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This paper studies the fundamental problem of learning energy-based model(EBM) in the latent space of the generator model. Learning such prior modeltypically requires running costly Markov Chain Monte Carlo (MCMC). Instead, wepropose to use noise contrastive estimation (NCE) to discriminatively learn theEBM through density ratio estimation between the latent prior density andlatent posterior density. However, the NCE typically fails to accuratelyestimate such density ratio given large gap between two densities. Toeffectively tackle this issue and learn more expressive prior models, wedevelop the adaptive multi-stage density ratio estimation which breaks theestimation into multiple stages and learn different stages of density ratiosequentially and adaptively. The latent prior model can be gradually learnedusing ratio estimated in previous stage so that the final latent space EBMprior can be naturally formed by product of ratios in different stages. Theproposed method enables informative and much sharper prior than existingbaselines, and can be trained efficiently. Our experiments demonstrate strongperformances in image generation and reconstruction as well as anomalydetection.

Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model