Learning Energy-Based Model with Variational Auto-Encoder as Amortized Sampler
This work addresses the challenge of efficient sampling for training energy-based models, which is a foundational problem in generative modeling for the machine learning community. It offers an incremental improvement to existing EBM training methodologies.
This paper tackles the problem of training energy-based models (EBMs) by addressing the difficulty of sampling from them due to intractable partition functions and mode mixing. The authors propose using a variational auto-encoder (VAE) to initialize finite-step MCMC, enabling efficient amortized sampling for EBM training. The resulting model generates samples comparable to GANs and EBMs and learns effective probabilistic distributions for supervised conditional learning tasks.
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.