sigcoeff

Sparse Signature Coefficient Recovery via Kernels

This package provides an example implementation for computing deep coefficients of the path signature transform using signature kernels on both CPU and GPU, to accompany the paper Sparse Signature Coefficient Recovery via Kernels. This method allows for parallelised computation of coefficients, with a time complexity independent of their depth.

Installation

pip install git+https://github.com/daniil-shmelev/sigcoeff.git

How to use the package

To run the below, see ./examples/example_usage.py

import torch
import sigcoeff

torch.manual_seed(42)

# Underlying path
len_x = 1000
dim = 10
X = torch.rand((len_x, dim), device="cpu")

# Target multi-index
multi_index = [1, 5, 2, 6, 3]

# Algorithm parameters
M = 2
dyadic_order = 3

#############################################
# Serial CPU computation
#############################################
coeff = sigcoeff.coeff(X, multi_index, scaling_depth=M, dyadic_order=dyadic_order, parallel=False)

#############################################
# Parallel CPU computation
#############################################
coeff = sigcoeff.coeff(X, multi_index, scaling_depth=M, dyadic_order=dyadic_order, parallel=True)

#############################################
# Parallel GPU computation
#############################################
coeff = sigcoeff.coeff(X.cuda(), multi_index, scaling_depth=M, dyadic_order=dyadic_order)

#############################################
# Varying dyadic orders for the two dimensions of the PDE grid
#############################################
coeff = sigcoeff.coeff(X.cuda(), multi_index, scaling_depth=M, dyadic_order=(3, 2))

#############################################
# Extraction of the entire grid of coefficients. I.e. all coefficients given by multi_index[:i],
# evaluated at all time points up to len_x. (CUDA only)
#############################################
coeff_grid = sigcoeff.coeff(X.cuda(), multi_index, scaling_depth=M, dyadic_order=dyadic_order, full=True)

Citation

@article{shmelev2024sparsesig,
  title={Sparse Signature Coefficient Recovery via Kernels},
  author={Shmelev, Daniil and Cristopher, Salvi},
  journal={arXiv preprint arXiv:2412.08579},
  year={2024}
}