Indeterminacy in Generative Models: Characterization and Strong Identifiability

TL;DR

This paper develops a theoretical framework to analyze indeterminacies in generative models, demonstrating that strong identifiability is achievable with flexible nonlinear generators, and introduces novel methods for ensuring unique latent representations.

Contribution

It provides a formal analysis of model indeterminacies, characterizes conditions for strong identifiability, and proposes new models that achieve this property with flexible generators.

Findings

Strong identifiability is possible with nonlinear generators.

Two models demonstrating strong identifiability are introduced.

Connections between optimal transport and identifiability are established.

Abstract

Most modern probabilistic generative models, such as the variational autoencoder (VAE), have certain indeterminacies that are unresolvable even with an infinite amount of data. Different tasks tolerate different indeterminacies, however recent applications have indicated the need for strongly identifiable models, in which an observation corresponds to a unique latent code. Progress has been made towards reducing model indeterminacies while maintaining flexibility, and recent work excludes many--but not all--indeterminacies. In this work, we motivate model-identifiability in terms of task-identifiability, then construct a theoretical framework for analyzing the indeterminacies of latent variable models, which enables their precise characterization in terms of the generator function and prior distribution spaces. We reveal that strong identifiability is possible even with highly flexible nonlinear generators, and give two such examples. One is a straightforward modification of iVAE (arXiv:1907.04809 [stat.ML]); the other uses triangular monotonic maps, leading to novel connections between optimal transport and identifiability.