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Indeterminacy and Strong Identifiability in Generative Models

Quanhan XiBenjamin Bloem-Reddy
Jun 2022
摘要
Most modern probabilistic generative models, such as the variationalautoencoder (VAE), have certain indeterminacies that are unresolvable even withan infinite amount of data. Different tasks tolerate different indeterminacies,however recent applications have indicated the need for strongly identifiablemodels, in which an observation corresponds to a unique latent code. Progresshas been made towards reducing model indeterminacies while maintainingflexibility, and recent work excludes many--but not all--indeterminacies. Inthis work, we motivate model-identifiability in terms of task-identifiability,then construct a theoretical framework for analyzing the indeterminacies oflatent variable models, which enables their precise characterization in termsof the generator function and prior distribution spaces. We reveal that strongidentifiability is possible even with highly flexible nonlinear generators, andgive two such examples. One is a straightforward modification of iVAE(arXiv:1907.04809 [stat.ML]); the other uses triangular monotonic maps, leadingto novel connections between optimal transport and identifiability.
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