A kernel Stein test of goodness of fit for sequential models

We propose a goodness-of-fit measure for probability densities modelling 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 unnormalised densities. Existing KSDs require the model to be defined on a fixed-dimension space. As our major contributions, 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 normalised, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.