Bayesian brain theory suggests that the brain employs generative models to understand the external world.

Weexamine GenerativeAdversarial Networks(GANs) through thelensofdeep Energy Based Models (EBMs), with the goal of exploiting the density model that follows from this formulation.

This paper studies the fundamental learning problem of the energy-based model (EBM).

Neural Information Processing Systems http://nips.cc/

Weshowthatthelearned model exhibits strong performances interms ofimage and text generation and anomaly detection.The one-pagecode can be found in supplementarymaterials.

Toeffectively tackle this issue and learn more expressiveprior models, wedevelop theadaptivemulti-stage density ratio estimation which breaks the estimation into multiple stages and learn different stages ofdensity ratiosequentially andadaptively. Thelatent priormodel canbe gradually learned using ratio estimated in previous stage so that the final latent spaceEBMpriorcanbenaturally formed byproduct ofratiosindifferentstages. The proposed method enables informativeand much sharper prior than existing baselines, and can be trained efficiently.

Neural transport augmented sampling, firstintroduced byParnoandMarzouk (2018),isageneral method for using normalizing flows to sample from a given densityπ. Thus, samples can be generated fromπ(θ)by running MCMC chain in theZ-space and pushing these samples onto theΘ-space usingT. Neural transport augmented samplers havebeen subsequently extended by Hoffman etal. In this paper, we proposed equivariant Stein variational gradient descent algorithm for sampling fromdensities thatareinvarianttosymmetry transformations. Another contributionofourworkis subsequently using this equivariant sampling method to efficiently train equivariant energy based models forprobabilistic modeling andinference.