = [log(0.31735951644387783 / (1 - 0.31735951644387783)) log(90632.50269636544)]' # random parameter value ("far" from truth + end + + pred_mean, pred_cov = predict(emulator, new_input, transform_to_real = true) + pred_sd = sqrt.([max(10 * eps(), pred_cov[1][i, i]) for i in 1:size(pred_cov[1], 1)]) + + + # NB pred_cov is a vector of matrices + tobj = load("truthobj_" * vid * "param.jld2")["truthobj"] + t_mean = tobj.mean[data_mask] + t_cov = tobj.cov[data_mask, data_mask] + + println("prediction error at truth for " * vid * " case:") + println(" mean: ", norm(t_mean - pred_mean)) + println(" cov: ", norm(t_cov - pred_cov[1])) + + save( + joinpath(data_save_directory, vid * "_" * expname * "_results.jld2"), + "pred_mean", + pred_mean, + "pred_cov", + pred_cov, + "pred_sd", + pred_sd, + ) + save(joinpath(data_save_directory, vid * "_" * expname * "_truth.jld2"), "true_mean", t_mean, "true_cov", t_cov) + end + + plot_input = [log(0.7 / 0.3) log(7200)]' # physical parameter value (at truth) + plot_mean, plot_cov = predict(emulator, plot_input, transform_to_real = true) + plot_sd = sqrt.([max(10 * eps(), plot_cov[1][i, i]) for i in 1:size(plot_cov[1], 1)]) + + + ids = [1:32, 33:64, 65:96] + plotnames = ["rh", "pr", "ext"] + + for (id, pn) in zip(ids, plotnames) + if data_mask == 1:96 + plt = plot( + collect(id), + plot_mean[id], + show = true, + ribbon = [2 * plot_sd[id]; 2 * plot_sd[id]], + linewidth = 5, + size = (600, 600), + label = "", + ) + figpath = joinpath(figure_save_directory, "predict_" * expname * "_" * pn * "_at_truth.png") + savefig(figpath) + println("plot saved at " * figpath) + else + if data_mask == id + plot_mask = 1:length(data_mask) + plt = plot( + collect(id), + plot_mean[plot_mask], + show = true, + ribbon = [2 * plot_sd[plot_mask]; 2 * plot_sd[plot_mask]], + linewidth = 5, + size = (600, 600), + label = "", + ) + figpath = joinpath(figure_save_directory, "predict_" * expname * "_" * pn * "_at_truth.png") + savefig(figpath) + println("plot saved at " * figpath) + end + end + + end + + + +end # for @time diff --git a/examples/GCM/priors.jld2 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+#precompiling is now done manually before +#julia -e 'using Pkg; Pkg.instantiate(); Pkg.API.precompile()' + +#run code +start=$(date +%s) + + +julia --project -t 28 emulate_sample_script.jl + +end=$(date +%s) +runtime=$((end-start)) +echo "********************" +echo "run time: $runtime" +echo "********************" + + diff --git a/examples/GCM/truthobj_meanparam.jld2 b/examples/GCM/truthobj_meanparam.jld2 new file mode 100644 index 0000000000000000000000000000000000000000..cef3b8f9c6ab069031ae99dc8e3bb877cddcd4d0 GIT binary patch literal 587846 zcmeFZcT^Qk^FK&V0+O@joRlO2+6_ujL=Zth1qA`gK?KAAiWxx^6$yfpF`$Bi0%A9k zL6IbqbIv(P-0S-|@Ba3CcK7W5xqF^D=i0Z!^vu+)DXKp8DGmMHUF?J%?0oHn&$zfd z3QORQROHy<5KUev)`#<~9|7Z5^{9Z3F_rHD0|8f2yI~Pwyb00rnXOq*e zq%~B3=NbOj^L2cD>@NH>K>c@~@qeAyclWaM-KqL#i01G7-`ge2-}(1`)cSRK&*RTmy1(Nzf5*Lj9PM4a$;jycj??}fcMS0Las2bU{5^)5iEsb5|4QIr3H&R8 zevyj*2AKdbWT199;jjd;fwX z>2v?cgJ=Gq_8-WEv}SQ~^7=o&&Q8j|7a##Jf9~A&pB>03ImpPBgyDY$s=9?tb(16# 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q_kf?T+kQunV^sR@V8@q-FM-|O*Wb& julia --project calibrate.jl \n and store results $data_save_file", - ), - ) - end - ekiobj = load(data_save_file)["eki"] - priors = load(data_save_file)["priors"] - truth_sample = load(data_save_file)["truth_sample"] - truth_sample_mean = load(data_save_file)["truth_sample_mean"] - truth_params_constrained = load(data_save_file)["truth_input_constrained"] #true parameters in constrained space - truth_params = transform_constrained_to_unconstrained(priors, truth_params_constrained) - Γy = ekiobj.obs_noise_cov - ### - ### Emulate: Gaussian Process Regression - ### - - # Emulate-sample settings - standardize = true - retained_svd_frac = 0.95 - - gppackage = Emulators.GPJL() - pred_type = Emulators.YType() - gauss_proc = GaussianProcess( - gppackage; - kernel = nothing, # use default squared exponential kernel - prediction_type = pred_type, - noise_learn = false, - ) - - # Standardize the output data - # Use median over all data since all data are the same type - truth_sample_norm = vcat(truth_sample...) - norm_factor = get_standardizing_factors(truth_sample_norm) - println(size(norm_factor)) - #norm_factor = vcat(norm_factor...) - norm_factor = fill(norm_factor, size(truth_sample)) - println("Standardization factors") - println(norm_factor) - - # Get training points from the EKP iteration number in the second input term - N_iter = 5 - input_output_pairs = Utilities.get_training_points(ekiobj, N_iter) - # Save data - @save joinpath(data_save_directory, "input_output_pairs.jld2") input_output_pairs - - normalized = true - emulator = Emulator( - gauss_proc, - input_output_pairs; - obs_noise_cov = Γy, - normalize_inputs = normalized, - standardize_outputs = standardize, - standardize_outputs_factors = norm_factor, - retained_svd_frac = retained_svd_frac, - ) - optimize_hyperparameters!(emulator) - - # Check how well the Gaussian Process regression predicts on the - # true parameters - #if retained_svd_frac==1.0 - y_mean, y_var = Emulators.predict(emulator, reshape(truth_params, :, 1), transform_to_real = true) - - println("GP prediction on true parameters: ") - println(vec(y_mean)) - println(" GP variance") - println(diag(y_var[1], 0)) - println("true data: ") - println(truth_sample_mean) # same, regardless of norm_factor - println("GP MSE: ") - println(mean((truth_sample_mean - vec(y_mean)) .^ 2)) - - #end - ### - ### Sample: Markov Chain Monte Carlo - ### - # initial values - u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) - println("initial parameters: ", u0) - - # First let's run a short chain to determine a good step size - truth_sample = truth_sample - mcmc = MCMCWrapper(RWMHSampling(), truth_sample, priors, emulator; init_params = u0) - new_step = optimize_stepsize(mcmc; init_stepsize = 0.1, N = 2000, discard_initial = 0) - - # Now begin the actual MCMC - println("Begin MCMC - with step size ", new_step) - chain = MarkovChainMonteCarlo.sample(mcmc, 100_000; stepsize = new_step, discard_initial = 2_000) - posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) - - post_mean = mean(posterior) - post_cov = cov(posterior) - println("post_mean") - println(post_mean) - println("post_cov") - println(post_cov) - println("D util") - println(det(inv(post_cov))) - println(" ") - - - # Plot the posteriors together with the priors and the true parameter values (in the constrained space) - n_params = length(truth_params) - save_directory = joinpath(figure_save_directory) - - posterior_distribution_unconstrained_dict = get_distribution(posterior) #as it is a Samples, the distribution are samples - posterior_samples_unconstrained_dict = get_distribution(posterior) #as it is a Samples, the distribution are samples - param_names = get_name(posterior) - posterior_samples_unconstrained_arr = vcat([posterior_samples_unconstrained_dict[n] for n in param_names]...) - posterior_samples = transform_unconstrained_to_constrained(priors, posterior_samples_unconstrained_arr) - - for idx in 1:n_params - if idx == 1 - param = "F" - xbounds = [F_true - 1.0, F_true + 1.0] - xs = collect(xbounds[1]:((xbounds[2] - xbounds[1]) / 100):xbounds[2]) - elseif idx == 2 - param = "A" - xbounds = [A_true - 1.0, A_true + 1.0] - xs = collect(xbounds[1]:((xbounds[2] - xbounds[1]) / 100):xbounds[2]) - elseif idx == 3 - param = "ω" - xs = collect((ω_true - 0.2):0.01:(ω_true + 0.2)) - xbounds = [xs[1], xs[end]] - else - throw("not implemented") + cases = [ + "GP", # diagonalize, train scalar GP, assume diag inputs + "RF-scalar-diagin", # diagonalize, train scalar RF, assume diag inputs (most comparable to GP) + "RF-scalar", # diagonalize, train scalar RF, don't asume diag inputs + "RF-vector-svd-diag", + "RF-vector-svd-nondiag", + "RF-vector-nosvd-diag", + "RF-vector-nosvd-nondiag", + ] + + #### CHOOSE YOUR CASE: + mask = 2:7 + for case in cases[mask] + + + #case = cases[7] + println("case: ", case) + + overrides = Dict("train_fraction" => 0.6, "verbose" => true) + + # Should be loaded: + τc = 5.0 + F_true = 8.0 # Mean F + A_true = 2.5 # Transient F amplitude + ω_true = 2.0 * π / (360.0 / τc) # Frequency of the transient F + #### + + exp_name = "Lorenz_histogram_F$(F_true)_A$(A_true)-w$(ω_true)" + rng_seed = 44011 + rng = Random.MersenneTwister(rng_seed) + + # loading relevant data + homedir = pwd() + println(homedir) + figure_save_directory = joinpath(homedir, "output/") + data_save_directory = joinpath(homedir, "output/") + data_save_file = joinpath(data_save_directory, "calibrate_results.jld2") + + if !isfile(data_save_file) + throw( + ErrorException( + "data file $data_save_file not found. \n First run: \n > julia --project calibrate.jl \n and store results $data_save_file", + ), + ) end - label = "true " * param - - histogram(posterior_samples[idx, :], bins = 100, normed = true, fill = :slategray, lab = "posterior") - prior_plot = get_distribution(mcmc.prior) + ekiobj = load(data_save_file)["eki"] + priors = load(data_save_file)["priors"] + truth_sample = load(data_save_file)["truth_sample"] + truth_sample_mean = load(data_save_file)["truth_sample_mean"] + truth_params_constrained = load(data_save_file)["truth_input_constrained"] #true parameters in constrained space + truth_params = transform_constrained_to_unconstrained(priors, truth_params_constrained) + Γy = ekiobj.obs_noise_cov + + n_params = length(truth_params) # "input dim" + output_dim = size(Γy, 1) + ### + ### Emulate: Gaussian Process Regression + ### + + # Emulate-sample settings + # choice of machine-learning tool + if case == "GP" + gppackage = Emulators.GPJL() + pred_type = Emulators.YType() + mlt = GaussianProcess( + gppackage; + kernel = nothing, # use default squared exponential kernel + prediction_type = pred_type, + noise_learn = false, + ) + elseif case ∈ ["RF-scalar", "RF-scalar-diagin"] + n_features = 300 + diagonalize_input = case == "RF-scalar-diagin" ? true : false + mlt = ScalarRandomFeatureInterface( + n_features, + n_params, + rng = rng, + diagonalize_input = diagonalize_input, + optimizer_options = overrides, + ) + elseif case ∈ ["RF-vector-svd-diag", "RF-vector-nosvd-diag", "RF-vector-svd-nondiag", "RF-vector-nosvd-nondiag"] + # do we want to assume that the outputs are decorrelated in the machine-learning problem? + diagonalize_output = case ∈ ["RF-vector-svd-diag", "RF-vector-nosvd-diag"] ? true : false + n_features = 300 + mlt = VectorRandomFeatureInterface( + n_features, + n_params, + output_dim, + rng = rng, + diagonalize_output = diagonalize_output, # assume outputs are decorrelated + optimizer_options = overrides, + ) + end - # This requires StatsPlots - xs_rows = permutedims(repeat(xs, 1, size(posterior_samples, 1)), (2, 1)) # This hack will enable us to apply the transformation using the full prior - xs_rows_unconstrained = transform_constrained_to_unconstrained(priors, xs_rows) - plot!( - xs, - pdf.(prior_plot[param_names[idx]], xs_rows_unconstrained[idx, :]), - w = 2.6, - color = :blue, - lab = "prior", + # Standardize the output data + # Use median over all data since all data are the same type + truth_sample_norm = vcat(truth_sample...) + norm_factor = get_standardizing_factors(truth_sample_norm) + println(size(norm_factor)) + #norm_factor = vcat(norm_factor...) + norm_factor = fill(norm_factor, size(truth_sample)) + println("Standardization factors") + println(norm_factor) + + # Get training points from the EKP iteration number in the second input term + N_iter = 6 # note we have 6 iterations stored + input_output_pairs = Utilities.get_training_points(ekiobj, N_iter - 1) # 1:N-1 + input_output_pairs_test = Utilities.get_training_points(ekiobj, N_iter:N_iter) # just "next" iteration used for testing + # Save data + @save joinpath(data_save_directory, "input_output_pairs.jld2") input_output_pairs + + standardize = true + retained_svd_frac = 1.0 + normalized = true + # do we want to use SVD to decorrelate outputs + decorrelate = case ∈ ["RF-vector-nosvd-diag", "RF-vector-nosvd-nondiag"] ? false : true + + emulator = Emulator( + mlt, + input_output_pairs; + obs_noise_cov = Γy, + normalize_inputs = normalized, + standardize_outputs = standardize, + standardize_outputs_factors = norm_factor, + retained_svd_frac = retained_svd_frac, + decorrelate = decorrelate, ) - #plot!(xs, mcmc.prior[idx].dist, w=2.6, color=:blue, lab="prior") - plot!([truth_params[idx]], seriestype = "vline", w = 2.6, lab = label) - plot!(xlims = xbounds) + optimize_hyperparameters!(emulator) + + # Check how well the Gaussian Process regression predicts on the + # true parameters + #if retained_svd_frac==1.0 + y_mean, y_var = Emulators.predict(emulator, reshape(truth_params, :, 1), transform_to_real = true) + y_mean_test, y_var_test = + Emulators.predict(emulator, get_inputs(input_output_pairs_test), transform_to_real = true) + + println("ML prediction on true parameters: ") + println(vec(y_mean)) + println("true data: ") + println(truth_sample_mean) # same, regardless of norm_factor + println(" ML predicted variance") + println(diag(y_var[1], 0)) + println("ML MSE (truth): ") + println(mean((truth_sample_mean - vec(y_mean)) .^ 2)) + println("ML MSE (next ensemble): ") + println(mean((get_outputs(input_output_pairs_test) - y_mean_test) .^ 2)) + + #end + ### + ### Sample: Markov Chain Monte Carlo + ### + # initial values + u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) + println("initial parameters: ", u0) + + # First let's run a short chain to determine a good step size + truth_sample = truth_sample + mcmc = MCMCWrapper(RWMHSampling(), truth_sample, priors, emulator; init_params = u0) + new_step = optimize_stepsize(mcmc; init_stepsize = 0.1, N = 2000, discard_initial = 0) + + # Now begin the actual MCMC + println("Begin MCMC - with step size ", new_step) + chain = MarkovChainMonteCarlo.sample(mcmc, 100_000; stepsize = new_step, discard_initial = 2_000) + posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) + + post_mean = mean(posterior) + post_cov = cov(posterior) + println("post_mean") + println(post_mean) + println("post_cov") + println(post_cov) + println("D util") + println(det(inv(post_cov))) + println(" ") + + constrained_truth_params = transform_unconstrained_to_constrained(posterior, truth_params) + param_names = get_name(posterior) + + posterior_samples = vcat([get_distribution(posterior)[name] for name in get_name(posterior)]...) #samples are columns + constrained_posterior_samples = + mapslices(x -> transform_unconstrained_to_constrained(posterior, x), posterior_samples, dims = 1) + + gr(dpi = 300, size = (300, 300)) + p = cornerplot(permutedims(constrained_posterior_samples, (2, 1)), label = param_names, compact = true) + plot!(p.subplots[1], [constrained_truth_params[1]], seriestype = "vline", w = 1.5, c = :steelblue, ls = :dash) # vline on top histogram + plot!(p.subplots[3], [constrained_truth_params[2]], seriestype = "hline", w = 1.5, c = :steelblue, ls = :dash) # hline on right histogram + plot!(p.subplots[2], [constrained_truth_params[1]], seriestype = "vline", w = 1.5, c = :steelblue, ls = :dash) # v & h line on scatter. + plot!(p.subplots[2], [constrained_truth_params[2]], seriestype = "hline", w = 1.5, c = :steelblue, ls = :dash) + figpath = joinpath(figure_save_directory, "posterior_2d-" * case * ".png") + savefig(figpath) - title!(param) - figpath = joinpath(figure_save_directory, "posterior_$(param)_" * exp_name * ".png") - savefig(figpath) - linkfig(figpath) + # Save data + save( + joinpath(data_save_directory, "posterior.jld2"), + "posterior", + posterior, + "input_output_pairs", + input_output_pairs, + "truth_params", + truth_params, + ) end - end main() diff --git a/src/CalibrateEmulateSample.jl b/src/CalibrateEmulateSample.jl index 9f227d0ee..f5956b175 100644 --- a/src/CalibrateEmulateSample.jl +++ b/src/CalibrateEmulateSample.jl @@ -14,13 +14,14 @@ import EnsembleKalmanProcesses: EnsembleKalmanProcesses, ParameterDistributions, export EnsembleKalmanProcesses, ParameterDistributions, Observations, DataContainers -# No internal deps, heavy external deps -#include("GaussianProcessEmulator.jl") -include("Emulator.jl") # Internal deps, light external deps include("Utilities.jl") +# No internal deps, heavy external deps +#include("GaussianProcessEmulator.jl") +include("Emulator.jl") + # Internal deps, light external deps include("MarkovChainMonteCarlo.jl") diff --git a/src/Emulator.jl b/src/Emulator.jl index e4fa76aa8..6f4d2572d 100644 --- a/src/Emulator.jl +++ b/src/Emulator.jl @@ -7,9 +7,11 @@ using Statistics using Distributions using LinearAlgebra using DocStringExtensions +using Random export Emulator +export build_models! export optimize_hyperparameters! export predict @@ -24,7 +26,7 @@ abstract type MachineLearningTool end # include the different <: ML models include("GaussianProcess.jl") #for GaussianProcess -# include("RandomFeature.jl") +include("RandomFeature.jl") # include("NeuralNetwork.jl") # etc. @@ -75,6 +77,8 @@ struct Emulator{FT <: AbstractFloat} retained_svd_frac::FT end +get_machine_learning_tool(emulator::Emulator) = emulator.machine_learning_tool + # Constructor for the Emulator Object function Emulator( machine_learning_tool::MachineLearningTool, @@ -83,6 +87,7 @@ function Emulator( normalize_inputs::Bool = true, standardize_outputs::Bool = false, standardize_outputs_factors::Union{AbstractVector{FT}, Nothing} = nothing, + decorrelate::Bool = true, retained_svd_frac::FT = 1.0, ) where {FT <: AbstractFloat} @@ -118,24 +123,35 @@ function Emulator( training_outputs = get_outputs(input_output_pairs) end - # [3.] Decorrelating the outputs [always performed] - - #Transform data if obs_noise_cov available - # (if obs_noise_cov==nothing, transformed_data is equal to data) - decorrelated_training_outputs, decomposition = - svd_transform(training_outputs, obs_noise_cov, retained_svd_frac = retained_svd_frac) + # [3.] Decorrelating the outputs, not performed for vector RF + if decorrelate + #Transform data if obs_noise_cov available + # (if obs_noise_cov==nothing, transformed_data is equal to data) + decorrelated_training_outputs, decomposition = + svd_transform(training_outputs, obs_noise_cov, retained_svd_frac = retained_svd_frac) + + # write new pairs structure + if retained_svd_frac < 1.0 + #note this changes the dimension of the outputs + training_pairs = PairedDataContainer(training_inputs, decorrelated_training_outputs) + input_dim, output_dim = size(training_pairs, 1) + else + training_pairs = PairedDataContainer(training_inputs, decorrelated_training_outputs) + end - # write new pairs structure - if retained_svd_frac < 1.0 - #note this changes the dimension of the outputs - training_pairs = PairedDataContainer(training_inputs, decorrelated_training_outputs) - input_dim, output_dim = size(training_pairs, 1) + # [4.] build an emulator + build_models!(machine_learning_tool, training_pairs) else - training_pairs = PairedDataContainer(training_inputs, decorrelated_training_outputs) + if decorrelate || !isa(machine_learning_tool, VectorRandomFeatureInterface) + throw(ArgumentError("$machine_learning_tool is incompatible with option Emulator(...,decorrelate = false)")) + end + decomposition = nothing + training_pairs = PairedDataContainer(training_inputs, training_outputs) + + # [4.] build an emulator - providing the noise covariance as a Tikhonov regularizer + build_models!(machine_learning_tool, training_pairs, regularization_matrix = obs_noise_cov) end - # [4.] build an emulator - build_models!(machine_learning_tool, training_pairs) return Emulator{FT}( machine_learning_tool, @@ -170,6 +186,7 @@ function predict( emulator::Emulator{FT}, new_inputs::AbstractMatrix{FT}; transform_to_real = false, + vector_rf_unstandardize = true, ) where {FT <: AbstractFloat} # Check if the size of new_inputs is consistent with the GP model's input # dimension. @@ -177,7 +194,7 @@ function predict( N_samples = size(new_inputs, 2) size(new_inputs, 1) == input_dim || - throw(ArgumentError("GP object and input observations do not have consistent dimensions")) + throw(ArgumentError("Emulator object and input observations do not have consistent dimensions")) # [1.] normalize normalized_new_inputs = normalize(emulator, new_inputs) @@ -186,28 +203,68 @@ function predict( ds_outputs, ds_output_var = predict(emulator.machine_learning_tool, normalized_new_inputs) # [3.] transform back to real coordinates or remain in decorrelated coordinates - if transform_to_real && emulator.decomposition === nothing - throw(ArgumentError("""Need SVD decomposition to transform back to original space, - but GaussianProcess.decomposition == nothing. - Try setting transform_to_real=false""")) - elseif transform_to_real && emulator.decomposition !== nothing - #transform back to real coords - cov becomes dense - s_outputs, s_output_cov = svd_reverse_transform_mean_cov(ds_outputs, ds_output_var, emulator.decomposition) - if output_dim == 1 - s_output_cov = [s_output_cov[i][1] for i in 1:N_samples] + if !isa(get_machine_learning_tool(emulator), VectorRandomFeatureInterface) + if transform_to_real && emulator.decomposition === nothing + throw(ArgumentError("""Need SVD decomposition to transform back to original space, + but GaussianProcess.decomposition == nothing. + Try setting transform_to_real=false""")) + elseif transform_to_real && emulator.decomposition !== nothing + + #transform back to real coords - cov becomes dense + s_outputs, s_output_cov = svd_reverse_transform_mean_cov(ds_outputs, ds_output_var, emulator.decomposition) + if output_dim == 1 + s_output_cov = reshape([s_output_cov[i][1] for i in 1:N_samples], 1, :) + end + + # [4.] unstandardize + return reverse_standardize(emulator, s_outputs, s_output_cov) + else + # remain in decorrelated, standardized coordinates (cov remains diagonal) + # Convert to vector of matrices to match the format + # when transform_to_real=true + ds_output_diagvar = vec([Diagonal(ds_output_var[:, j]) for j in 1:N_samples]) + if output_dim == 1 + ds_output_diagvar = reshape([ds_output_diagvar[i][1] for i in 1:N_samples], 1, :) + end + return ds_outputs, ds_output_diagvar end - # [4.] unstandardize - return reverse_standardize(emulator, s_outputs, s_output_cov) else - # remain in decorrelated, standardized coordinates (cov remains diagonal) - # Convert to vector of matrices to match the format - # when transform_to_real=true - ds_output_diagvar = vec([Diagonal(ds_output_var[:, j]) for j in 1:N_samples]) - if output_dim == 1 - ds_output_diagvar = [ds_output_diagvar[i][1] for i in 1:N_samples] + # create a vector of covariance matrices + ds_output_covvec = vec([ds_output_var[:, :, j] for j in 1:N_samples]) + + if emulator.decomposition === nothing # without applying SVD + if vector_rf_unstandardize + # [4.] unstandardize + return reverse_standardize(emulator, ds_outputs, ds_output_covvec) + else + return ds_outputs, ds_output_covvec + end + + else #if we applied SVD + if transform_to_real # ...and want to return coordinates + s_outputs, s_output_cov = + svd_reverse_transform_mean_cov(ds_outputs, ds_output_covvec, emulator.decomposition) + if output_dim == 1 + s_output_cov = reshape([s_output_cov[i][1] for i in 1:N_samples], 1, :) + end + # [4.] unstandardize + return reverse_standardize(emulator, s_outputs, s_output_cov) + else #... and want to stay in decorrelated standardized coordinates + diag_out_flag = get_diagonalize_output(get_machine_learning_tool(emulator)) + if diag_out_flag + ds_output_diagvar = vec([Diagonal(ds_output_covvec[j]) for j in 1:N_samples]) # extracts diagonal + if output_dim == 1 + ds_output_diagvar = ([ds_output_covvec[i][1, 1] for i in 1:N_samples], 1, :) # extracts value + end + return ds_outputs, ds_output_diagvar + else + return ds_outputs, ds_output_covvec + end + end end - return ds_outputs, ds_output_diagvar + end + end # Normalization, Standardization, and Decorrelation @@ -244,10 +301,14 @@ $(DocStringExtensions.TYPEDSIGNATURES) Standardize with a vector of factors (size equal to output dimension). """ function standardize( - outputs::AbstractVecOrMat{FT}, - output_covs::Vector{<:Union{AbstractMatrix{FT}, UniformScaling{FT}}}, - factors::AbstractVector{FT}, -) where {FT <: AbstractFloat} + outputs::VorM, + output_covs::VofMUS, + factors::V, +) where { + VorM <: AbstractVecOrMat, + VofMUS <: Union{AbstractVector{<:AbstractMatrix}, AbstractVector{<:UniformScaling}}, + V <: AbstractVector, +} # Case where `output_covs` is a Vector of covariance matrices n = length(factors) outputs = outputs ./ factors @@ -273,10 +334,15 @@ function standardize( end function standardize( - outputs::AbstractVecOrMat{FT}, - output_cov::Union{AbstractMatrix{FT}, UniformScaling{FT}}, - factors::AbstractVector{FT}, -) where {FT <: AbstractFloat} + outputs::VorM, + output_cov::MorVorUS, + factors::V, +) where { + VorM <: AbstractVecOrMat, + MorVorUS <: Union{AbstractMatrix, AbstractVector{<:AbstractFloat}, UniformScaling}, # must be vector of floats or could cause inf. loop with other method definition. + V <: AbstractVector, +} + # Case where `output_cov` is a single covariance matrix stdized_out, stdized_covs = standardize(outputs, [output_cov], factors) return stdized_out, stdized_covs[1] @@ -291,9 +357,13 @@ dimension). `output_cov` is a Vector of covariance matrices, such as is returned """ function reverse_standardize( emulator::Emulator{FT}, - outputs::AbstractVecOrMat{FT}, - output_covs::Union{AbstractMatrix{FT}, Vector{<:AbstractMatrix{FT}}}, -) where {FT <: AbstractFloat} + outputs::VorM, + output_covs::VorMtwo, +) where { + VorM <: AbstractVecOrMat, + VorMtwo <: AbstractVecOrMat, # can be different type + FT <: AbstractFloat, +} if emulator.standardize_outputs return standardize(outputs, output_covs, 1.0 ./ emulator.standardize_outputs_factors) else @@ -375,6 +445,7 @@ $(DocStringExtensions.TYPEDSIGNATURES) Transform the mean and covariance back to the original (correlated) coordinate system - `μ` - predicted mean; size *output\\_dim* × *N\\_predicted\\_points*. - `σ2` - predicted variance; size *output\\_dim* × *N\\_predicted\\_points*. + - predicted covariance; size *N\\_predicted\\_points* array of size *output\\_dim* × *output\\_dim*. - `decomposition` - SVD decomposition of *obs\\_noise\\_cov*. Returns the transformed mean (size *output\\_dim* × *N\\_predicted\\_points*) and variance. @@ -386,12 +457,20 @@ each element is a matrix of size *output\\_dim* × *output\\_dim*. """ function svd_reverse_transform_mean_cov( μ::AbstractMatrix{FT}, - σ2::AbstractMatrix{FT}, + σ2::AbstractVector,# vector of output_dim x output_dim matrices decomposition::SVD, ) where {FT <: AbstractFloat} - @assert size(μ) == size(σ2) - output_dim, N_predicted_points = size(σ2) + N_predicted_points = length(σ2) + if !(eltype(σ2) <: AbstractMatrix) + throw( + ArgumentError( + "input σ2 must be a vector of eltype <: AbstractMatrix, instead eltype(σ2) = ", + string(eltype(σ2)), + ), + ) + end + # We created meanvGP = D_inv * Vt * mean_v so meanv = V * D * meanvGP sqrt_singular_values = Diagonal(sqrt.(decomposition.S)) transformed_μ = decomposition.V * sqrt_singular_values * μ @@ -400,13 +479,27 @@ function svd_reverse_transform_mean_cov( # Back transformation for j in 1:N_predicted_points - σ2_j = decomposition.V * sqrt_singular_values * Diagonal(σ2[:, j]) * sqrt_singular_values * decomposition.Vt + σ2_j = decomposition.V * sqrt_singular_values * σ2[j] * sqrt_singular_values * decomposition.Vt transformed_σ2[j] = Symmetric(σ2_j) end return transformed_μ, transformed_σ2 + end +function svd_reverse_transform_mean_cov( + μ::AbstractMatrix{FT}, + σ2::AbstractMatrix{FT}, + decomposition::SVD, +) where {FT <: AbstractFloat} + @assert size(μ) == size(σ2) + output_dim, N_predicted_points = size(σ2) + σ2_as_cov = vec([Diagonal(σ2[:, j]) for j in 1:N_predicted_points]) + + return svd_reverse_transform_mean_cov(μ, σ2_as_cov, decomposition) +end + + end diff --git a/src/MarkovChainMonteCarlo.jl b/src/MarkovChainMonteCarlo.jl index 1abb1134b..2e376b32e 100644 --- a/src/MarkovChainMonteCarlo.jl +++ b/src/MarkovChainMonteCarlo.jl @@ -165,7 +165,10 @@ function EmulatorPosteriorModel( # Vector of N_samples covariance matrices. For MH, N_samples is always 1, so we # have to reshape()/re-cast input/output; simpler to do here than add a # predict() method. - g, g_cov = Emulators.predict(em, reshape(θ, :, 1), transform_to_real = false) + g, g_cov = + Emulators.predict(em, reshape(θ, :, 1), transform_to_real = false, vector_rf_unstandardize = false) + #TODO vector_rf will always unstandardize, but other methods will not, so we require this additional flag. + if isa(g_cov[1], Real) return logpdf(MvNormal(obs_sample, g_cov[1] * I), vec(g)) + get_logpdf(prior, θ) else diff --git a/src/RandomFeature.jl b/src/RandomFeature.jl new file mode 100644 index 000000000..3465d2c0d --- /dev/null +++ b/src/RandomFeature.jl @@ -0,0 +1,661 @@ + +using RandomFeatures +const RF = RandomFeatures +using EnsembleKalmanProcesses +const EKP = EnsembleKalmanProcesses +using ..ParameterDistributions +using ..Utilities +using StableRNGs +using Random + +abstract type RandomFeatureInterface <: MachineLearningTool end + +abstract type MultithreadType end +struct TullioThreading <: MultithreadType end +struct EnsembleThreading <: MultithreadType end + +#common functions +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Converts a flat array into a cholesky factor. +""" +function flat_to_chol(x::V) where {V <: AbstractVector} + choldim = Int(floor(sqrt(2 * length(x)))) + cholmat = zeros(choldim, choldim) + for i in 1:choldim + for j in 1:i + cholmat[i, j] = x[sum(0:(i - 1)) + j] + end + end + return cholmat +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Builds Covariance matrices from a flat array of hyperparameters +""" +function hyperparameters_from_flat( + x::VV, + input_dim::Int, + output_dim::Int, + diagonalize_input::Bool, + diagonalize_output::Bool, +) where {VV <: AbstractVector} + # if dim = 1 then parameters are a 1x1 matrix + # if we diagonalize then parameters are diagonal entries + constant + # if we don't diagonalize then parameters are a cholesky product + constant on diagonal. + + #input space + if input_dim == 1 + in_max = 1 + U = x[in_max] * ones(1, 1) + elseif diagonalize_input + in_max = input_dim + 2 + U = convert(Matrix, x[in_max - 1] * (Diagonal(x[1:(in_max - 2)]) + x[in_max] * I)) + elseif !diagonalize_input + in_max = Int(input_dim * (input_dim + 1) / 2) + 2 + cholU = flat_to_chol(x[1:(in_max - 2)]) + U = x[in_max - 1] * (cholU * permutedims(cholU, (2, 1)) + x[in_max] * I) + end + + # output_space + out_min = in_max + 1 + if output_dim == 1 + V = x[end] * ones(1, 1) + elseif diagonalize_output + V = convert(Matrix, x[end - 1] * (Diagonal(x[out_min:(end - 2)]) + x[end] * I)) + elseif !diagonalize_output + cholV = flat_to_chol(x[out_min:(end - 2)]) + V = x[end - 1] * (cholV * permutedims(cholV, (2, 1)) + x[end] * I) + end + + # sometimes this process does not give a (numerically) symmetric matrix + U = 0.5 * (U + permutedims(U, (2, 1))) + V = 0.5 * (V + permutedims(V, (2, 1))) + + return U, V + +end + +function hyperparameters_from_flat(x::VV, input_dim::Int, diagonalize_input::Bool) where {VV <: AbstractVector} + output_dim = 1 + diagonalize_output = false + U, V = hyperparameters_from_flat(x, input_dim, output_dim, diagonalize_input, diagonalize_output) + # Note that the scalar setting has a slight inconsistency from the 1-D output vector case + # We correct here by rescaling U using the single hyperparameter in V + return V[1, 1] * U +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Builds a prior over the hyperparameters (i.e. the cholesky/diagaonal or individaul entries of the input/output covariances). +For example, the case where the input covariance ``U = γ_1 * (LL^T + γ_2 I)``, +we set priors for the entries of the lower triangular matrix ``L`` as normal, and constant scalings ``γ_i`` as log-normal to retain positivity. +""" +function build_default_prior(input_dim::Int, output_dim::Int, diagonalize_input::Bool, diagonalize_output::Bool) + n_hp_in = n_hyperparameters_cov(input_dim, diagonalize_input) + n_hp_out = n_hyperparameters_cov(output_dim, diagonalize_output) + + # if dim = 1 , positive constant + # elseif diagonalized, positive on diagonal and positive scalings + # else chol factor, and positive scalings + if input_dim > 1 + if diagonalize_input + param_diag = constrained_gaussian("input_prior_diagonal", 1.0, 1.0, 0.0, Inf, repeats = n_hp_in - 2) + param_scaling = constrained_gaussian("input_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2) + input_prior = combine_distributions([param_diag, param_scaling]) + else + param_chol = constrained_gaussian("input_prior_cholesky", 0.0, 1.0, -Inf, Inf, repeats = n_hp_in - 2) + param_scaling = constrained_gaussian("input_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2) + input_prior = combine_distributions([param_chol, param_scaling]) + end + else + input_prior = constrained_gaussian("input_prior", 1.0, 1.0, 0.0, Inf) + end + + if output_dim > 1 + if diagonalize_output + param_diag = constrained_gaussian("output_prior_diagonal", 1.0, 1.0, 0.0, Inf, repeats = n_hp_out - 2) + param_scaling = constrained_gaussian("output_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2) + output_prior = combine_distributions([param_diag, param_scaling]) + else + param_chol = constrained_gaussian("output_prior_cholesky", 0.0, 1.0, -Inf, Inf, repeats = n_hp_out - 2) + param_scaling = constrained_gaussian("output_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2) + output_prior = combine_distributions([param_chol, param_scaling]) + end + else + output_prior = constrained_gaussian("output_prior", 1.0, 1.0, 0.0, Inf) + end + + return combine_distributions([input_prior, output_prior]) + +end + +function build_default_prior(input_dim::Int, diagonalize_input::Bool) + #scalar case consistent with vector case + output_dim = 1 + diagonalize_output = false + return build_default_prior(input_dim, output_dim, diagonalize_input, diagonalize_output) +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +The number of hyperparameters required to characterize covariance (determined from `hyperparameters_from_flat`). +""" +function n_hyperparameters_cov(dim::Int, diagonalize::Bool) + n_hp = 0 + n_hp += diagonalize ? dim : Int(dim * (dim + 1) / 2) # inputs: diagonal or cholesky + n_hp += (dim > 1) ? 2 : 0 # add two more for constant diagonal in each case. + return n_hp +end + + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Calculate number of hyperparameters required to create the default prior in the given input/output space (determined from `hyperparameters_from_flat`) +""" +function calculate_n_hyperparameters(input_dim::Int, output_dim::Int, diagonalize_input::Bool, diagonalize_output::Bool) + n_hp_in = n_hyperparameters_cov(input_dim, diagonalize_input) + n_hp_out = n_hyperparameters_cov(output_dim, diagonalize_output) + return n_hp_in + n_hp_out +end + +function calculate_n_hyperparameters(input_dim::Int, diagonalize_input::Bool) + #scalar case consistent with vector case + output_dim = 1 + diagonalize_output = false + return calculate_n_hyperparameters(input_dim, output_dim, diagonalize_input, diagonalize_output) +end + + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Calculates key quantities (mean, covariance, and coefficients) of the objective function to be optimized for hyperparameter training. Buffers: mean_store, cov_store, buffer are provided to aid memory management. +""" +function calculate_mean_cov_and_coeffs( + rfi::RFI, + rng::RNG, + l::ForVM, + regularization::MorUSorD, + n_features::Int, + n_train::Int, + n_test::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + io_pairs::PairedDataContainer, + decomp_type::S, + mean_store::M, + cov_store::A, + buffer::A, + multithread_type::MT, +) where { + RFI <: RandomFeatureInterface, + RNG <: AbstractRNG, + ForVM <: Union{AbstractFloat, AbstractVecOrMat}, + S <: AbstractString, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, + M <: AbstractMatrix{<:AbstractFloat}, + A <: AbstractArray{<:AbstractFloat, 3}, + MT <: MultithreadType, +} + + # split data into train/test + itrain = get_inputs(io_pairs)[:, 1:n_train] + otrain = get_outputs(io_pairs)[:, 1:n_train] + io_train_cost = PairedDataContainer(itrain, otrain) + itest = get_inputs(io_pairs)[:, (n_train + 1):end] + otest = get_outputs(io_pairs)[:, (n_train + 1):end] + input_dim = size(itrain, 1) + output_dim = size(otrain, 1) + + # build and fit the RF + rfm = RFM_from_hyperparameters( + rfi, + rng, + l, + regularization, + n_features, + batch_sizes, + input_dim, + output_dim, + multithread_type, + ) + fitted_features = RF.Methods.fit(rfm, io_train_cost, decomposition_type = decomp_type) + + #we want to calc 1/var(y-mean)^2 + lambda/m * coeffs^2 in the end + thread_opt = isa(multithread_type, TullioThreading) + RF.Methods.predict!( + rfm, + fitted_features, + DataContainer(itest), + mean_store, + cov_store, + buffer, + tullio_threading = thread_opt, + ) + # sizes (output_dim x n_test), (output_dim x output_dim x n_test) + scaled_coeffs = sqrt(1 / n_features) * RF.Methods.get_coeffs(fitted_features) + + # we add the additional complexity term + # TODO only cholesky and SVD available + if decomp_type == "cholesky" + chol_fac = RF.Methods.get_decomposition(RF.Methods.get_feature_factors(fitted_features)).L + complexity = 2 * sum(log(chol_fac[i, i]) for i in 1:size(chol_fac, 1)) + else + svd_singval = RF.Methods.get_decomposition(RF.Methods.get_feature_factors(fitted_features)).S + complexity = sum(log, svd_singval) # note this is log(abs(det)) + end + return scaled_coeffs, complexity + +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Estimation of objective function (marginal log-likelihood) variability for optimization of hyperparameters. Calculated empirically by calling many samples of the objective at a "reasonable" value. `multithread_type` is used as dispatch, either `ensemble` (thread over the empirical samples) or `tullio` (serial samples, and thread the linear algebra within each sample) +""" +function estimate_mean_and_coeffnorm_covariance( + rfi::RFI, + rng::RNG, + l::ForVM, + regularization::MorUSorD, + n_features::Int, + n_train::Int, + n_test::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + io_pairs::PairedDataContainer, + n_samples::Int, + decomp_type::S, + multithread_type::TullioThreading; + repeats::Int = 1, +) where { + RFI <: RandomFeatureInterface, + RNG <: AbstractRNG, + ForVM <: Union{AbstractFloat, AbstractVecOrMat}, + S <: AbstractString, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, +} + + output_dim = size(get_outputs(io_pairs), 1) + + means = zeros(output_dim, n_samples, n_test) + mean_of_covs = zeros(output_dim, output_dim, n_test) + moc_tmp = similar(mean_of_covs) + mtmp = zeros(output_dim, n_test) + buffer = zeros(n_test, output_dim, n_features) + complexity = zeros(1, n_samples) + coeffl2norm = zeros(1, n_samples) + println("estimate cov with " * string(n_samples * repeats) * " iterations...") + + for i in ProgressBar(1:n_samples) + for j in 1:repeats + c, cplxty = calculate_mean_cov_and_coeffs( + rfi, + rng, + l, + regularization, + n_features, + n_train, + n_test, + batch_sizes, + io_pairs, + decomp_type, + mtmp, + moc_tmp, + buffer, + multithread_type, + ) + + # m output_dim x n_test + # v output_dim x output_dim x n_test + # c n_features + # cplxty 1 + + # update vbles needed for cov + means[:, i, :] .+= mtmp ./ repeats + coeffl2norm[1, i] += sqrt(sum(abs2, c)) / repeats + complexity[1, i] += cplxty / repeats + + # update vbles needed for mean + @. mean_of_covs += moc_tmp / (repeats * n_samples) + + end + end + means = permutedims(means, (3, 2, 1)) + mean_of_covs = permutedims(mean_of_covs, (3, 1, 2)) + + approx_σ2 = zeros(n_test * output_dim, n_test * output_dim) + blockmeans = zeros(n_test * output_dim, n_samples) + for i in 1:n_test + id = ((i - 1) * output_dim + 1):(i * output_dim) + approx_σ2[id, id] = mean_of_covs[i, :, :] # this ordering, so we can take a mean/cov in dims = 2. + blockmeans[id, :] = permutedims(means[i, :, :], (2, 1)) + end + + if !isposdef(approx_σ2) + println("approx_σ2 not posdef") + approx_σ2 = posdef_correct(approx_σ2) + end + + Γ = cov(vcat(blockmeans, coeffl2norm, complexity), dims = 2) + + + return Γ, approx_σ2 + +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Evaluate an objective function (marginal log-likelihood) over an ensemble of hyperparameter values (used for EKI). `multithread_type` is used as dispatch, either `ensemble` (thread over the ensemble members) or `tullio` (serial samples, and thread the linear algebra within each sample) +""" +function calculate_ensemble_mean_and_coeffnorm( + rfi::RFI, + rng::RNG, + lvecormat::VorM, + regularization::MorUSorD, + n_features::Int, + n_train::Int, + n_test::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + io_pairs::PairedDataContainer, + decomp_type::S, + multithread_type::TullioThreading; + repeats::Int = 1, +) where { + RFI <: RandomFeatureInterface, + RNG <: AbstractRNG, + VorM <: AbstractVecOrMat, + S <: AbstractString, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, +} + if isa(lvecormat, AbstractVector) + lmat = reshape(lvecormat, 1, :) + else + lmat = lvecormat + end + N_ens = size(lmat, 2) + output_dim = size(get_outputs(io_pairs), 1) + + means = zeros(output_dim, N_ens, n_test) + mean_of_covs = zeros(output_dim, output_dim, n_test) + buffer = zeros(n_test, output_dim, n_features) + complexity = zeros(1, N_ens) + coeffl2norm = zeros(1, N_ens) + moc_tmp = similar(mean_of_covs) + mtmp = zeros(output_dim, n_test) + + println("calculating " * string(N_ens * repeats) * " ensemble members...") + + for i in ProgressBar(1:N_ens) + for j in collect(1:repeats) + l = lmat[:, i] + + c, cplxty = calculate_mean_cov_and_coeffs( + rfi, + rng, + l, + regularization, + n_features, + n_train, + n_test, + batch_sizes, + io_pairs, + decomp_type, + mtmp, + moc_tmp, + buffer, + multithread_type, + ) + # m output_dim x n_test + # v output_dim x output_dim x n_test + # c n_features + means[:, i, :] += mtmp ./ repeats + @. mean_of_covs += moc_tmp / (repeats * N_ens) + coeffl2norm[1, i] += sqrt(sum(c .^ 2)) / repeats + complexity[1, i] += cplxty / repeats + end + end + means = permutedims(means, (3, 2, 1)) + mean_of_covs = permutedims(mean_of_covs, (3, 1, 2)) + blockcovmat = zeros(n_test * output_dim, n_test * output_dim) + blockmeans = zeros(n_test * output_dim, N_ens) + for i in 1:n_test + id = ((i - 1) * output_dim + 1):(i * output_dim) + blockcovmat[id, id] = mean_of_covs[i, :, :] + blockmeans[id, :] = permutedims(means[i, :, :], (2, 1)) + end + + if !isposdef(blockcovmat) + println("blockcovmat not posdef") + blockcovmat = posdef_correct(blockcovmat) + end + + return vcat(blockmeans, coeffl2norm, complexity), blockcovmat + +end + + +function estimate_mean_and_coeffnorm_covariance( + rfi::RFI, + rng::RNG, + l::ForVM, + regularization::MorUSorD, + n_features::Int, + n_train::Int, + n_test::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + io_pairs::PairedDataContainer, + n_samples::Int, + decomp_type::S, + multithread_type::EnsembleThreading; + repeats::Int = 1, +) where { + RFI <: RandomFeatureInterface, + RNG <: AbstractRNG, + ForVM <: Union{AbstractFloat, AbstractVecOrMat}, + S <: AbstractString, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, +} + + output_dim = size(get_outputs(io_pairs), 1) + + println("estimate cov with " * string(n_samples * repeats) * " iterations...") + + nthreads = Threads.nthreads() + rng_seed = randperm(rng, 10^5)[1] # dumb way to get a random integer in 1:10^5 + rng_list = [Random.MersenneTwister(rng_seed + i) for i in 1:nthreads] + + c_list = [zeros(1, n_samples) for i in 1:nthreads] + cp_list = [zeros(1, n_samples) for i in 1:nthreads] + m_list = [zeros(output_dim, n_samples, n_test) for i in 1:nthreads] + moc_list = [zeros(output_dim, output_dim, n_test) for i in 1:nthreads] + moc_tmp_list = [zeros(output_dim, output_dim, n_test) for i in 1:nthreads] + mtmp_list = [zeros(output_dim, n_test) for i in 1:nthreads] + buffer_list = [zeros(n_test, output_dim, n_features) for i in 1:nthreads] + + + Threads.@threads for i in ProgressBar(1:n_samples) + tid = Threads.threadid() + rngtmp = rng_list[tid] + mtmp = mtmp_list[tid] + moc_tmp = moc_tmp_list[tid] + buffer = buffer_list[tid] + for j in 1:repeats + + c, cplxty = calculate_mean_cov_and_coeffs( + rfi, + rngtmp, + l, + regularization, + n_features, + n_train, + n_test, + batch_sizes, + io_pairs, + decomp_type, + mtmp, + moc_tmp, + buffer, + multithread_type, + ) + + + # m output_dim x n_test + # v output_dim x output_dim x n_test + # c n_features + # cplxty 1 + + # update vbles needed for cov + # update vbles needed for cov + m_list[tid][:, i, :] += mtmp ./ repeats + c_list[tid][1, i] += sqrt(sum(abs2, c)) / repeats + cp_list[tid][1, i] += cplxty / repeats + + # update vbles needed for mean + @. moc_list[tid] += moc_tmp ./ (repeats * n_samples) + + end + end + + #put back together after threading + mean_of_covs = sum(moc_list) + means = sum(m_list) + coeffl2norm = sum(c_list) + complexity = sum(cp_list) + means = permutedims(means, (3, 2, 1)) + mean_of_covs = permutedims(mean_of_covs, (3, 1, 2)) + + approx_σ2 = zeros(n_test * output_dim, n_test * output_dim) + blockmeans = zeros(n_test * output_dim, n_samples) + for i in 1:n_test + id = ((i - 1) * output_dim + 1):(i * output_dim) + approx_σ2[id, id] = mean_of_covs[i, :, :] # this ordering, so we can take a mean/cov in dims = 2. + blockmeans[id, :] = permutedims(means[i, :, :], (2, 1)) + end + + if !isposdef(approx_σ2) + println("approx_σ2 not posdef") + approx_σ2 = posdef_correct(approx_σ2) + end + + Γ = cov(vcat(blockmeans, coeffl2norm, complexity), dims = 2) + return Γ, approx_σ2 + +end + +function calculate_ensemble_mean_and_coeffnorm( + rfi::RFI, + rng::RNG, + lvecormat::VorM, + regularization::MorUSorD, + n_features::Int, + n_train::Int, + n_test::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + io_pairs::PairedDataContainer, + decomp_type::S, + multithread_type::EnsembleThreading; + repeats::Int = 1, +) where { + RFI <: RandomFeatureInterface, + RNG <: AbstractRNG, + VorM <: AbstractVecOrMat, + S <: AbstractString, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, +} + if isa(lvecormat, AbstractVector) + lmat = reshape(lvecormat, 1, :) + else + lmat = lvecormat + end + N_ens = size(lmat, 2) + output_dim = size(get_outputs(io_pairs), 1) + + + + println("calculating " * string(N_ens * repeats) * " ensemble members...") + + nthreads = Threads.nthreads() + + means = zeros(output_dim, N_ens, n_test) + complexity = zeros(1, N_ens) + coeffl2norm = zeros(1, N_ens) + + c_list = [zeros(1, N_ens) for i in 1:nthreads] + cp_list = [zeros(1, N_ens) for i in 1:nthreads] + m_list = [zeros(output_dim, N_ens, n_test) for i in 1:nthreads] + moc_list = [zeros(output_dim, output_dim, n_test) for i in 1:nthreads] + buffer_list = [zeros(n_test, output_dim, n_features) for i in 1:nthreads] + moc_tmp_list = [zeros(output_dim, output_dim, n_test) for i in 1:nthreads] + mtmp_list = [zeros(output_dim, n_test) for i in 1:nthreads] + rng_seed = randperm(rng, 10^5)[1] # dumb way to get a random integer in 1:10^5 + rng_list = [Random.MersenneTwister(rng_seed + i) for i in 1:nthreads] + Threads.@threads for i in ProgressBar(1:N_ens) + tid = Threads.threadid() + rngtmp = rng_list[tid] + mtmp = mtmp_list[tid] + moc_tmp = moc_tmp_list[tid] + buffer = buffer_list[tid] + l = lmat[:, i] + for j in collect(1:repeats) + + c, cplxty = calculate_mean_cov_and_coeffs( + rfi, + rngtmp, + l, + regularization, + n_features, + n_train, + n_test, + batch_sizes, + io_pairs, + decomp_type, + mtmp, + moc_tmp, + buffer, + multithread_type, + ) + + # m output_dim x n_test + # v output_dim x output_dim x n_test + # c n_features + m_list[tid][:, i, :] += mtmp ./ repeats + @. moc_list[tid] += moc_tmp ./ (repeats * N_ens) + c_list[tid][1, i] += sqrt(sum(c .^ 2)) / repeats + cp_list[tid][1, i] += cplxty / repeats + + end + end + + # put back together after threading + mean_of_covs = sum(moc_list) + means = sum(m_list) + coeffl2norm = sum(c_list) + complexity = sum(cp_list) + means = permutedims(means, (3, 2, 1)) + mean_of_covs = permutedims(mean_of_covs, (3, 1, 2)) + blockcovmat = zeros(n_test * output_dim, n_test * output_dim) + blockmeans = zeros(n_test * output_dim, N_ens) + for i in 1:n_test + id = ((i - 1) * output_dim + 1):(i * output_dim) + blockcovmat[id, id] = mean_of_covs[i, :, :] + blockmeans[id, :] = permutedims(means[i, :, :], (2, 1)) + end + + if !isposdef(blockcovmat) + println("blockcovmat not posdef") + blockcovmat = posdef_correct(blockcovmat) + end + + return vcat(blockmeans, coeffl2norm, complexity), blockcovmat + +end + +include("ScalarRandomFeature.jl") +include("VectorRandomFeature.jl") diff --git a/src/ScalarRandomFeature.jl b/src/ScalarRandomFeature.jl new file mode 100644 index 000000000..dbc26d11b --- /dev/null +++ b/src/ScalarRandomFeature.jl @@ -0,0 +1,437 @@ +export ScalarRandomFeatureInterface +# getters already exported in VRFI + +""" +$(DocStringExtensions.TYPEDEF) + +Structure holding the Scalar Random Feature models. + +# Fields +$(DocStringExtensions.TYPEDFIELDS) + +""" +struct ScalarRandomFeatureInterface{S <: AbstractString, RNG <: AbstractRNG} <: RandomFeatureInterface + "vector of `RandomFeatureMethod`s, contains the feature structure, batch-sizes and regularization" + rfms::Vector{RF.Methods.RandomFeatureMethod} + "vector of `Fit`s, containing the matrix decomposition and coefficients of RF when fitted to data" + fitted_features::Vector{RF.Methods.Fit} + "batch sizes" + batch_sizes::Union{Dict{S, Int}, Nothing} + "n_features" + n_features::Union{Int, Nothing} + "input dimension" + input_dim::Int + "choice of random number generator" + rng::RNG + "Assume inputs are decorrelated for ML" + diagonalize_input::Bool + "Random Feature decomposition, choose from \"svd\" or \"cholesky\" (default)" + feature_decomposition::S + "dictionary of options for hyperparameter optimizer" + optimizer_options::Dict{S} +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the rfms field +""" +get_rfms(srfi::ScalarRandomFeatureInterface) = srfi.rfms + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the fitted_features field +""" +get_fitted_features(srfi::ScalarRandomFeatureInterface) = srfi.fitted_features + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets batch_sizes the field +""" +get_batch_sizes(srfi::ScalarRandomFeatureInterface) = srfi.batch_sizes + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the n_features field +""" +get_n_features(srfi::ScalarRandomFeatureInterface) = srfi.n_features + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the input_dim field +""" +get_input_dim(srfi::ScalarRandomFeatureInterface) = srfi.input_dim + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the rng field +""" +get_rng(srfi::ScalarRandomFeatureInterface) = srfi.rng + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the diagonalize_input field +""" +get_diagonalize_input(srfi::ScalarRandomFeatureInterface) = srfi.diagonalize_input + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the feature_decomposition field +""" +get_feature_decomposition(srfi::ScalarRandomFeatureInterface) = srfi.feature_decomposition + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +gets the optimizer_options field +""" +get_optimizer_options(srfi::ScalarRandomFeatureInterface) = srfi.optimizer_options + + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Constructs a `ScalarRandomFeatureInterface <: MachineLearningTool` interface for the `RandomFeatures.jl` package for multi-input and single- (or decorrelated-)output emulators. + - `n_features` - the number of random features + - `input_dim` - the dimension of the input space + - `diagonalize_input = false` - whether to assume independence in input space (Note, whens set `true`, this tool will approximate directly the behaviour of the scalar-valued GaussianProcess with ARD kernel) + - `batch_sizes = nothing` - Dictionary of batch sizes passed `RandomFeatures.jl` object (see definition there) + - `rng = Random.GLOBAL_RNG` - random number generator + - `feature_decomposition = "cholesky"` - choice of how to store decompositions of random features, `cholesky` or `svd` available + - `optimizer_options = nothing` - Dict of options to pass into EKI optimization of hyperparameters (defaults created in `ScalarRandomFeatureInterface` constructor): + - "prior": the prior for the hyperparameter optimization + - "n_ensemble": number of ensemble members + - "n_iteration": number of eki iterations + - "cov_sample_multiplier": increase for more samples to estimate covariance matrix in optimization (default 10.0, minimum 1.0) + - "tikhonov": tikhonov regularization parameter if >0 + - "inflation": additive inflation ∈ [0,1] with 0 being no inflation + - "train_fraction": e.g. 0.8 (default) means 80:20 train - test split + - "multithread": how to multithread. "ensemble" (default) threads across ensemble members "tullio" threads random feature matrix algebra + - "verbose" => false, verbose optimizer statements +""" +function ScalarRandomFeatureInterface( + n_features::Int, + input_dim::Int; + diagonalize_input::Bool = false, + batch_sizes::Union{Dict{S, Int}, Nothing} = nothing, + rng::RNG = Random.GLOBAL_RNG, + feature_decomposition::S = "cholesky", + optimizer_options::Union{Dict{S}, Nothing} = nothing, +) where {S <: AbstractString, RNG <: AbstractRNG} + # Initialize vector for GP models + rfms = Vector{RF.Methods.RandomFeatureMethod}(undef, 0) + fitted_features = Vector{RF.Methods.Fit}(undef, 0) + + + n_hp = calculate_n_hyperparameters(input_dim, diagonalize_input) + prior = build_default_prior(input_dim, diagonalize_input) + + # default optimizer settings + optimizer_opts = Dict( + "prior" => prior, #the hyperparameter_prior + "n_ensemble" => max(ndims(prior) + 1, 10), #number of ensemble + "n_iteration" => 5, # number of eki iterations + "cov_sample_multiplier" => 10.0, # multiplier for samples to estimate covariance in optimization scheme + "inflation" => 1e-4, # additive inflation ∈ [0,1] with 0 being no inflation + "train_fraction" => 0.8, # 80:20 train - test split + "multithread" => "ensemble", # instead of "tullio" + "verbose" => false, # verbose optimizer statements + ) + + if !isnothing(optimizer_options) + for key in keys(optimizer_options) + optimizer_opts[key] = optimizer_options[key] + end + end + + opt_tmp = Dict() + for key in keys(optimizer_opts) + if key != "prior" + opt_tmp[key] = optimizer_opts[key] + end + end + @info("hyperparameter optimization with EKI configured with $opt_tmp") + + return ScalarRandomFeatureInterface{S, RNG}( + rfms, + fitted_features, + batch_sizes, + n_features, + input_dim, + rng, + diagonalize_input, + feature_decomposition, + optimizer_opts, + ) +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Builds the random feature method from hyperparameters. We use cosine activation functions and a MatrixVariateNormal(M,U,V) distribution (from `Distributions.jl`) with mean M=0, and input covariance U built from cholesky factorization or diagonal components based on the diagonalize_input flag. +""" +function RFM_from_hyperparameters( + srfi::ScalarRandomFeatureInterface, + rng::RNG, + l::ForVM, + regularization::MorUSorD, # just a 1x1 matrix though + n_features::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + input_dim::Int, + multithread_type::MT; +) where { + RNG <: AbstractRNG, + ForVM <: Union{Real, AbstractVecOrMat}, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, + S <: AbstractString, + MT <: MultithreadType, +} + diagonalize_input = get_diagonalize_input(srfi) + + M = zeros(input_dim) #scalar output + U = hyperparameters_from_flat(l, input_dim, diagonalize_input) + if !isposdef(U) + println("U not posdef - correcting") + U = posdef_correct(U) + end + + dist = MvNormal(M, U) + pd = ParameterDistribution( + Dict( + "distribution" => Parameterized(dist), + "constraint" => repeat([no_constraint()], input_dim), + "name" => "xi", + ), + ) + feature_sampler = RF.Samplers.FeatureSampler(pd, rng = rng) + # Learn hyperparameters for different feature types + + sf = RF.Features.ScalarFourierFeature(n_features, feature_sampler) + thread_opt = isa(multithread_type, TullioThreading) # if we want to multithread with tullio + if isnothing(batch_sizes) + return RF.Methods.RandomFeatureMethod(sf, regularization = regularization, tullio_threading = thread_opt) + else + return RF.Methods.RandomFeatureMethod( + sf, + regularization = regularization, + batch_sizes = batch_sizes, + tullio_threading = thread_opt, + ) + end +end + +#removes vector-only input arguments +RFM_from_hyperparameters( + srfi::ScalarRandomFeatureInterface, + rng::RNG, + l::ForVM, + regularization::MorUS, # just a 1x1 matrix though + n_features::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + input_dim::Int, + output_dim::Int, + multithread_type::MT; +) where { + RNG <: AbstractRNG, + ForVM <: Union{Real, AbstractVecOrMat}, + MorUS <: Union{Matrix, UniformScaling}, + S <: AbstractString, + MT <: MultithreadType, +} = RFM_from_hyperparameters(srfi, rng, l, regularization, n_features, batch_sizes, input_dim, multithread_type) + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Builds the random feature method from hyperparameters. We use cosine activation functions and a Multivariate Normal distribution (from `Distributions.jl`) with mean M=0, and input covariance U built from cholesky factorization or diagonal components based on the diagonalize_input flag. +""" +function build_models!( + srfi::ScalarRandomFeatureInterface, + input_output_pairs::PairedDataContainer{FT}, +) where {FT <: AbstractFloat} + # get inputs and outputs + input_values = get_inputs(input_output_pairs) + output_values = get_outputs(input_output_pairs) + n_rfms, n_data = size(output_values) + noise_sd = 1.0 + + input_dim = size(input_values, 1) + + rfms = get_rfms(srfi) + fitted_features = get_fitted_features(srfi) + n_features = get_n_features(srfi) + batch_sizes = get_batch_sizes(srfi) + rng = get_rng(srfi) + decomp_type = get_feature_decomposition(srfi) + optimizer_options = get_optimizer_options(srfi) + + #regularization = I = 1.0 in scalar case + regularization = I + # Optimize features with EKP for each output dim + # [1.] Split data into test/train 80/20 + train_fraction = optimizer_options["train_fraction"] + n_train = Int(floor(train_fraction * n_data)) + n_test = n_data - n_train + n_features_opt = min(n_features, Int(floor(2 * n_test))) #we take a specified number of features for optimization. + idx_shuffle = randperm(rng, n_data) + + @info ( + "hyperparameter learning for $n_rfms models using $n_train training points, $n_test validation points and $n_features_opt features" + ) + for i in 1:n_rfms + + + io_pairs_opt = PairedDataContainer( + input_values[:, idx_shuffle], + reshape(output_values[i, idx_shuffle], 1, size(output_values, 2)), + ) + + multithread = optimizer_options["multithread"] + if multithread == "ensemble" + multithread_type = EnsembleThreading() + elseif multithread == "tullio" + multithread_type = TullioThreading() + else + throw( + ArgumentError( + "Unknown optimizer option for multithreading, please choose from \"tullio\" (allows Tullio.jl to control threading in RandomFeatures.jl, or \"loops\" (threading optimization loops)", + ), + ) + end + # [2.] Estimate covariance at mean value + prior = optimizer_options["prior"] + μ_hp = transform_unconstrained_to_constrained(prior, mean(prior)) + + cov_sample_multiplier = optimizer_options["cov_sample_multiplier"] + n_cov_samples_min = n_test + 2 + n_cov_samples = Int(floor(n_cov_samples_min * max(cov_sample_multiplier, 1.0))) + + internal_Γ, approx_σ2 = estimate_mean_and_coeffnorm_covariance( + srfi, + rng, + μ_hp, + regularization, + n_features_opt, + n_train, + n_test, + batch_sizes, + io_pairs_opt, + n_cov_samples, + decomp_type, + multithread_type, + ) + + Γ = internal_Γ + Γ[1:n_test, 1:n_test] += approx_σ2 + Γ[(n_test + 1):end, (n_test + 1):end] += I + + # [3.] set up EKP optimization + n_ensemble = optimizer_options["n_ensemble"] + n_iteration = optimizer_options["n_iteration"] + opt_verbose_flag = optimizer_options["verbose"] + initial_params = construct_initial_ensemble(rng, prior, n_ensemble) + min_complexity = log(det(regularization)) + data = vcat(get_outputs(io_pairs_opt)[(n_train + 1):end], 0.0, min_complexity) + ekiobj = EKP.EnsembleKalmanProcess(initial_params, data, Γ, Inversion(), rng = rng, verbose = opt_verbose_flag) + err = zeros(n_iteration) + + # [4.] optimize with EKP + for i in 1:n_iteration + + #get parameters: + lvec = transform_unconstrained_to_constrained(prior, get_u_final(ekiobj)) + + g_ens, _ = calculate_ensemble_mean_and_coeffnorm( + srfi, + rng, + lvec, + regularization, + n_features_opt, + n_train, + n_test, + batch_sizes, + io_pairs_opt, + decomp_type, + multithread_type, + ) + inflation = optimizer_options["inflation"] + if inflation > 0 + EKP.update_ensemble!(ekiobj, g_ens, additive_inflation = true, use_prior_cov = true, s = inflation) # small regularizing inflation + else + EKP.update_ensemble!(ekiobj, g_ens) # small regularizing inflation + end + err[i] = get_error(ekiobj)[end] #mean((params_true - mean(params_i,dims=2)).^2) + + end + + # [5.] extract optimal hyperparameters + hp_optimal = get_ϕ_mean_final(prior, ekiobj)[:] + + io_pairs_i = PairedDataContainer(input_values, reshape(output_values[i, :], 1, size(output_values, 2))) + # Now, fit new RF model with the optimized hyperparameters + rfm_i = RFM_from_hyperparameters( + srfi, + rng, + hp_optimal, + regularization, + n_features, + batch_sizes, + input_dim, + multithread_type, + ) + fitted_features_i = RF.Methods.fit(rfm_i, io_pairs_i, decomposition_type = decomp_type) #fit features + + push!(rfms, rfm_i) + push!(fitted_features, fitted_features_i) + end + +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Empty method, as optimization takes place within the build_models stage +""" +function optimize_hyperparameters!(srfi::ScalarRandomFeatureInterface, args...; kwargs...) + @info("Random Features already trained. continuing...") +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Prediction of data observation (not latent function) at new inputs (passed in as columns in a matrix). That is, we add the observational noise into predictions. +""" +function predict(srfi::ScalarRandomFeatureInterface, new_inputs::MM) where {MM <: AbstractMatrix} + M = length(get_rfms(srfi)) + N_samples = size(new_inputs, 2) + # Predicts columns of inputs: input_dim × N_samples + μ = zeros(M, N_samples) + σ2 = zeros(M, N_samples) + optimizer_options = get_optimizer_options(srfi) + multithread = optimizer_options["multithread"] + if multithread == "ensemble" + tullio_threading = false + elseif multithread == "tullio" + tullio_threading = true + end + + for i in 1:M + μ[i, :], σ2[i, :] = RF.Methods.predict( + get_rfms(srfi)[i], + get_fitted_features(srfi)[i], + DataContainer(new_inputs), + tullio_threading = tullio_threading, + ) + end + + # add the noise contribution from the regularization + σ2[:, :] = σ2[:, :] .+ 1.0 + + return μ, σ2 +end diff --git a/src/Utilities.jl b/src/Utilities.jl index eb354842e..e1a625892 100644 --- a/src/Utilities.jl +++ b/src/Utilities.jl @@ -14,7 +14,7 @@ export get_training_points export get_obs_sample export orig2zscore export zscore2orig - +export posdef_correct """ $(DocStringExtensions.TYPEDSIGNATURES) @@ -22,13 +22,20 @@ Extract the training points needed to train the Gaussian process regression. - `ekp` - EnsembleKalmanProcess holding the parameters and the data that were produced during the Ensemble Kalman (EK) process. -- `N_train_iterations` - Number of EK layers/iterations to train on. +- `train_iterations` - Number (or indices) EK layers/iterations to train on. """ -function get_training_points(ekp::EnsembleKalmanProcess{FT, IT, P}, N_train_iterations::IT) where {FT, IT, P} - - # Note u[end] does not have an equivalent g - iter_range = (get_N_iterations(ekp) - N_train_iterations + 1):get_N_iterations(ekp) +function get_training_points( + ekp::EnsembleKalmanProcess{FT, IT, P}, + train_iterations::Union{IT, AbstractVector{IT}}, +) where {FT, IT, P} + + if !isa(train_iterations, AbstractVector) + # Note u[end] does not have an equivalent g + iter_range = (get_N_iterations(ekp) - train_iterations + 1):get_N_iterations(ekp) + else + iter_range = train_iterations + end u_tp = [] g_tp = [] @@ -114,4 +121,30 @@ function zscore2orig(Z::AbstractMatrix{FT}, mean::AbstractVector{FT}, std::Abstr end +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Makes square matrix `mat` positive definite, by symmetrizing and bounding the minimum eigenvalue below by `tol` +""" +function posdef_correct(mat::AbstractMatrix; tol::Real = 1e8 * eps()) + if !issymmetric(mat) + out = 0.5 * (mat + permutedims(mat, (2, 1))) #symmetrize + if isposdef(out) + # very often, small numerical errors cause asymmetry, so cheaper to add this branch + return out + end + else + out = mat + end + + nugget = abs(minimum(eigvals(out))) + for i in 1:size(out, 1) + out[i, i] += nugget + tol #add to diag + end + return out +end + + + + end # module diff --git a/src/VectorRandomFeature.jl b/src/VectorRandomFeature.jl new file mode 100644 index 000000000..20eb9f2de --- /dev/null +++ b/src/VectorRandomFeature.jl @@ -0,0 +1,567 @@ +using ProgressBars + +export VectorRandomFeatureInterface +export get_rfms, + get_fitted_features, + get_batch_sizes, + get_n_features, + get_input_dim, + get_output_dim, + get_rng, + get_diagonalize_input, + get_diagonalize_output, + get_optimizer_options + +""" +$(DocStringExtensions.TYPEDEF) + +Structure holding the Vector Random Feature models. + +# Fields +$(DocStringExtensions.TYPEDFIELDS) + +""" +struct VectorRandomFeatureInterface{S <: AbstractString, RNG <: AbstractRNG} <: RandomFeatureInterface + "A vector of `RandomFeatureMethod`s, contains the feature structure, batch-sizes and regularization" + rfms::Vector{RF.Methods.RandomFeatureMethod} + "vector of `Fit`s, containing the matrix decomposition and coefficients of RF when fitted to data" + fitted_features::Vector{RF.Methods.Fit} + "batch sizes" + batch_sizes::Union{Dict{S, Int}, Nothing} + "number of features" + n_features::Union{Int, Nothing} + "input dimension" + input_dim::Int + "output_dimension" + output_dim::Int + "rng" + rng::RNG + "regularization" + regularization::Vector{Union{Matrix, UniformScaling, Diagonal}} + "Assume inputs are decorrelated for ML" + diagonalize_input::Bool + "Assume outputs are decorrelated for ML. Note: emulator(..., decorrelate=true) by default" + diagonalize_output::Bool + "Random Feature decomposition, choose from \"svd\" or \"cholesky\" (default)" + feature_decomposition::S + "dictionary of options for hyperparameter optimizer" + optimizer_options::Dict +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the rfms field +""" +get_rfms(vrfi::VectorRandomFeatureInterface) = vrfi.rfms + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the fitted_features field +""" +get_fitted_features(vrfi::VectorRandomFeatureInterface) = vrfi.fitted_features + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the batch_sizes field +""" +get_batch_sizes(vrfi::VectorRandomFeatureInterface) = vrfi.batch_sizes + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the n_features field +""" +get_n_features(vrfi::VectorRandomFeatureInterface) = vrfi.n_features + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the input_dim field +""" +get_input_dim(vrfi::VectorRandomFeatureInterface) = vrfi.input_dim + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the output_dim field +""" +get_output_dim(vrfi::VectorRandomFeatureInterface) = vrfi.output_dim + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the rng field +""" +get_rng(vrfi::VectorRandomFeatureInterface) = vrfi.rng + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the regularization field +""" +get_regularization(vrfi::VectorRandomFeatureInterface) = vrfi.regularization + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the diagonalize_input field +""" +get_diagonalize_input(vrfi::VectorRandomFeatureInterface) = vrfi.diagonalize_input + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the diagonalize_output field +""" +get_diagonalize_output(vrfi::VectorRandomFeatureInterface) = vrfi.diagonalize_output + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the feature_decomposition field +""" +get_feature_decomposition(vrfi::VectorRandomFeatureInterface) = vrfi.feature_decomposition + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Gets the optimizer_options field +""" +get_optimizer_options(vrfi::VectorRandomFeatureInterface) = vrfi.optimizer_options + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Constructs a `VectorRandomFeatureInterface <: MachineLearningTool` interface for the `RandomFeatures.jl` package for multi-input and multi-output emulators. + - `n_features` - the number of random features + - `input_dim` - the dimension of the input space + - `output_dim` - the dimension of the output space + - `diagonalize_input = false` - whether to assume independence in input space + - `diagonalize_output::Bool = false` - whether to assume independence in output space (even if set true, this is not the same as a list of scalar-valued models, as hyperparameters will be shared between models in this case) + - `batch_sizes = nothing` - Dictionary of batch sizes passed `RandomFeatures.jl` object (see definition there) + - `rng = Random.GLOBAL_RNG` - random number generator + - `feature_decomposition = "cholesky"` - choice of how to store decompositions of random features, `cholesky` or `svd` available + - `optimizer_options = nothing` - Dict of options to pass into EKI optimization of hyperparameters (defaults created in `VectorRandomFeatureInterface` constructor): + - "prior": the prior for the hyperparameter optimization + - "n_ensemble": number of ensemble members + - "n_iteration": number of eki iterations + - "cov_sample_multiplier": increase for more samples to estimate covariance matrix in optimization (default 10.0, minimum 1.0) + - "tikhonov": tikhonov regularization parameter if > 0 + - "inflation": additive inflation ∈ [0,1] with 0 being no inflation + - "train_fraction": e.g. 0.8 (default) means 80:20 train - test split + - "multithread": how to multithread. "ensemble" (default) threads across ensemble members "tullio" threads random feature matrix algebra + - "verbose" => false, verbose optimizer statements + +""" +function VectorRandomFeatureInterface( + n_features::Int, + input_dim::Int, + output_dim::Int; + diagonalize_input::Bool = false, + diagonalize_output::Bool = false, + batch_sizes::Union{Dict{S, Int}, Nothing} = nothing, + rng::RNG = Random.GLOBAL_RNG, + feature_decomposition::S = "cholesky", + optimizer_options::Union{Dict{S}, Nothing} = nothing, +) where {S <: AbstractString, RNG <: AbstractRNG} + + # Initialize vector for RF model + rfms = Vector{RF.Methods.RandomFeatureMethod}(undef, 0) + fitted_features = Vector{RF.Methods.Fit}(undef, 0) + regularization = Vector{Union{Matrix, UniformScaling, Nothing}}(undef, 0) + + #Optimization Defaults + n_hp = calculate_n_hyperparameters(input_dim, output_dim, diagonalize_input, diagonalize_output) + prior = build_default_prior(input_dim, output_dim, diagonalize_input, diagonalize_output) + + optimizer_opts = Dict( + "prior" => prior, #the hyperparameter_prior + "n_ensemble" => max(ndims(prior) + 1, 10), #number of ensemble + "n_iteration" => 5, # number of eki iterations + "cov_sample_multiplier" => 10.0, # multiplier for samples to estimate covariance in optimization scheme + "tikhonov" => 0, # tikhonov regularization parameter if >0 + "inflation" => 1e-4, # additive inflation ∈ [0,1] with 0 being no inflation + "train_fraction" => 0.8, # 80:20 train - test split + "multithread" => "ensemble", # instead of "tullio" + "verbose" => false, # verbose optimizer statements + ) + + if !isnothing(optimizer_options) + for key in keys(optimizer_options) + optimizer_opts[key] = optimizer_options[key] + end + end + + opt_tmp = Dict() + for key in keys(optimizer_opts) + if key != "prior" + opt_tmp[key] = optimizer_opts[key] + end + end + @info("hyperparameter optimization with EKI configured with $opt_tmp") + + return VectorRandomFeatureInterface{S, RNG}( + rfms, + fitted_features, + batch_sizes, + n_features, + input_dim, + output_dim, + rng, + regularization, + diagonalize_input, + diagonalize_output, + feature_decomposition, + optimizer_opts, + ) +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Builds the random feature method from hyperparameters. We use cosine activation functions and a Matrixvariate Normal distribution with mean M=0, and input(output) covariance U(V) built from cholesky factorization or diagonal components based on the diagonalize_input(diagonalize_output) flag. +""" +function RFM_from_hyperparameters( + vrfi::VectorRandomFeatureInterface, + rng::RNG, + l::ForVM, + regularization::MorUSorD, + n_features::Int, + batch_sizes::Union{Dict{S, Int}, Nothing}, + input_dim::Int, + output_dim::Int, + multithread_type::MT; +) where { + S <: AbstractString, + RNG <: AbstractRNG, + ForVM <: Union{AbstractFloat, AbstractVecOrMat}, + MorUSorD <: Union{Matrix, UniformScaling, Diagonal}, + MT <: MultithreadType, +} + diagonalize_input = get_diagonalize_input(vrfi) + diagonalize_output = get_diagonalize_output(vrfi) + + M = zeros(input_dim, output_dim) # n x p mean + U, V = hyperparameters_from_flat(l, input_dim, output_dim, diagonalize_input, diagonalize_output) + + if !isposdef(U) + println("U not posdef - correcting") + U = posdef_correct(U) + end + if !isposdef(V) + println("V not posdef - correcting") + V = posdef_correct(V) + end + + dist = MatrixNormal(M, U, V) + pd = ParameterDistribution( + Dict( + "distribution" => Parameterized(dist), + "constraint" => repeat([no_constraint()], input_dim * output_dim), + "name" => "xi", + ), + ) + feature_sampler = RF.Samplers.FeatureSampler(pd, output_dim, rng = rng) + vff = RF.Features.VectorFourierFeature(n_features, output_dim, feature_sampler) + + thread_opt = isa(multithread_type, TullioThreading) # if we want to multithread with tullio + if isnothing(batch_sizes) + return RF.Methods.RandomFeatureMethod(vff, regularization = regularization, tullio_threading = thread_opt) + else + return RF.Methods.RandomFeatureMethod( + vff, + regularization = regularization, + batch_sizes = batch_sizes, + tullio_threading = thread_opt, + ) + end +end + + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Build Vector Random Feature model for the input-output pairs subject to regularization, and optimizes the hyperparameters with EKP. +""" +function build_models!( + vrfi::VectorRandomFeatureInterface, + input_output_pairs::PairedDataContainer{FT}; + regularization_matrix::Union{M, Nothing} = nothing, +) where {FT <: AbstractFloat, M <: AbstractMatrix} + + # get inputs and outputs + input_values = get_inputs(input_output_pairs) + output_values = get_outputs(input_output_pairs) + n_rfms, n_data = size(output_values) + + input_dim = size(input_values, 1) + output_dim = size(output_values, 1) + # there are less hyperparameters when we diagonalize + diagonalize_input = get_diagonalize_input(vrfi) + diagonalize_output = get_diagonalize_output(vrfi) + n_hp = calculate_n_hyperparameters(input_dim, output_dim, diagonalize_input, diagonalize_output) + + rfms = get_rfms(vrfi) + fitted_features = get_fitted_features(vrfi) + n_features = get_n_features(vrfi) + batch_sizes = get_batch_sizes(vrfi) + decomp_type = get_feature_decomposition(vrfi) + optimizer_options = get_optimizer_options(vrfi) + multithread = optimizer_options["multithread"] + if multithread == "ensemble" + multithread_type = EnsembleThreading() + elseif multithread == "tullio" + multithread_type = TullioThreading() + else + throw( + ArgumentError( + "Unknown optimizer option for multithreading, please choose from \"tullio\" (allows Tullio.jl to control threading in RandomFeatures.jl, or \"loops\" (threading optimization loops)", + ), + ) + end + prior = optimizer_options["prior"] + rng = get_rng(vrfi) + + if ndims(prior) > n_hp + # comes from having a truncated output_dimension + # TODO not really a truncation here, resetting to default + @info "truncating hyperparameter space to default in first $n_hp dimensions, due to truncation of output space" + prior = constrained_gaussian("cholesky_factors", 1.0, 1.0, 0.0, Inf, repeats = n_hp) + + end + + # Optimize feature cholesky factors with EKP + # [1.] Split data into test/train (e.g. 80/20) + train_fraction = optimizer_options["train_fraction"] + n_train = Int(floor(train_fraction * n_data)) # 20% split + n_test = n_data - n_train + if diagonalize_output + n_features_opt = min(n_features, Int(floor(4 * n_train))) #we take a specified number of features for optimization. MAGIC NUMBER + else + # note the n_features_opt should NOT exceed output_dim * n_train or the regularization is replaced with a diagonal approx. + n_features_opt = max(min(n_features, Int(floor(4 * sqrt(n_train * output_dim)))), Int(floor(1.9 * n_train)))#we take a specified number of features for optimization. MAGIC NUMBER + end + @info ( + "hyperparameter learning using $n_train training points, $n_test validation points and $n_features_opt features" + ) + + + # regularization_matrix = nothing when we use scaled SVD to decorrelate the space, + # in this setting, noise = I + if regularization_matrix === nothing + regularization = I + else + reg_mat = regularization_matrix + if !isposdef(regularization_matrix) + reg_mat = posdef_correct(regularization_matrix) + println("RF regularization matrix is not positive definite, correcting") + + else + # think of the regularization_matrix as the observational noise covariance, or a related quantity + regularization = exp((1 / output_dim) * sum(log.(eigvals(reg_mat)))) * I #i.e. det(M)^{1/output_dim} I + + #regularization = reg_mat #using the full p.d. tikhonov exp. EXPENSIVE, and challenge get complexity terms + end + end + + + idx_shuffle = randperm(rng, n_data) + + io_pairs_opt = PairedDataContainer( + input_values[:, idx_shuffle], + reshape(output_values[:, idx_shuffle], :, size(output_values, 2)), + ) + + # [2.] Estimate covariance at mean value + μ_hp = transform_unconstrained_to_constrained(prior, mean(prior)) + cov_sample_multiplier = optimizer_options["cov_sample_multiplier"] + + if diagonalize_output + n_cov_samples_min = n_test + 2 # diagonal case + else + n_cov_samples_min = (n_test * output_dim + 2) # min required for + end + n_cov_samples = Int(floor(n_cov_samples_min * max(cov_sample_multiplier, 1.0))) + + internal_Γ, approx_σ2 = estimate_mean_and_coeffnorm_covariance( + vrfi, + rng, + μ_hp, # take mean values + regularization, + n_features_opt, + n_train, + n_test, + batch_sizes, + io_pairs_opt, + n_cov_samples, + decomp_type, + multithread_type, + ) + + tikhonov_opt_val = optimizer_options["tikhonov"] + if tikhonov_opt_val == 0 + # Build the covariance + Γ = internal_Γ + Γ[1:(n_test * output_dim), 1:(n_test * output_dim)] += approx_σ2 + Γ[(n_test * output_dim + 1):end, (n_test * output_dim + 1):end] += I + + #in diag case we have data logdet = λ^m, in non diag case we have logdet(Λ^) to match the different reg matrices. + min_complexity = + isa(regularization, UniformScaling) ? n_features_opt * log(regularization.λ) : + n_features_opt / output_dim * 2 * sum(log.(diag(cholesky(regularization).L))) + + data = vcat(reshape(get_outputs(io_pairs_opt)[:, (n_train + 1):end], :, 1), 0.0, min_complexity) #flatten data + + elseif tikhonov_opt_val > 0 + # augment the state to add tikhonov + outsize = size(internal_Γ, 1) + Γ = zeros(outsize + n_hp, outsize + n_hp) + Γ[1:outsize, 1:outsize] = internal_Γ + Γ[1:(n_test * output_dim), 1:(n_test * output_dim)] += approx_σ2 + Γ[(n_test * output_dim + 1):outsize, (n_test * output_dim + 1):outsize] += I + + Γ[(outsize + 1):end, (outsize + 1):end] = tikhonov_opt_val .* cov(prior) + + #TODO the min complexity here is not the correct object in the non-diagonal case + min_complexity = + isa(regularization, UniformScaling) ? n_features_opt * log(regularization.λ) : + n_features_opt / output_dim * 2 * sum(log.(diag(cholesky(regularization).L))) + + data = vcat( + reshape(get_outputs(io_pairs_opt)[:, (n_train + 1):end], :, 1), + 0.0, + min_complexity, + zeros(size(Γ, 1) - outsize, 1), + ) #flatten data with additional zeros + else + throw( + ArgumentError( + "Tikhonov parameter must be non-negative, instead received tikhonov_opt_val=$tikhonov_opt_val", + ), + ) + end + + # [3.] set up EKP optimization + n_ensemble = optimizer_options["n_ensemble"] # minimal ensemble size n_hp, + n_iteration = optimizer_options["n_iteration"] + opt_verbose_flag = optimizer_options["verbose"] + + if !isposdef(Γ) + Γ = posdef_correct(Γ) + end + + initial_params = construct_initial_ensemble(rng, prior, n_ensemble) + + ekiobj = EKP.EnsembleKalmanProcess(initial_params, data[:], Γ, Inversion(), rng = rng, verbose = opt_verbose_flag) + err = zeros(n_iteration) + + # [4.] optimize with EKP + for i in 1:n_iteration + #get parameters: + lvec = get_ϕ_final(prior, ekiobj) + + g_ens, _ = calculate_ensemble_mean_and_coeffnorm( + vrfi, + rng, + lvec, + regularization, + n_features_opt, + n_train, + n_test, + batch_sizes, + io_pairs_opt, + decomp_type, + multithread_type, + ) + if tikhonov_opt_val > 0 + # augment with the computational parameters (u not ϕ) + uvecormat = get_u_final(ekiobj) + if isa(uvecormat, AbstractVector) + umat = reshape(uvecormat, 1, :) + else + umat = uvecormat + end + + g_ens = vcat(g_ens, umat) + end + inflation = optimizer_options["inflation"] + if inflation > 0 + EKP.update_ensemble!(ekiobj, g_ens, additive_inflation = true, use_prior_cov = true, s = inflation) # small regularizing inflation + else + EKP.update_ensemble!(ekiobj, g_ens) # small regularizing inflation + end + err[i] = get_error(ekiobj)[end] #mean((params_true - mean(params_i,dims=2)).^2) + + end + + # [5.] extract optimal hyperparameters + hp_optimal = get_ϕ_mean_final(prior, ekiobj)[:] + # Now, fit new RF model with the optimized hyperparameters + + rfm_tmp = RFM_from_hyperparameters( + vrfi, + rng, + hp_optimal, + regularization, + n_features, + batch_sizes, + input_dim, + output_dim, + multithread_type, + ) + fitted_features_tmp = fit(rfm_tmp, input_output_pairs, decomposition_type = decomp_type) + + + push!(rfms, rfm_tmp) + push!(fitted_features, fitted_features_tmp) + push!(get_regularization(vrfi), regularization) + +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Empty method, as optimization takes place within the build_models stage +""" +function optimize_hyperparameters!(vrfi::VectorRandomFeatureInterface, args...; kwargs...) + @info("Random Features already trained. continuing...") +end + +""" +$(DocStringExtensions.TYPEDSIGNATURES) + +Prediction of data observation (not latent function) at new inputs (passed in as columns in a matrix). That is, we add the observational noise into predictions. +""" +function predict(vrfi::VectorRandomFeatureInterface, new_inputs::M) where {M <: AbstractMatrix} + input_dim = get_input_dim(vrfi) + output_dim = get_output_dim(vrfi) + rfm = get_rfms(vrfi)[1] + ff = get_fitted_features(vrfi)[1] + optimizer_options = get_optimizer_options(vrfi) + multithread = optimizer_options["multithread"] + if multithread == "ensemble" + tullio_threading = false + elseif multithread == "tullio" + tullio_threading = true + end + + N_samples = size(new_inputs, 2) + # Predicts columns of inputs: input_dim × N_samples + μ, σ2 = RF.Methods.predict(rfm, ff, DataContainer(new_inputs), tullio_threading = tullio_threading) + # sizes (output_dim x n_test), (output_dim x output_dim x n_test) + # add the noise contribution from the regularization + # note this is because we are predicting the data here, not the latent function. + lambda = get_regularization(vrfi)[1] + for i in 1:N_samples + σ2[:, :, i] = 0.5 * (σ2[:, :, i] + permutedims(σ2[:, :, i], (2, 1))) + lambda + + if !isposdef(σ2[:, :, i]) + σ2[:, :, i] = posdef_correct(σ2[:, :, i]) + end + end + + return μ, σ2 +end diff --git a/test/GaussianProcess/runtests.jl b/test/GaussianProcess/runtests.jl index 53624cc56..5935f834a 100644 --- a/test/GaussianProcess/runtests.jl +++ b/test/GaussianProcess/runtests.jl @@ -214,7 +214,7 @@ using CalibrateEmulateSample.DataContainers @test μ4_noise_from_Σ[:, 3] ≈ [0.0, 0.0] atol = tol_mu @test μ4_noise_from_Σ[:, 4] ≈ [0.0, -2.0] atol = tol_mu - # check match between the means and variances (should be similar at least + # check match between the variances (should be similar at least) @test all(isapprox.(σ4²_noise_from_Σ, σ4²_noise_learnt, rtol = 2 * tol_mu)) diff --git a/test/RandomFeature/runtests.jl b/test/RandomFeature/runtests.jl new file mode 100644 index 000000000..e1792514f --- /dev/null +++ b/test/RandomFeature/runtests.jl @@ -0,0 +1,306 @@ +using Test +using Random +using RandomFeatures +using LinearAlgebra, Distributions + +using CalibrateEmulateSample.Emulators +using CalibrateEmulateSample.DataContainers +using CalibrateEmulateSample.ParameterDistributions +using RandomFeatures + +seed = 10101010 +rng = Random.MersenneTwister(seed) + +@testset "RandomFeatures" begin + + @testset "ScalarRandomFeatureInterface" begin + + input_dim = 2 + n_features = 200 + batch_sizes = Dict("train" => 100, "test" => 100, "feature" => 100) + diagonalize_input = false + #build interface + n_input_hp = Int(input_dim * (input_dim + 1) / 2) + 2 # see calculate_n_hyperparameters for details + n_output_hp = 1 + + # prior built from: + # input: γ₁*(Cholesky_factor + γ₂ * I ) + # output: γ₃ + # where γᵢ positive + prior = combine_distributions([ + constrained_gaussian("input_prior_cholesky", 0.0, 1.0, -Inf, Inf, repeats = n_input_hp - 2), + constrained_gaussian("input_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2), + constrained_gaussian("output_prior", 1.0, 1.0, 0.0, Inf), + ]) + + optimizer_options = Dict( + "prior" => prior, + "n_ensemble" => max(ndims(prior) + 1, 10), + "n_iteration" => 5, + "cov_sample_multiplier" => 10.0, + "inflation" => 1e-4, + "train_fraction" => 0.8, + "multithread" => "ensemble", + "verbose" => false, + ) + + srfi = ScalarRandomFeatureInterface( + n_features, + input_dim, + batch_sizes = batch_sizes, + rng = rng, + diagonalize_input = diagonalize_input, + optimizer_options = optimizer_options, + ) + + @test isa(get_rfms(srfi), Vector{RandomFeatures.Methods.RandomFeatureMethod}) + @test isa(get_fitted_features(srfi), Vector{RandomFeatures.Methods.Fit}) + @test get_batch_sizes(srfi) == batch_sizes + @test get_n_features(srfi) == n_features + @test get_input_dim(srfi) == input_dim + @test get_rng(srfi) == rng + @test get_diagonalize_input(srfi) == diagonalize_input + @test get_optimizer_options(srfi) == optimizer_options + + # check defaults + srfi2 = ScalarRandomFeatureInterface(n_features, input_dim) + @test get_batch_sizes(srfi2) === nothing + @test get_rng(srfi2) == Random.GLOBAL_RNG + @test get_diagonalize_input(srfi2) == false + @test get_optimizer_options(srfi2) == optimizer_options # we just set the defaults above + + end + + @testset "VectorRandomFeatureInterface" begin + + rng = Random.MersenneTwister(seed) + + input_dim = 2 + output_dim = 3 + n_features = 200 + batch_sizes = Dict("train" => 100, "test" => 100, "feature" => 100) + diagonalize_input = true + diagonalize_output = false + + n_input_hp = Int(input_dim) + 2 + n_output_hp = Int(output_dim * (output_dim + 1) / 2) + 2 + + # prior built from: + # input: γ₁*(Cholesky_factor_in + γ₂ * I) + # output: γ₃*(Cholesky_factor_out + γ₄ * I) + # where γᵢ positive + prior = combine_distributions([ + constrained_gaussian("input_prior_diagonal", 1.0, 1.0, 0.0, Inf, repeats = n_input_hp - 2), + constrained_gaussian("input_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2), + constrained_gaussian("output_prior_cholesky", 0.0, 1.0, -Inf, Inf, repeats = n_output_hp - 2), + constrained_gaussian("output_prior_scaling", 1.0, 1.0, 0.0, Inf, repeats = 2), + ]) + + optimizer_options = Dict( + "prior" => prior, + "n_ensemble" => max(ndims(prior) + 1, 10), + "n_iteration" => 5, + "tikhonov" => 0, + "cov_sample_multiplier" => 10.0, + "inflation" => 1e-4, + "train_fraction" => 0.8, + "multithread" => "ensemble", + "verbose" => false, + ) + + #build interfaces + vrfi = VectorRandomFeatureInterface( + n_features, + input_dim, + output_dim, + rng = rng, + batch_sizes = batch_sizes, + diagonalize_input = diagonalize_input, + diagonalize_output = diagonalize_output, + optimizer_options = optimizer_options, + ) + + @test isa(get_rfms(vrfi), Vector{RandomFeatures.Methods.RandomFeatureMethod}) + @test isa(get_fitted_features(vrfi), Vector{RandomFeatures.Methods.Fit}) + @test get_batch_sizes(vrfi) == batch_sizes + @test get_n_features(vrfi) == n_features + @test get_input_dim(vrfi) == input_dim + @test get_output_dim(vrfi) == output_dim + @test get_rng(vrfi) == rng + @test get_diagonalize_input(vrfi) == diagonalize_input + @test get_diagonalize_output(vrfi) == diagonalize_output + @test get_optimizer_options(vrfi) == optimizer_options + + + #check defaults + vrfi2 = VectorRandomFeatureInterface(n_features, input_dim, output_dim, diagonalize_input = diagonalize_input) + + @test get_batch_sizes(vrfi2) === nothing + @test get_rng(vrfi2) == Random.GLOBAL_RNG + @test get_diagonalize_input(vrfi2) == true + @test get_diagonalize_output(vrfi2) == false + @test get_optimizer_options(vrfi2) == optimizer_options # we just set the defaults above + + end + + @testset "RF within Emulator: 1D -> 1D" begin + + # Training data + input_dim = 1 + output_dim = 1 + n = 40 # number of training points + x = reshape(2.0 * π * rand(n), 1, n) # unif(0,2π) predictors/features: 1 x n + obs_noise_cov = 0.05^2 * I + y = reshape(sin.(x) + 0.05 * randn(n)', 1, n) # predictands/targets: 1 x n + iopairs = PairedDataContainer(x, y, data_are_columns = true) + + ntest = 40 + new_inputs = reshape(2.0 * π * rand(ntest), 1, ntest) + new_outputs = sin.(new_inputs) + + # RF parameters + n_features = 100 + diagonalize_input = true + # Scalar RF options to mimic squared-exp ARD kernel + srfi = ScalarRandomFeatureInterface(n_features, input_dim, diagonalize_input = diagonalize_input, rng = rng) + + # Vector RF options to mimic squared-exp ARD kernel (in 1D) + vrfi = VectorRandomFeatureInterface( + n_features, + input_dim, + output_dim, + diagonalize_input = diagonalize_input, + rng = rng, + ) + + # build emulators + em_srfi = Emulator(srfi, iopairs, obs_noise_cov = obs_noise_cov) + em_vrfi = Emulator(vrfi, iopairs, obs_noise_cov = obs_noise_cov) + + # just see if it prints something + @test_logs (:info,) Emulators.optimize_hyperparameters!(em_srfi) + @test_logs (:info,) Emulators.optimize_hyperparameters!(em_vrfi) + + # predict and test at the new inputs + tol_μ = 0.1 * ntest + μs, σs² = Emulators.predict(em_srfi, new_inputs, transform_to_real = true) + @test size(μs) == (1, ntest) + @test size(σs²) == (1, ntest) + @test isapprox.(norm(μs - new_outputs), 0, atol = tol_μ) + @test all(isapprox.(vec(σs²), 0.05^2 * ones(ntest), atol = 1e-2)) + + μv, σv² = Emulators.predict(em_vrfi, new_inputs, transform_to_real = true) + @test size(μv) == (1, ntest) + @test size(σv²) == (1, ntest) + @test isapprox.(norm(μv - new_outputs), 0, atol = tol_μ) + @test all(isapprox.(vec(σv²), 0.05^2 * ones(ntest), atol = 1e-2)) + + end + @testset "RF within Emulator: 2D -> 2D" begin + # Generate training data + n = 100 # number of training points + + input_dim = 2 # input dim + output_dim = 2 # output dim + X = 2.0 * π * rand(input_dim, n) # [0,2π]x[0,2π] + + # G(x1, x2) + g1x = sin.(X[1, :]) .+ cos.(X[2, :]) + g2x = sin.(X[1, :]) .- cos.(X[2, :]) + gx = zeros(2, n) + gx[1, :] = g1x + gx[2, :] = g2x + + # Add noise η + μ = zeros(output_dim) + Σ = 0.05 * [[0.5, 0.2] [0.2, 0.5]] # d x d + noise_samples = rand(MvNormal(μ, Σ), n) + + # y = G(x) + η + Y = gx .+ noise_samples + + iopairs = PairedDataContainer(X, Y, data_are_columns = true) + + + # RF parameters + n_features = 150 + + # Test a few options for RF + # 1) scalar + diag in + # 2) scalar + # 3) vector + diag out + # 4) vector + + srfi_diagin = ScalarRandomFeatureInterface(n_features, input_dim, diagonalize_input = true, rng = rng) + srfi = ScalarRandomFeatureInterface(n_features, input_dim, diagonalize_input = false, rng = rng) + + vrfi_diagout = VectorRandomFeatureInterface( + n_features, + input_dim, + output_dim, + diagonalize_input = false, + diagonalize_output = true, + optimizer_options = Dict("train_fraction" => 0.7), + rng = rng, + ) + + vrfi = VectorRandomFeatureInterface( + n_features, + input_dim, + output_dim, + diagonalize_input = false, + diagonalize_output = false, + optimizer_options = Dict("train_fraction" => 0.7), + rng = rng, + ) + + # build emulators + # svd: scalar, scalar + diag in, vector + diag out, vector + # no-svd: vector + em_srfi_svd_diagin = Emulator(srfi_diagin, iopairs, obs_noise_cov = Σ) + em_srfi_svd = Emulator(srfi, iopairs, obs_noise_cov = Σ) + + em_vrfi_svd_diagout = Emulator(vrfi_diagout, iopairs, obs_noise_cov = Σ) + em_vrfi_svd = Emulator(vrfi, iopairs, obs_noise_cov = Σ) + + em_vrfi = Emulator(vrfi, iopairs, obs_noise_cov = Σ, decorrelate = false) + + #TODO truncated SVD option for vector (involves resizing prior) + + ntest = 100 + new_inputs = 2.0 * π * rand(input_dim, ntest) # [0,2π]x[0,2π] + + outx = zeros(2, ntest) + outx[1, :] = sin.(new_inputs[1, :]) .+ cos.(new_inputs[2, :]) + outx[2, :] = sin.(new_inputs[1, :]) .- cos.(new_inputs[2, :]) + + μ_ssd, σ²_ssd = Emulators.predict(em_srfi_svd_diagin, new_inputs, transform_to_real = true) + μ_ss, σ²_ss = Emulators.predict(em_srfi_svd, new_inputs, transform_to_real = true) + μ_vsd, σ²_vsd = Emulators.predict(em_vrfi_svd_diagout, new_inputs, transform_to_real = true) + μ_vs, σ²_vs = Emulators.predict(em_vrfi_svd, new_inputs, transform_to_real = true) + μ_v, σ²_v = Emulators.predict(em_vrfi, new_inputs) + + tol_μ = 0.1 * ntest * output_dim + @test isapprox.(norm(μ_ssd - outx), 0, atol = tol_μ) + @test isapprox.(norm(μ_ss - outx), 0, atol = tol_μ) + @test isapprox.(norm(μ_vsd - outx), 0, atol = tol_μ) + @test isapprox.(norm(μ_vs - outx), 0, atol = tol_μ) + @test isapprox.(norm(μ_v - outx), 0, atol = 4 * tol_μ) # a more approximate option so likely less good approx + + # An example with the other threading option + vrfi_tul = VectorRandomFeatureInterface( + n_features, + input_dim, + output_dim, + diagonalize_input = false, + diagonalize_output = false, + optimizer_options = Dict("train_fraction" => 0.7, "multithread" => "tullio"), + rng = rng, + ) + em_vrfi_svd_tul = Emulator(vrfi_tul, iopairs, obs_noise_cov = Σ) + μ_vs_tul, σ²_vs_tul = Emulators.predict(em_vrfi_svd_tul, new_inputs, transform_to_real = true) + @test isapprox.(norm(μ_vs_tul - outx), 0, atol = tol_μ) + + end + +end diff --git a/test/Utilities/runtests.jl b/test/Utilities/runtests.jl index bec9283ef..54e1ad7c9 100644 --- a/test/Utilities/runtests.jl +++ b/test/Utilities/runtests.jl @@ -60,4 +60,17 @@ using CalibrateEmulateSample.DataContainers @test get_inputs(training_points) ≈ initial_ensemble @test get_outputs(training_points) ≈ g_ens + #positive definiteness + mat = reshape(collect(-3:(-3 + 10^2 - 1)), 10, 10) + tol = 1e12 * eps() + @test !isposdef(mat) + + pdmat = posdef_correct(mat) + @test isposdef(pdmat) + @test minimum(eigvals(pdmat)) >= (1 - 1e-4) * 1e8 * eps() #eigvals is approximate so need a bit of give here + + pdmat2 = posdef_correct(mat, tol = tol) + @test isposdef(pdmat2) + @test minimum(eigvals(pdmat2)) >= (1 - 1e-4) * tol + end diff --git a/test/runtests.jl b/test/runtests.jl index c48b2aa9d..eeda04c7c 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -24,7 +24,7 @@ end end end - for submodule in ["Emulator", "GaussianProcess", "MarkovChainMonteCarlo", "Utilities"] + for submodule in ["Emulator", "GaussianProcess", "RandomFeature", "MarkovChainMonteCarlo", "Utilities"] if all_tests || has_submodule(submodule) || "CalibrateEmulateSample" in ARGS include_test(submodule) end