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Identifiability of deep generative models without auxiliary information
Bohdan Kivva · Goutham Rajendran · Pradeep Ravikumar · Bryon Aragam

Tue Dec 06 09:00 AM -- 11:00 AM (PST) @
We prove identifiability of a broad class of deep latent variable models that (a) have universal approximation capabilities and (b) are the decoders of variational autoencoders that are commonly used in practice. Unlike existing work, our analysis does not require weak supervision, auxiliary information, or conditioning in the latent space. Specifically, we show that for a broad class of generative (i.e. unsupervised) models with universal approximation capabilities, the side information $u$ is not necessary: We prove identifiability of the entire generative model where we do not observe $u$ and only observe the data $x$. The models we consider match autoencoder architectures used in practice that leverage mixture priors in the latent space and ReLU/leaky-ReLU activations in the encoder, such as VaDE and MFC-VAE. Our main result is an identifiability hierarchy that significantly generalizes previous work and exposes how different assumptions lead to different ``strengths'' of identifiability, and includes certain ``vanilla'' VAEs with isotropic Gaussian priors as a special case. For example, our weakest result establishes (unsupervised) identifiability up to an affine transformation, and thus partially resolves an open problem regarding model identifiability raised in prior work. These theoretical results are augmented with experiments on both simulated and real data.

Author Information

Bohdan Kivva (University of Chicago)
Goutham Rajendran (CS @ University of Chicago --> ML @ Carnegie Mellon University)

I obtained my CS PhD from UChicago. Recently, I've been actively working on causal representation learning and generative models. Some of my recent side projects were on NeRF (Computer vision) and Automatic Speech Recognition. I also have extensive competitive programming experience and a track publication record.

Pradeep Ravikumar (Carnegie Mellon University)
Bryon Aragam (University of Chicago)

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