Learning Energy-Based Model with Variational Auto-Encoder as Amortized Sampler

TL;DR

This paper introduces a joint training method combining a variational auto-encoder with an energy-based model to enable efficient sampling and improve maximum likelihood training, leading to high-quality sample generation.

Contribution

It proposes a novel variational MCMC teaching algorithm that jointly trains a VAE and an EBM, enhancing sampling efficiency and model training.

Findings

Generated samples comparable to GANs and EBMs.

Effective for supervised conditional learning tasks.

Provides a new perspective on joint model training.

Abstract

Due to the intractable partition function, training energy-based models (EBMs) by maximum likelihood requires Markov chain Monte Carlo (MCMC) sampling to approximate the gradient of the Kullback-Leibler divergence between data and model distributions. However, it is non-trivial to sample from an EBM because of the difficulty of mixing between modes. In this paper, we propose to learn a variational auto-encoder (VAE) to initialize the finite-step MCMC, such as Langevin dynamics that is derived from the energy function, for efficient amortized sampling of the EBM. With these amortized MCMC samples, the EBM can be trained by maximum likelihood, which follows an "analysis by synthesis" scheme; while the VAE learns from these MCMC samples via variational Bayes. We call this joint training algorithm the variational MCMC teaching, in which the VAE chases the EBM toward data distribution. We interpret the learning algorithm as a dynamic alternating projection in the context of information geometry. Our proposed models can generate samples comparable to GANs and EBMs. Additionally, we demonstrate that our model can learn effective probabilistic distribution toward supervised conditional learning tasks.