Model Criticism in Latent Space
This provides a tool for researchers and practitioners using latent variable models to better diagnose model fit, though it is incremental as it adapts existing criticism ideas to a specific model class.
The paper tackles model criticism for latent variable models by performing assessments in the latent space rather than in data space, enabling more direct evaluation of prior and likelihood assumptions. It demonstrates the method on factor analysis, linear dynamical systems, and Gaussian processes.
Model criticism is usually carried out by assessing if replicated data generated under the fitted model looks similar to the observed data, see e.g. Gelman, Carlin, Stern, and Rubin [2004, p. 165]. This paper presents a method for latent variable models by pulling back the data into the space of latent variables, and carrying out model criticism in that space. Making use of a model's structure enables a more direct assessment of the assumptions made in the prior and likelihood. We demonstrate the method with examples of model criticism in latent space applied to factor analysis, linear dynamical systems and Gaussian processes.