PyRKHSstats

A Python package implementing a variety of statistical/machine learning methods that rely on kernels (e.g. HSIC for independence testing).

Overview

• Independence testing with HSIC (Hilbert-Schmidt Independence Criterion), as introduced in A Kernel Statistical Test of Independence, A. Gretton, K. Fukumizu, C. Hui Teo, L. Song, B. Schölkopf, and A. Smola (NIPS 2007).
• Measurement of conditional independence with HSCIC (Hilbert-Schmidt Conditional Independence Criterion), as introduced in A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings, J. Park and K. Muandet (NeurIPS 2020).
• The Kernel-based Conditional Independence Test (KCIT), as introduced in Kernel-based Conditional Independence Test and Application in Causal Discovery, K. Zhang, J. Peters, D. Janzing, B. Schölkopf (UAI 2011).
• Two-sample testing (also known as homogeneity testing) with the MMD (Maximum Mean Discrepancy), as presented in A Fast, Consistent Kernel Two-Sample Test, A. Gretton, K. Fukumizu, Z. Harchaoui, and B. K. Sriperumbudur (NIPS 2009) and in A Kernel Two-Sample Test, A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. Smola (JMLR, volume 13, 2012).

Implementations available

The following table details the implementation schemes for the different resources available in the package.

In development

• Joint independence testing with dHSIC.
• Goodness-of-fit testing.
• Methods for time series models.
• Bayesian statistical kernel methods.
• Regression by independence maximisation.