Learning Neural Random Fields with Inclusive Auxiliary Generators

Neural random fields (NRFs), which are defined by using neural networks to implement potential functions in undirected models (sometimes known as energy-based models), provide an interesting family of model spaces for machine learning, besides various directed models such as generative adversarial networks (GANs). In this paper we propose a new approach, the inclusive-NRF approach, to learning NRFs for continuous data (e.g. images), by developing inclusive-divergence minimized auxiliary generators and stochastic gradient sampling. As demonstrations of how the new approach can be flexibly and effectively used, specific inclusive-NRF models are developed and thoroughly evaluated for a number of tasks - unsupervised/supervised image generation, semi-supervised classification and anomaly detection. The proposed models consistently achieve strong experimental results in all these tasks compared to state-of-the-art methods. Remarkably, in addition to superior sample generation, one fundamental additional benefit of our inclusive-NRF approach is that, unlike GANs, it directly provides (unnormalized) density estimate for sample evaluation. With these contributions and results, this paper significantly advances the learning and applications of undirected models to a new level, both theoretically and empirically, which have never been obtained before.