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Auto-Encoding Variational Bayes

2013/12/20 by Diederik P. Kingma, Diederik P Kingma, Max Welling +2 · 3 voices · 15,631 citations
Computer Science · Mathematics · #Algorithm #Applied mathematics #Approximate inference #Artificial intelligence #Bayes' theorem #Bayesian Methods and Mixture Models #Bayesian inference #Bayesian probability #Computer science #Differentiable function #Estimator #Gaussian Processes and Bayesian Inference #Inference #Latent variable #Machine Learning and Algorithms #Mathematics #Posterior probability #Probabilistic logic #Statistics #Upper and lower bounds

paper · pdf · open access · doi:10.48550/arxiv.1312.6114

published in UvA-DARE (University of Amsterdam) (University of Amsterdam)

openalex publication_date 2013/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

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