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.dev20240607.tar.gz (33.8 kB view details)

Uploaded Source

Built Distribution

File details

Details for the file jaxkern-nightly-0.0.5.dev20240607.tar.gz.

File metadata

File hashes

Hashes for jaxkern-nightly-0.0.5.dev20240607.tar.gz
Algorithm Hash digest
SHA256 1c04c11147a0e7c9827c02a3c63c2d57e03f47fc92e23f1bf491d128b25f3eb7
MD5 e843924b8ae9fba46e8776f549a074cf
BLAKE2b-256 5dcc054701dccd10c10707c955b10a6fc89d01b898332d9069d113fb01c97c9f

See more details on using hashes here.

File details

Details for the file jaxkern_nightly-0.0.5.dev20240607-py3-none-any.whl.

File metadata

File hashes

Hashes for jaxkern_nightly-0.0.5.dev20240607-py3-none-any.whl
Algorithm Hash digest
SHA256 b2914976490bdadde092d3b518e0b91f075f38993e23c16e9a90242b45433313
MD5 766176d18f4a63914aa4ce4863c45baf
BLAKE2b-256 5dc1be80c4f6e15ad63c972f15640c75d869fe7a8b08af4eecdaf20ee3a65301

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