SigPDE

SigPDE is a Python package for efficient computation of the untruncated signature kernel by solving a Goursat PDE outlined in the paper The Signature Kernel is the solution of a Goursat PDE

The package also includes implementations of the robust, untruncated signature kernel as outlined in the paper Signature moments to characterize laws of stochastic processes.

Currently, only GPU PyTorch implementations are available.

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How to Use the Package

import torch
import sigpde.torch as sig

# Parameters
batch_size = 30
length = 50
dim = 30
dyadic_order = 2

# Sample data on GPU
x = torch.randn((batch_size, length, dim), device='cuda')
y = torch.randn((batch_size, length, dim), device='cuda')

# Define kernels
static_kernel = sig.kernels.LinearKernel()
kernel = sig.SigPDE(static_kernel, dyadic_order)
robust_kernel = sig.RobustSigPDE(static_kernel, dyadic_order)

# Pairwise computation
kernel.pairwise(x, y)
kernel.pairwise(x)

robust_kernel.pairwise(x, y)
robust_kernel.pairwise(x)

# Gram matrix computation
kernel.gram(x, y)
kernel.gram(x)

robust_kernel.gram(x)
robust_kernel.gram(x, y)

# Compute normalization factors with the robust kernel
robust_kernel.normalization(x)

# Custom normalization function
# Default is: 2 - 1 / (1 + log(x))
# Must satisfy: f(x) <= x for all x >= 1
def my_normalizer(x):
    return 2 - 1 / x.pow(0.1)

# Pairwise computation with custom normalizer
robust_kernel.pairwise(x, normalizer=my_normalizer)

References

1. Salvi et al., 2021 - "The Signature Kernel Is the Solution of a Goursat PDE"
2. Chevyrev & Oberhauser, 2022 - "Signature moments to characterize laws of stochastic processes"