Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains

• URL: http://arxiv.org/abs/2010.01845v2
• Date: Wed, 2 Jun 2021 15:37:29 GMT
• Title: Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains
• Authors: Francisco J. R. Ruiz, Michalis K. Titsias, Taylan Cemgil, Arnaud Doucet
• Abstract summary: The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture. We develop a training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.
• Score: 34.77971292478243
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is challenging since the computation of the marginal likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a ML training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We obtain the estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and with finite variance. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.

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