Invited Talk - Arthur Gretton: Relative goodness-of-fit tests for models with latent variables.

I will describe a nonparametric, kernel-based test to assess the relative goodness of fit of latent variable models with intractable unnormalized densities. The test generalises the kernel Stein discrepancy (KSD) tests of (Liu et al., 2016, Chwialkowski et al., 2016, Yang et al., 2018, Jitkrittum et al., 2018) which require exact access to unnormalized densities. We will rely on the simple idea of using an approximate observed-variable marginal in place of the exact, intractable one. As the main theoretical contribution, the new test has a well-controlled type-I error, once we have properly corrected the threshold. In the case of models with low-dimensional latent structure and high-dimensional observations, our test significantly outperforms the relative maximum mean discrepancy test, which cannot exploit the latent structure.