Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit
This work addresses the need for better non-parametric goodness-of-fit tests for unnormalized distributions, particularly in complex scenarios like truncated distributions or compositional data, and is incremental as it builds on existing KSD methods.
The paper tackles the problem of improving kernel Stein discrepancy (KSD) tests for goodness-of-fit by proposing a unifying framework called standardisation-function KSD (Sf-KSD) to study different Stein operators, showing that it controls type-I error well and achieves higher test power than existing approaches.
Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works focused on studying kernel choices to boost test performances. However, the choices of (non-unique) Stein operators also have considerable effect on the test performances. Inspired by the standardisation technique that was originally developed to better derive approximation properties for normal distributions, we present a unifying framework, called standardisation-function kernel Stein discrepancy (Sf-KSD), to study different Stein operators in KSD-based tests for goodness-of-fit. We derive explicitly how the proposed framework relates to existing KSD-based tests and show that Sf-KSD can be used as a guide to develop novel kernel-based non-parametric tests on complex data scenarios, e.g. truncated distributions or compositional data. Experimental results demonstrate that the proposed tests control type-I error well and achieve higher test power than existing approaches.