On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models

by   Erik Nijkamp, et al.

This study investigates the effects Markov Chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. In general, we find that the majority of techniques used to stabilize training in previous studies can the opposite effect. Stable ML learning with a ConvNet potential can be achieved with only a few hyper-parameters and no regularization. With this minimal framework, we identify a variety of ML learning outcomes depending on the implementation of MCMC sampling. On one hand, we show that it is easy to train an energy-based model which can sample realistic images with short-run Langevin. ML can be effective and stable even when MCMC samples have much higher energy than true steady-state samples throughout training. Based on this insight, we introduce an ML method with noise initialization for MCMC, high-quality short-run synthesis, and the same budget as ML with informative MCMC initialization such as CD or PCD. Unlike previous models, this model can obtain realistic high-diversity samples from a noise signal after training with no auxiliary models. On the other hand, models learned with highly non-convergent MCMC do not have a valid steady-state and cannot be considered approximate unnormalized densities of the training data because long-run MCMC samples differ greatly from the data. We show that it is much harder to train an energy-based model where long-run and steady-state MCMC samples have realistic appearance. To our knowledge, long-run MCMC samples of all previous models result in unrealistic images. With correct tuning of Langevin noise, we train the first models for which long-run and steady-state MCMC samples are realistic images.


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