Model Criticism in Latent Space

TL;DR

This paper introduces a novel approach for model criticism in latent variable models by analyzing data in the latent space, providing a more direct assessment of model assumptions, demonstrated on various models.

Contribution

It proposes a new method for model criticism in latent space, leveraging model structure for improved assumption checking in latent variable models.

Findings

Effective in factor analysis, linear dynamical systems, and Gaussian processes

Enables direct assessment of prior and likelihood assumptions

Improves model validation in latent variable frameworks

Abstract

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.