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+import{_ as t,c as e,o as i,a7 as s}from"./chunks/framework.Bblfi-75.js";const a="/NeuroTreeModels.jl/v1.1.0/assets/decision-tree.Dqh78YdA.png",n="/NeuroTreeModels.jl/v1.1.0/assets/neurotree.vCO5vhkM.png",f=JSON.parse('{"title":"NeuroTree - A differentiable tree operator for tabular data","description":"","frontmatter":{},"headers":[],"relativePath":"design.md","filePath":"design.md","lastUpdated":null}'),r={name:"design.md"},l=s('NeuroTree - A differentiable tree operator for tabular data Overview This work introduces NeuroTree a differentiable binary tree operator adapted for the treatment of tabular data.
Address the shortcoming of traditional trees greediness: all node and leaves are learned simultaneously. It provides the ability to learn an optimal configuration across all the tree levels. The notion extent also to the collection of trees that are simultaneously learned.
Extend the notion of forest/bagging and boosting.
Although the predictions from the all the trees forming a NeuroTree operator are averaged, each of the tree prediction is tuned simultaneously. This is different from boosting (ex XGBoost) where each tree is learned sequentially and over the residual from previous trees. Also, unlike random forest and bagging, trees aren't learned in isolation but tuned collaboratively, resulting in predictions that account for all of the other tree predictions. General operator compatible for composition.
Allows integration within Flux's Chain like other standard operators from NNLib. Composition is also illustrated through the built-in StackTree layer, a residual composition of multiple NeuroTree building blocks. Compatible with general purpose machine learning framework.
Architecture A NeuroTree operator acts as collection of complete binary trees, ie. trees without any pruned node. To be differentiable, hence trainable using first-order gradient based methods (ex. Adam optimiser), each tree path implements a soft decision rather than a hard one like in traditional decision tree.
To introduce the implementation of a NeuroTree, we first get back to the architecture of a basic decision tree.
The above is a binary decision tree of depth 2.
Highlighted in green is the decision path taken for a given sample. It goes into depth number of binary decisions, resulting in the path node1 → node3 → leaf3.
One way to view the role of the decision nodes (gray background) is to provide an index of the leaf prediction to fetch (index 3 in the figure). Such indexing view is applicable given that node routing relies on hard conditions: either true or false.
An alternative perspective that we adopt here is that tree nodes collectively provide weights associated to each leaf. A tree prediction becomes the weighted sum of the leaf's values and the leaf's weights. In regular decision trees, since all conditions are binary, leaf weights take the form of a mask. In the above example, the mask is [0, 0, 1, 0].
By relaxing these hard conditions into soft ones, the mask takes the form of a probability vector associated to each leaf, where ∑(leaf_weights) = 1 and where each each leaf_weight element is [0, 1]. A tree prediction can be obtained with the dot product: leaf_values' * leaf_weights.
The following illustrate how a basic decision tree is represented as a single differentiable tree within NeuroTree:
Node weights To illustrate how a NeuroTree derives the soft decision probability (referred to NW1 - NW3 in the above figure), we first break down how a traditional tree split condition is derived from 2 underlying decisions:
Selection of the feature on which to perform the condition .Such selection can be represented as the application of a binary mask where all elements are set to false except for that single selected feature where it's set to true.
Selection of the condition's threshold value .For a given observation, if the selected feature's value is below that threshold, then the node decision is set to false (pointing to left child), and true otherwise (pooinnting to right child).
In NeuroTree, these 2 hard steps are translated into soft, differentiable ones.
Leaf weights Computing the leaf weights consists of accumulating the weights through each tree branch. It's the technically more challenging part as such computation cannot be represented as a form of matrix multiplication, unlike other common operators like Dense, Conv or MultiHeadAttention / Transformer. Performing probability accumulation though a tree index naturally leads to in-place element wise operations, which are notoriously not friendly for auto-differentiation engines. Since NeuroTree was intended to integrate with the Flux.jl ecosystem, Zygote.jl acts as the underlying AD, the approach used was to manually implement backward / adjoint of the terminal leaf function and instruct the AD to use that custom rule rather than attempt to differentiate a non-AD compliant function.
Below are the algo and actual implementation of the forward and backward function that compute the leaf weights. For brevity, the loops over each observation of the batch and each tree are omitted. Parallelism, both on CPU and GPU, is obtained through parallelization over the tree and batch dimensions.
Forward
julia function leaf_weights! (nw) cw = ones ( eltype (nw), 2 * size (nw, 1 ) + 1 ) for i = 2 : 2 : size (cw, 1 ) cw[i] = cw[i >> 1 ] * nw[i >> 1 ] cw[i + 1 , tree, batch] = cw[i >> 1 ] * ( 1 - nw[i >> 1 ]) end lw = cw[ size (nw, 1 ) + 1 : size (cw, 1 )] return (cw, lw) end Backward
julia function Δ_leaf_weights! (Δnw, ȳ, cw, nw, max_depth, node_offset) for i in axes (nw, 1 ) depth = floor (Int, log2 (i)) # current depth level - starting at 0 step = 2 ^ (max_depth - depth) # iteration length leaf_offset = step * (i - 2 ^ depth) # offset on the leaf row for j = ( 1 + leaf_offset) : (step ÷ 2 + leaf_offset) k = j + node_offset # move from leaf position to full tree position Δnw[i] += ȳ[j] * cw[k] / nw[i] end for j = ( 1 + leaf_offset + step ÷ 2 ) : (step + leaf_offset) k = j + node_offset Δnw[i] -= ȳ[j] * cw[k] / ( 1 - nw[i]) end end return nothing end Tree prediction Composability Benchmarks For each dataset and algo, the following methodology is followed:
Data is split in three parts: train, eval and test
A random grid of 16 hyper-parameters is generated
For each parameter configuration, a model is trained on train data until the evaluation metric tracked against the eval stops improving (early stopping)
The trained model is evaluated against the test data
The metric presented in below are the ones obtained on the test for the model that generated the best eval metric.
Source code available at MLBenchmarks.jl .
For performance assessment, benchmarks is run on the following selection of common Tabular datasets:
Year : min squared error regression. 515,345 observations, 90 features.
MSRank : ranking problem with min squared error regression. 1,200,192 observations, 136 features.
YahooRank : ranking problem with min squared error regression. 709,877 observations, 519 features.
Higgs : 2-level classification with logistic regression. 11,000,000 observations, 28 features.
Boston Housing : min squared error regression.
Titanic : 2-level classification with logistic regression. 891 observations, 7 features.
Comparison is performed against the following algos (implementation in link) considered as state of the art on classification tasks:
Boston model_type train_time mse gini neurotrees 12.8 18.9 0.947 evotrees 0.206 19.7 0.927 xgboost 0.0648 19.4 0.935 lightgbm 0.865 25.4 0.926 catboost 0.0511 13.9 0.946
Titanic model_type train_time logloss accuracy neurotrees 7.58 0.407 0.828 evotrees 0.673 0.382 0.828 xgboost 0.0379 0.375 0.821 lightgbm 0.615 0.390 0.836 catboost 0.0326 0.388 0.836
Year model_type train_time mse gini neurotrees 280.0 76.4 0.652 evotrees 18.6 80.1 0.627 xgboost 17.2 80.2 0.626 lightgbm 8.11 80.3 0.624 catboost 80.0 79.2 0.635
MSRank model_type train_time mse ndcg neurotrees 39.1 0.578 0.462 evotrees 37.0 0.554 0.504 xgboost 12.5 0.554 0.503 lightgbm 37.5 0.553 0.503 catboost 15.1 0.558 0.497
Yahoo model_type train_time mse ndcg neurotrees 417.0 0.584 0.781 evotrees 687.0 0.545 0.797 xgboost 120.0 0.547 0.798 lightgbm 244.0 0.540 0.796 catboost 161.0 0.561 0.794
Higgs model_type train_time logloss accuracy neurotrees 12300.0 0.452 0.781 evotrees 2620.0 0.464 0.776 xgboost 1390.0 0.462 0.776 lightgbm 1330.0 0.461 0.779 catboost 7180.0 0.464 0.775
Discussion NeuroTreeModels can achieve top tier performance on both small (Boston) and large (Higgs) datasets. Its performance trailed on the two ranking regression problems (MSRank and Yahoo). Although the large number of features is a distinguishing characteristic of the Yahoo dataset, the 136 features of MSRank are not materially different for the YEAR dataset (90 features), and on which NeuroTreeMoels outperform all other algos. Considering that no sparsity mechanism is present in the feature selection for the node conditions, datasets with a very large number of features may present a challenge. Substituting the default tanh activation with a sparsity inducing one such as hardsigmoid or EntrOpt has not resulted in improvement from the experiments.
Another potential weakness may stem from the soft nature of the decision criteria. Traditional trees can isolate the effect of a specific feature value. This can be notably meaningful in a situation where a numeric feature taking a value of 0 may carry a particular meaning (ex. missing, unknown value). Such stump the effect of a feature should be harder to pick with NeuroTree's soft condition.
References `,57),h=[l];function o(d,p,g,k,c,y){return i(),e("div",null,h)}const u=t(r,[["render",o]]);export{f as __pageData,u as default};
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Type .
NeuroTreeRegressor(;kwargs...)
A model type for constructing a NeuroTreeRegressor, based on NeuroTreeModels.jl , and implementing both an internal API and the MLJ model interface.
Hyper-parameters
loss=:mse: Loss to be be minimized during training. One of:
:mse
:mae
:logloss
:mlogloss
:gaussian_mle
nrounds=10: Max number of rounds (epochs).
lr=1.0f-2: Learning rate. Must be > 0. A lower eta results in slower learning, typically requiring a higher nrounds.
wd=0.f0: Weight decay applied to the gradients by the optimizer.
batchsize=2048: Batch size.
actA=:tanh: Activation function applied to each of input variable for determination of split node weight. Can be one of:
outsize=1: Number of predictions returned by the model. Typically only used for classification tasks and set to the number of target levels / classes.
depth=6: Depth of a tree. Must be >= 1. A tree of depth 1 has 2 prediction leaf nodes. A complete tree of depth N contains 2^N terminal leaves and 2^N - 1 split nodes. Compute cost is proportional to 2^depth. Typical optimal values are in the 3 to 5 range.
ntrees=64: Number of trees (per stack).
hidden_size=16: Size of hidden layers. Applicable only when stack_size > 1.
stack_size=1: Number of stacked NeuroTree blocks.
init_scale=1.0: Scaling factor applied to the predictions weights. Values in the ]0, 1] short result in best performance.
MLE_tree_split=false: Whether independent models are buillt for each of the 2 parameters (mu, sigma) of the the gaussian_mle loss.
rng=123: Either an integer used as a seed to the random number generator or an actual random number generator (::Random.AbstractRNG).
device=:cpu: Device to use. Either :cpu or :gpu (recommended as it improves significantly the training speed).
gpuID=0: ID of the GPU to use for training.
Internal API
Do config = NeuroTreeRegressor() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in NeuroTreeRegressor(loss=...).
Training model
A model is trained using fit
julia m = fit (config, dtrain; feature_names, target_name, kwargs ... ) Inference
Models act as a functor. returning predictions when called as a function with features as argument:
MLJ Interface
From MLJ, the type can be imported using:
julia NeuroTreeRegressor = @load NeuroTreeRegressor pkg = NeuroTreeModels Do model = NeuroTreeRegressor() to construct an instance with default hyper-parameters. Provide keyword arguments to override hyper-parameter defaults, as in NeuroTreeRegressor(loss=...).
Training model
In MLJ or MLJBase, bind an instance model to data with mach = machine(model, X, y) where
X: any table of input features (eg, a DataFrame) whose columns each have one of the following element scitypes: Continuous, Count, or <:OrderedFactor; check column scitypes with schema(X)
y: is the target, which can be any AbstractVector whose element scitype is <:Continuous; check the scitype with scitype(y)
Train the machine using fit!(mach, rows=...).
Operations
predict(mach, Xnew): return predictions of the target given features Xnew having the same scitype as X above.Fitted parameters
The fields of fitted_params(mach) are:
:fitresult: The NeuroTreeModel object.Report
The fields of report(mach) are:
:features: The names of the features encountered in training.Examples
Internal API
julia using NeuroTreeModels, DataFrames config = NeuroTreeRegressor (depth = 5 , nrounds = 10 ) nobs, nfeats = 1_000 , 5 dtrain = DataFrame ( randn (nobs, nfeats), :auto ) dtrain . y = rand (nobs) feature_names, target_name = names (dtrain, r" x " ), "y" m = fit (config, dtrain; feature_names, target_name) p = m (dtrain) MLJ Interface
julia using MLJBase, NeuroTreeModels m = NeuroTreeRegressor (depth = 5 , nrounds = 10 ) X, y = @load_boston mach = machine (m, X, y) |> fit! p = predict (mach, X) source
NeuroTreeModel # NeuroTreeModels.NeuroTreeModel —
Type .
A NeuroTreeModel is made of a collection of Tree, either regular NeuroTree or StackTree. Prediction is the sum of all the trees composing a NeuroTreeModel.
source
Getting started with NeuroTreeModels.jl Installation julia ] add NeuroTreeModels Configuring a model A model configuration is defined with the NeuroTreeRegressor constructor:
julia using NeuroTreeModels, DataFrames config = NeuroTreeRegressor ( loss = :mse , nrounds = 10 , num_trees = 16 , depth = 5 , ) Training Building and training a model according to the above config is done with NeuroTreeModels.fit . See the docs for additional features, notably early stopping support through the tracking of an evaluation metric.
julia nobs, nfeats = 1_000 , 5 dtrain = DataFrame ( randn (nobs, nfeats), :auto ) dtrain . y = rand (nobs) feature_names, target_name = names (dtrain, r" x " ), "y" m = NeuroTreeModels . fit (config, dtrain; feature_names, target_name) Inference MLJ NeuroTreeModels.jl supports the MLJ Interface.
julia using MLJBase, NeuroTreeModels m = NeuroTreeRegressor (depth = 5 , nrounds = 10 ) X, y = @load_boston mach = machine (m, X, y) |> fit! p = predict (mach, X) Benchmarks Benchmarking against prominent ML libraries for tabular is performed at MLBenchmarks.jl .
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diff --git a/v1.1.0/assets/tutorials-classification-iris.md.DVImRnRk.js b/v1.1.0/assets/tutorials-classification-iris.md.DVImRnRk.js
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+import{_ as s,c as i,o as a,a7 as n}from"./chunks/framework.Bblfi-75.js";const y=JSON.parse('{"title":"Classification on Iris dataset","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials-classification-iris.md","filePath":"tutorials-classification-iris.md","lastUpdated":null}'),t={name:"tutorials-classification-iris.md"},h=n(`Classification on Iris dataset We will use the iris dataset, which is included in the MLDatasets package. This dataset consists of measurements of the sepal length, sepal width, petal length, and petal width for three different types of iris flowers: Setosa, Versicolor, and Virginica.
Getting started To begin, we will load the required packages and the dataset:
julia using NeuroTreeModels using MLDatasets using DataFrames using Statistics : mean using CategoricalArrays using Random Random . seed! ( 123 ) Preprocessing Before we can train our model, we need to preprocess the dataset. We will convert the class variable, which specifies the type of iris flower, into a categorical variable.
julia df = MLDatasets . Iris () . dataframe df[ ! , :class ] = categorical (df[ ! , :class ]) df[ ! , :class ] .= levelcode .(df[ ! , :class ]) target_name = "class" feature_names = setdiff ( names (df), [target_name]) train_ratio = 0.8 train_indices = randperm ( nrow (df))[ 1 : Int (train_ratio * nrow (df))] dtrain = df[train_indices, :] deval = df[ setdiff ( 1 : nrow (df), train_indices), :] Training Now we are ready to train our model. We first define a model configuration using the NeuroTreeRegressorNeuroTreeModels.fitdeval argument to enable the usage of early stopping.
julia config = NeuroTreeRegressor ( device = :cpu , loss = :mlogloss , nrounds = 400 , outsize = 3 , depth = 4 , lr = 2e-2 , ) m = NeuroTreeModels . fit ( config, dtrain; deval, target_name, feature_names, metric = :mlogloss , print_every_n = 10 , early_stopping_rounds = 2 , ) Diagnosis Finally, we can get predictions by passing training and testing data to our model. We can then evaluate the accuracy of our model, which should be over 95% for this simple classification problem.
julia p_train = m (dtrain) p_eval = m (deval) julia julia > mean (dtrain[ ! , target_name] .== NeuroTreeModels . onecold (p_train ' )) 0.9833333333333333 julia > mean (deval[ ! , target_name] .== NeuroTreeModels . onecold (p_eval ' )) 1.0 Logistic Regression on Titanic Dataset We will use the Titanic dataset, which is included in the MLDatasets package. It describes the survival status of individual passengers on the Titanic. The model will be approached as a logistic regression problem, although a Classifier model could also have been used (see the Classification - Iris tutorial).
Getting started To begin, we will load the required packages and the dataset:
julia using NeuroTreeModels using MLDatasets using DataFrames using Statistics : mean using StatsBase : median using CategoricalArrays using Random Random . seed! ( 123 ) Preprocessing A first step in data processing is to prepare the input features in a model compatible format.
EvoTrees' Tables API supports input that are either Real (incl. Bool) or Categorical. Bool variables are treated as unordered, 2-levels categorical variables. A recommended approach for String features such as Sex is to convert them into an unordered Categorical.
For dealing with features with missing values such as Age, a common approach is to first create an Bool indicator variable capturing the info on whether a value is missing. Then, the missing values can be imputed (replaced by some default values such as mean or median, or more sophisticated approach such as predictions from another model).
julia df = MLDatasets . Titanic () . dataframe # convert string feature to Categorical transform! (df, :Sex => categorical => :Sex ) transform! (df, :Sex => ByRow (levelcode) => :Sex ) # treat string feature and missing values transform! (df, :Age => ByRow (ismissing) => :Age_ismissing ) transform! (df, :Age => (x -> coalesce .(x, median ( skipmissing (x)))) => :Age ); # remove unneeded variables df = df[:, Not ([ :PassengerId , :Name , :Embarked , :Cabin , :Ticket ])] The full data can now be split according to train and eval indices. Target and feature names are also set.
julia train_ratio = 0.8 train_indices = randperm ( nrow (df))[ 1 : Int ( round (train_ratio * nrow (df)))] dtrain = df[train_indices, :] deval = df[ setdiff ( 1 : nrow (df), train_indices), :] target_name = "Survived" feature_names = setdiff ( names (df), [target_name]) Training Now we are ready to train our model. We first define a model configuration using the NeuroTreeRegressorNeuroTreeModels.fitdeval argument to enable the usage of early stopping.
julia config = NeuroTreeRegressor ( device = :cpu , loss = :logloss , nrounds = 400 , depth = 4 , lr = 2e-2 , ) m = NeuroTreeModels . fit ( config, dtrain; deval, target_name, feature_names, metric = :logloss , print_every_n = 10 , early_stopping_rounds = 2 , ) Diagnosis We can get predictions by passing training and testing data to our model. We can then evaluate the accuracy of our model, which should be around 85%.
julia p_train = m (dtrain) p_eval = m (deval) julia julia > mean ((p_train .> 0.5 ) .== dtrain[ ! , target_name]) 0.8527349228611 julia > mean ((p_eval .> 0.5 ) .== deval[ ! , target_name]) 0.8426966292134831 Regression on Boston Housing Dataset We will use the Boston Housing dataset, which is included in the MLDatasets package. It's derived from information collected by the U.S. Census Service concerning housing in the area of Boston. Target variable represents the median housing value.
Getting started To begin, we will load the required packages and the dataset:
julia using NeuroTreeModels using MLDatasets using DataFrames using Statistics : mean, std using CategoricalArrays using Random Random . seed! ( 123 ) Preprocessing Before we can train our model, we need to preprocess the dataset. We will split our data according to train and eval indices, and separate features from the target variable.
julia df = MLDatasets . BostonHousing () . dataframe feature_names = setdiff ( names (df), [ "MEDV" ]) train_ratio = 0.8 train_indices = randperm ( nrow (df))[ 1 : Int ( round (train_ratio * nrow (df)))] dtrain = df[train_indices, :] deval = df[ setdiff ( 1 : nrow (df), train_indices), :] _mean, _std = mean (dtrain . MEDV), std (dtrain . MEDV) transform! (dtrain, :MEDV => (x -> (x .- _mean) ./ _std) => "target" ) transform! (deval, :MEDV => (x -> (x .- _mean) ./ _std) => "target" ) target_name = "target" Training Now we are ready to train our model. We first define a model configuration using the NeuroTreeRegressorNeuroTreeModels.fitdeval argument to enable the usage of early stopping.
julia config = NeuroTreeRegressor ( device = :cpu , loss = :mse , nrounds = 400 , depth = 5 , lr = 2e-2 , ) m = NeuroTreeModels . fit ( config, dtrain; deval, target_name, feature_names, metric = :mse , print_every_n = 10 , early_stopping_rounds = 2 , ) Diagnosis Finally, we can get predictions by passing training and testing data to our model. We can then apply various evaluation metric, such as the MAE (mean absolute error):
julia p_train = m (dtrain) .* _std .+ _mean p_eval = m (deval) .* _std .+ _mean julia julia > mean ( abs .(p_train .- dtrain[ ! , "MEDV" ])) 0.8985784079860025 julia > mean ( abs .(p_eval .- deval[ ! , "MEDV" ])) 2.3287859731914597 NeuroTree - A differentiable tree operator for tabular data | NeuroTreeModels
+ NeuroTreeModels
+ Skip to content NeuroTreeModels.jl
Differentiable tree-based models for tabular data
Models | NeuroTreeModels
+ Getting started with NeuroTreeModels.jl | NeuroTreeModels
+ Classification on Iris dataset | NeuroTreeModels
+ Logistic Regression on Titanic Dataset | NeuroTreeModels
+ Regression on Boston Housing Dataset | NeuroTreeModels
+ 
