Skip to main content

Kernels in Jax.

Project description


This project has now been incorporated into GPJax.

JaxKern's logo

Kernels in Jax.

codecov CircleCI Documentation Status PyPI version Downloads Slack Invite

Introduction

JaxKern is Python library for working with kernel functions in JAX. We currently support the following kernels:

  • Stationary
    • Radial basis function (Squared exponential)
    • Matérn
    • Powered exponential
    • Rational quadratic
    • White noise
    • Periodic
  • Non-stationary
    • Linear
    • Polynomial
  • Non-Euclidean
    • Graph kernels

In addition to this, we implement kernel approximations using the Random Fourier feature approach.

Example

The following code snippet demonstrates how the first order Matérn kernel can be computed and, subsequently, approximated using random Fourier features.

import jaxkern as jk
import jax.numpy as jnp
import jax.random as jr
key = jr.PRNGKey(123)

# Define the points on which we'll evaluate the kernel
X = jr.uniform(key, shape = (10, 1), minval=-3., maxval=3.)
Y = jr.uniform(key, shape = (20, 1), minval=-3., maxval=3.)

# Instantiate the kernel and its parameters
kernel = jk.Matern32()
params = kernel.init_params(key)

# Compute the 10x10 Gram matrix
Kxx = kernel.gram(params, X)

# Compute the 10x20 cross-covariance matrix
Kxy = kernel.cross_covariance(params, X, Y)

# Build a RFF approximation
approx = RFF(kernel, num_basis_fns = 5)
rff_params = approx.init_params(key)

# Build an approximation to the Gram matrix
Qff = approx.gram(rff_params, X)

Code Structure

All kernels are supplied with a gram and cross_covariance method. When computing a Gram matrix, there is often some structure in the data (e.g., Markov) that can be exploited to yield a sparse matrix. To instruct JAX how to operate on this, the return type of gram is a Linear Operator from JaxLinOp.

Within GPJax, all kernel computations are handled using JaxKern.

Documentation

A full set of documentation is a work in progress. However, many of the details in JaxKern can be found in the GPJax documentation.

Project details


Release history Release notifications | RSS feed

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

jaxkern-nightly-0.0.5.dev20240921.tar.gz (33.7 kB view details)

Uploaded Source

Built Distribution

File details

Details for the file jaxkern-nightly-0.0.5.dev20240921.tar.gz.

File metadata

File hashes

Hashes for jaxkern-nightly-0.0.5.dev20240921.tar.gz
Algorithm Hash digest
SHA256 e59e6473b3c125a13c186e4dd4f5180048a8c7bb1fcdc27bb56b86f7ebd12b89
MD5 2c2e853b308d095f4fb4236995877b4d
BLAKE2b-256 7ab9d54046d50c5a85c3e7105a6f37829d8f54784ebbf577dda5ad5fa25fecc5

See more details on using hashes here.

File details

Details for the file jaxkern_nightly-0.0.5.dev20240921-py3-none-any.whl.

File metadata

File hashes

Hashes for jaxkern_nightly-0.0.5.dev20240921-py3-none-any.whl
Algorithm Hash digest
SHA256 cccc70262fc15769af5d2382b278394d2b68e6def0fc08222f1b790059bbf76a
MD5 4e9bbe5daf20f523e0df5c4fd90c26b6
BLAKE2b-256 bbc0366094d5bb142f3ee9f1a333ef34b2b193dc9213ff8078ae367200b7c5f3

See more details on using hashes here.

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page