Advances in computing have enabled us to develop increasingly complex statistical models. However, their complexity poses challenges in their evaluation. The central theme of the thesis is addressing intractability and interpretability in model evaluations. The key tools considered in the thesis are kernel and Stein’s methods: Kernel methods provide flexible means of specifying features for comparing models, and Stein’s method further allows us to incorporate model structures in evaluation.

The first part of the thesis addresses the question of intractability. The focus is on latent variable models, a large class of models used in practice, including factor models, topic models for text, and hidden Markov models. The kernel Stein discrepancy (KSD), a kernel-based discrepancy, is extended to deal with this model class. Based on this extension, a statistical hypothesis test of relative goodness of fit is developed, enabling us to compare competing latent variable models that are known up to normalization.

The second part of the thesis concerns the question of interpretability with two contributed works. First, interpretable relative goodness-of-fit tests are developed using kernel-based discrepancies developed in Chwialkowski et al. (2015); Jitkrittum et al. (2016); Jitkrittum et al. (2017). These tests allow the user to choose features for comparison and discover aspects distinguishing two models. Second, a convergence property of the KSD is established. Specifically, the KSD is shown to control an integral probability metric defined by a class of polynomially growing continuous functions. In particular, this development allows us to evaluate both unnormalized statistical models and sample approximations to posterior distributions in terms of moments.