Indeterminacy in Generative Models: Characterization and Strong Identifiability
This addresses the need for strongly identifiable models in applications requiring unique latent representations, offering a foundational advance in probabilistic generative modeling.
The paper tackles the problem of indeterminacy in generative models by developing a theoretical framework to characterize and achieve strong identifiability, where each observation corresponds to a unique latent code, and demonstrates this is possible with flexible nonlinear generators through two examples.
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.