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Indeterminacy in latent variable models : characterization and strong identifiability Xi, Quanhan


Latent variable models posit that an unobserved, or latent, set of variables describe the statistical properties of the observed data. The inferential goal is to recover the unobserved values, which can then be used for a variety of down-stream tasks. Recently, generative models, which attempt learn a deterministic mapping (the generator) from the latent to observed variables, have become popular for a variety of applications. However, arbitrarily different latent values may give rise to the same dataset especially in modern non-linear models, an issue known as latent variable indeterminacy. In the presence of indeterminacy, many scientific problems which generative models aim to solve become ill-defined. In this thesis, we develop a mathematical framework to analyze the indeterminacies of a wide range of generative models by framing it as a special type of statistical identifiability. By doing so, we unify existing model-specific derivations from various corners of the diverse literature on identifiability in latent variable models. Using our framework, we also derive conditions to eliminate indeterminacies completely while maintaining the flexibility of modern methods. Using these conditions, we are able to target precisely the sources of indeterminacy to derive novel results on the weak and strong identifiability of popular generative models, and variations thereof.

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