A Kernel Stein Test of Goodness of Fit for Sequential Models

Jerome Baum, Heishiro Kanagawa, Arthur Gretton
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:1936-1953, 2023.

Abstract

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-baum23a, title = {A Kernel Stein Test of Goodness of Fit for Sequential Models}, author = {Baum, Jerome and Kanagawa, Heishiro and Gretton, Arthur}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {1936--1953}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/baum23a/baum23a.pdf}, url = {https://proceedings.mlr.press/v202/baum23a.html}, abstract = {We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.} }
Endnote
%0 Conference Paper %T A Kernel Stein Test of Goodness of Fit for Sequential Models %A Jerome Baum %A Heishiro Kanagawa %A Arthur Gretton %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-baum23a %I PMLR %P 1936--1953 %U https://proceedings.mlr.press/v202/baum23a.html %V 202 %X We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.
APA
Baum, J., Kanagawa, H. & Gretton, A.. (2023). A Kernel Stein Test of Goodness of Fit for Sequential Models. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:1936-1953 Available from https://proceedings.mlr.press/v202/baum23a.html.

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