Baume, Jerome; Kanagawa, Heishiro; Gretton, Arthur; (2023) A Kernel Stein Test of Goodness of Fit for Sequential Models. In: Proceedings of the International Conference on Machine Learning. ICML Proceedings (In press).

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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 variabledimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-offit 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.

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