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We propose a goodness-of-fit measure for probability densities modelingobservations with varying dimensionality, such as text documents of differinglengths or variable-length sequences. The proposed measure is an instance ofthe kernel Stein discrepancy (KSD), which has been used to constructgoodness-of-fit tests for unnormalized densities. The KSD is defined by itsStein operator: current operators used in testing apply to fixed-dimensionalspaces. As our main contribution, we extend the KSD to the variable-dimensionsetting by identifying appropriate Stein operators, and propose a novel KSDgoodness-of-fit test. As with the previous variants, the proposed KSD does notrequire the density to be normalized, allowing the evaluation of a large classof models. Our test is shown to perform well in practice on discrete sequentialdata benchmarks.

A kernel Stein test of goodness of fit for sequential models