sigkerax 0.0.1

Signature kernel computations via PDE solvers in JAX

Sigkerax

Sigkerax is a JAX library for signature kernels.

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Features include:

• Custom static kernels (at time of writing only linear and RBF kernels are implemented);
• All the benefits of working with JAX: autodiff, autoparallelism, GPU/TPU support etc.

Installation

pip install sigkerax

Requires Python 3.8+, JAX 0.4.11+.

Documentation

Coming soon...

Quick example

Lineax can solve a least squares problem with an explicit matrix operator:

import jax
import jax.numpy as jnp
from sigkerax.static_kernels import linear_kernel
from sigkerax.solver import FiniteDifferenceSolver
from sigkerax.sigkernel import SigKernel

static_kernel = lambda x, y: linear_kernel(x, y, scale=1.0)
pde_solver = FiniteDifferenceSolver(static_kernel=static_kernel)
signature_kernel = SigKernel(pde_solver=pde_solver, ds=1e-3, dt=1e-3, add_time=False)

batch_dim1, batch_dim2, length1, length2, channels = 20, 50, 100, 200, 10
key1, key2 = jax.random.split(jax.random.PRNGKey(0))
first_batch_paths = jax.random.normal(key1, shape=(batch_dim1, length1, channels)).cumsum(axis=1)
second_batch_paths = jax.random.normal(key2, shape=(batch_dim2, length2, channels)).cumsum(axis=1)
sigker_matrix = signature_kernel.kernel_matrix(first_batch_paths, second_batch_paths)

Other signature libraries in JAX

Signax: signatures.