Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit

Wenkai Xu
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:1575-1597, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-xu22b, title = { Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit }, author = {Xu, Wenkai}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {1575--1597}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/xu22b/xu22b.pdf}, url = {https://proceedings.mlr.press/v151/xu22b.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit %A Wenkai Xu %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-xu22b %I PMLR %P 1575--1597 %U https://proceedings.mlr.press/v151/xu22b.html %V 151 %X 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.
APA
Xu, W.. (2022). Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:1575-1597 Available from https://proceedings.mlr.press/v151/xu22b.html.

Related Material