CoLA integration

.github/workflows/build_docs.yml

@@ -19,7 +19,7 @@ jobs:
     strategy:
       matrix:
         os: ["ubuntu-latest"]
-        python-version: ["3.8"]
+        python-version: ["3.10"]
 
     steps:
       # Grap the latest commit from the branch

.github/workflows/integration.yml

@@ -13,7 +13,7 @@ jobs:
       matrix:
         # Select the Python versions to test against
         os: ["ubuntu-latest", "macos-latest"]
-        python-version: ["3.8", "3.9", "3.10", "3.11"]
+        python-version: ["3.10", "3.11"]
       fail-fast: true
     steps:
       - name: Check out the code

.github/workflows/test_docs.yml

@@ -17,7 +17,7 @@ jobs:
     strategy:
       matrix:
         os: ["ubuntu-latest"]
-        python-version: ["3.8"]
+        python-version: ["3.10"]
 
     steps:
       # Grap the latest commit from the branch

.github/workflows/tests.yml

@@ -13,7 +13,7 @@ jobs:
       matrix:
         # Select the Python versions to test against
         os: ["ubuntu-latest", "macos-latest"]
-        python-version: ["3.8", "3.9", "3.10", "3.11"]
+        python-version: ["3.10", "3.11"]
       fail-fast: true
     steps:
       - name: Check out the code

docs/examples/classification.py

@@ -207,13 +207,17 @@
 # datapoints below.
 
 # %%
+import cola
+from gpjax.lower_cholesky import lower_cholesky
+
 gram, cross_covariance = (kernel.gram, kernel.cross_covariance)
 jitter = 1e-6
 
 # Compute (latent) function value map estimates at training points:
 Kxx = opt_posterior.prior.kernel.gram(x)
 Kxx += identity_matrix(D.n) * jitter
-Lx = Kxx.to_root()
+Kxx = cola.PSD(Kxx)
+Lx = lower_cholesky(Kxx)
 f_hat = Lx @ opt_posterior.latent
 
 # Negative Hessian,  H = -∇²p_tilde(y|f):
@@ -250,16 +254,13 @@ def construct_laplace(test_inputs: Float[Array, "N D"]) -> tfd.MultivariateNorma
     Kxt = opt_posterior.prior.kernel.cross_covariance(x, test_inputs)
     Kxx = opt_posterior.prior.kernel.gram(x)
     Kxx += identity_matrix(D.n) * jitter
-    Lx = Kxx.to_root()
-
-    # Lx⁻¹ Kxt
-    Lx_inv_Ktx = Lx.solve(Kxt)
+    Kxx = cola.PSD(Kxx)
 
     # Kxx⁻¹ Kxt
-    Kxx_inv_Ktx = Lx.T.solve(Lx_inv_Ktx)
+    Kxx_inv_Kxt = cola.solve(Kxx, Kxt)
 
     # Ktx Kxx⁻¹[ H⁻¹ ] Kxx⁻¹ Kxt
-    laplace_cov_term = jnp.matmul(jnp.matmul(Kxx_inv_Ktx.T, H_inv), Kxx_inv_Ktx)
+    laplace_cov_term = jnp.matmul(jnp.matmul(Kxx_inv_Kxt.T, H_inv), Kxx_inv_Kxt)
 
     mean = map_latent_dist.mean()
     covariance = map_latent_dist.covariance() + laplace_cov_term

docs/examples/constructing_new_kernels.py

@@ -108,7 +108,7 @@
 # like our RBF kernel to act on the first, second and fourth dimensions.
 
 # %%
-slice_kernel = gpx.kernels.RBF(active_dims=[0, 1, 3], lengthscale = jnp.ones((3,)))
+slice_kernel = gpx.kernels.RBF(active_dims=[0, 1, 3], lengthscale=jnp.ones((3,)))
 
 # %% [markdown]
 #

gpjax/__init__.py

@@ -29,8 +29,8 @@
     RFF,
     AbstractKernel,
     BasisFunctionComputation,
-    ConstantDiagonalKernelComputation,
     CatKernel,
+    ConstantDiagonalKernelComputation,
     DenseKernelComputation,
     DiagonalKernelComputation,
     EigenKernelComputation,

gpjax/citation.py

@@ -2,13 +2,13 @@
     dataclass,
     fields,
 )
+from functools import singledispatch
 
 from beartype.typing import (
     Dict,
     Union,
 )
 from jaxlib.xla_extension import PjitFunction
-from plum import dispatch
 
 from gpjax.kernels import (
     RFF,
@@ -26,8 +26,6 @@
     NonConjugateMLL,
 )
 
-MaternKernels = Union[Matern12, Matern32, Matern52]
-MLLs = Union[ConjugateMLL, NonConjugateMLL, LogPosteriorDensity]
 CitationType = Union[str, Dict[str, str]]
 
 
@@ -89,24 +87,26 @@ class BookCitation(AbstractCitation):
 ####################
 # Default citation
 ####################
-@dispatch
-def cite(tree) -> NullCitation:
+@singledispatch
+def cite(tree) -> AbstractCitation:
     return NullCitation()
 
 
 ####################
 # Default citation
 ####################
-@dispatch
-def cite(tree: PjitFunction) -> JittedFnCitation:
+@cite.register(PjitFunction)
+def _(tree):
     return JittedFnCitation()
 
 
 ####################
 # Kernel citations
 ####################
-@dispatch
-def cite(tree: MaternKernels) -> PhDThesisCitation:
+@cite.register(Matern12)
+@cite.register(Matern32)
+@cite.register(Matern52)
+def _(tree) -> PhDThesisCitation:
     citation = PhDThesisCitation(
         citation_key="matern1960SpatialV",
         authors="Bertil Matérn",
@@ -121,8 +121,8 @@ def cite(tree: MaternKernels) -> PhDThesisCitation:
     return citation
 
 
-@dispatch
-def cite(tree: ArcCosine) -> PaperCitation:
+@cite.register(ArcCosine)
+def _(_) -> PaperCitation:
     return PaperCitation(
         citation_key="cho2009kernel",
         authors="Cho, Youngmin and Saul, Lawrence",
@@ -132,8 +132,8 @@ def cite(tree: ArcCosine) -> PaperCitation:
     )
 
 
-@dispatch
-def cite(tree: GraphKernel) -> PaperCitation:
+@cite.register(GraphKernel)
+def _(tree) -> PaperCitation:
     return PaperCitation(
         citation_key="borovitskiy2021matern",
         title="Matérn Gaussian Processes on Graphs",
@@ -146,8 +146,8 @@ def cite(tree: GraphKernel) -> PaperCitation:
     )
 
 
-@dispatch
-def cite(tree: RFF) -> PaperCitation:
+@cite.register(RFF)
+def _(tree) -> PaperCitation:
     return PaperCitation(
         citation_key="rahimi2007random",
         authors="Rahimi, Ali and Recht, Benjamin",
@@ -161,8 +161,10 @@ def cite(tree: RFF) -> PaperCitation:
 ####################
 # Objective citations
 ####################
-@dispatch
-def cite(tree: MLLs) -> BookCitation:
+@cite.register(ConjugateMLL)
+@cite.register(NonConjugateMLL)
+@cite.register(LogPosteriorDensity)
+def _(tree) -> BookCitation:
     return BookCitation(
         citation_key="rasmussen2006gaussian",
         title="Gaussian Processes for Machine Learning",
@@ -173,8 +175,8 @@ def cite(tree: MLLs) -> BookCitation:
     )
 
 
-@dispatch
-def cite(tree: CollapsedELBO) -> PaperCitation:
+@cite.register(CollapsedELBO)
+def _(tree) -> PaperCitation:
     return PaperCitation(
         citation_key="titsias2009variational",
         title="Variational learning of inducing variables in sparse Gaussian processes",
@@ -184,8 +186,8 @@ def cite(tree: CollapsedELBO) -> PaperCitation:
     )
 
 
-@dispatch
-def cite(tree: ELBO) -> PaperCitation:
+@cite.register(ELBO)
+def _(tree) -> PaperCitation:
     return PaperCitation(
         citation_key="hensman2013gaussian",
         title="Gaussian Processes for Big Data",

gpjax/gaussian_distribution.py

@@ -19,6 +19,11 @@
     Optional,
     Tuple,
 )
+import cola
+from cola.ops import (
+    Dense,
+    Identity,
+)
 from jax import vmap
 import jax.numpy as jnp
 import jax.random as jr
@@ -28,10 +33,7 @@
 )
 import tensorflow_probability.substrates.jax as tfp
 
-from gpjax.linops import (
-    IdentityLinearOperator,
-    LinearOperator,
-)
+from gpjax.lower_cholesky import lower_cholesky
 from gpjax.typing import (
     Array,
     KeyArray,
@@ -49,15 +51,15 @@ def _check_loc_scale(loc: Optional[Any], scale: Optional[Any]) -> None:
     if loc is not None and loc.ndim < 1:
         raise ValueError("The parameter `loc` must have at least one dimension.")
 
-    if scale is not None and scale.ndim < 2:
+    if scale is not None and len(scale.shape) < 2:  # scale.ndim < 2:
         raise ValueError(
             "The `scale` must have at least two dimensions, but "
             f"`scale.shape = {scale.shape}`."
         )
 
-    if scale is not None and not isinstance(scale, LinearOperator):
+    if scale is not None and not isinstance(scale, cola.LinearOperator):
         raise ValueError(
-            f"scale must be a LinearOperator or a JAX array, but got {type(scale)}"
+            f"The `scale` must be a cola.LinearOperator but got {type(scale)}"
         )
 
     if scale is not None and (scale.shape[-1] != scale.shape[-2]):
@@ -79,7 +81,7 @@ class GaussianDistribution(tfd.Distribution):
 
     Args:
         loc (Optional[Float[Array, " N"]]): The mean of the distribution. Defaults to None.
-        scale (Optional[LinearOperator]): The scale matrix of the distribution. Defaults to None.
+        scale (Optional[cola.LinearOperator]): The scale matrix of the distribution. Defaults to None.
 
     Returns
     -------
@@ -94,7 +96,7 @@ class GaussianDistribution(tfd.Distribution):
     def __init__(
         self,
         loc: Optional[Float[Array, " N"]] = None,
-        scale: Optional[LinearOperator] = None,
+        scale: Optional[cola.LinearOperator] = None,
     ) -> None:
         r"""Initialises the distribution."""
         _check_loc_scale(loc, scale)
@@ -112,10 +114,10 @@ def __init__(
 
         # If not specified, set the scale to the identity matrix.
         if scale is None:
-            scale = IdentityLinearOperator(num_dims)
+            scale = Identity(shape=(num_dims, num_dims), dtype=loc.dtype)
 
         self.loc = loc
-        self.scale = scale
+        self.scale = cola.PSD(scale)
 
     def mean(self) -> Float[Array, " N"]:
         r"""Calculates the mean."""
@@ -135,11 +137,11 @@ def covariance(self) -> Float[Array, "N N"]:
 
     def variance(self) -> Float[Array, " N"]:
         r"""Calculates the variance."""
-        return self.scale.diagonal()
+        return cola.diag(self.scale)
 
     def stddev(self) -> Float[Array, " N"]:
         r"""Calculates the standard deviation."""
-        return jnp.sqrt(self.scale.diagonal())
+        return jnp.sqrt(cola.diag(self.scale))
 
     @property
     def event_shape(self) -> Tuple:
@@ -149,7 +151,10 @@ def event_shape(self) -> Tuple:
     def entropy(self) -> ScalarFloat:
         r"""Calculates the entropy of the distribution."""
         return 0.5 * (
-            self.event_shape[0] * (1.0 + jnp.log(2.0 * jnp.pi)) + self.scale.log_det()
+            self.event_shape[0] * (1.0 + jnp.log(2.0 * jnp.pi))
+            + cola.logdet(
+                self.scale, method="dense"
+            )  # <--- Seems to be an issue with CoLA!
         )
 
     def log_prob(
@@ -168,20 +173,23 @@ def log_prob(
         mu = self.loc
         sigma = self.scale
         n = mu.shape[-1]
+
         if mask is not None:
             y = jnp.where(mask, 0.0, y)
             mu = jnp.where(mask, 0.0, mu)
-            sigma_masked = jnp.where(mask[None] + mask[:, None], 0.0, sigma.matrix)
-            sigma = sigma.replace(
-                matrix=jnp.where(jnp.diag(mask), 1 / (2 * jnp.pi), sigma_masked)
+            sigma_masked = jnp.where(mask[None] + mask[:, None], 0.0, sigma.to_dense())
+            sigma = cola.PSD(
+                Dense(jnp.where(jnp.diag(mask), 1 / (2 * jnp.pi), sigma_masked))
             )
 
         # diff, y - µ
         diff = y - mu
 
         # compute the pdf, -1/2[ n log(2π) + log|Σ| + (y - µ)ᵀΣ⁻¹(y - µ) ]
         return -0.5 * (
-            n * jnp.log(2.0 * jnp.pi) + sigma.log_det() + diff.T @ sigma.solve(diff)
+            n * jnp.log(2.0 * jnp.pi)
+            + cola.logdet(sigma, method="dense")  # <--- Seems to be an issue with CoLA!
+            + diff.T @ cola.solve(sigma, diff)
         )
 
     def _sample_n(self, key: KeyArray, n: int) -> Float[Array, "n N"]:
@@ -195,7 +203,7 @@ def _sample_n(self, key: KeyArray, n: int) -> Float[Array, "n N"]:
             Float[Array, "n N"]: The samples.
         """
         # Obtain covariance root.
-        sqrt = self.scale.to_root()
+        sqrt = lower_cholesky(self.scale)
 
         # Gather n samples from standard normal distribution Z = [z₁, ..., zₙ]ᵀ.
         Z = jr.normal(key, shape=(n, *self.event_shape))
@@ -263,24 +271,26 @@ def _kl_divergence(q: GaussianDistribution, p: GaussianDistribution) -> ScalarFl
     sigma_p = p.scale
 
     # Find covariance roots.
-    sqrt_p = sigma_p.to_root()
-    sqrt_q = sigma_q.to_root()
+    sqrt_p = lower_cholesky(sigma_p)
+    sqrt_q = lower_cholesky(sigma_q)
 
     # diff, μp - μq
     diff = mu_p - mu_q
 
     # trace term, tr[Σp⁻¹ Σq] = tr[(LpLpᵀ)⁻¹(LqLqᵀ)] = tr[(Lp⁻¹Lq)(Lp⁻¹Lq)ᵀ] = (fr[LqLp⁻¹])²
     trace = _frobenius_norm_squared(
-        sqrt_p.solve(sqrt_q.to_dense())
+        cola.solve(sqrt_p, sqrt_q.to_dense())
     )  # TODO: Not most efficient, given the `to_dense()` call (e.g., consider diagonal p and q). Need to abstract solving linear operator against another linear operator.
 
     # Mahalanobis term, (μp - μq)ᵀ Σp⁻¹ (μp - μq) = tr [(μp - μq)ᵀ [LpLpᵀ]⁻¹ (μp - μq)] = (fr[Lp⁻¹(μp - μq)])²
     mahalanobis = jnp.sum(
-        jnp.square(sqrt_p.solve(diff))
+        jnp.square(cola.solve(sqrt_p, diff))
     )  # TODO: Need to improve this. Perhaps add a Mahalanobis method to ``LinearOperator``s.
 
     # KL[q(x)||p(x)] = [ [(μp - μq)ᵀ Σp⁻¹ (μp - μq)] - n - log|Σq| + log|Σp| + tr[Σp⁻¹ Σq] ] / 2
-    return (mahalanobis - n_dim - sigma_q.log_det() + sigma_p.log_det() + trace) / 2.0
+    return (
+        mahalanobis - n_dim - cola.logdet(sigma_q) + cola.logdet(sigma_p) + trace
+    ) / 2.0
 
 
 __all__ = [