Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model
This addresses the challenge of efficient latent space modeling for generative tasks, though it is incremental as it builds on noise contrastive estimation.
The paper tackles the problem of learning energy-based models in latent spaces without costly MCMC by proposing adaptive multi-stage density ratio estimation, resulting in a more informative and sharper prior that improves image generation, reconstruction, and anomaly detection.
This paper studies the fundamental problem of learning energy-based model (EBM) in the latent space of the generator model. Learning such prior model typically requires running costly Markov Chain Monte Carlo (MCMC). Instead, we propose to use noise contrastive estimation (NCE) to discriminatively learn the EBM through density ratio estimation between the latent prior density and latent posterior density. However, the NCE typically fails to accurately estimate such density ratio given large gap between two densities. To effectively tackle this issue and learn more expressive prior models, we develop the adaptive multi-stage density ratio estimation which breaks the estimation into multiple stages and learn different stages of density ratio sequentially and adaptively. The latent prior model can be gradually learned using ratio estimated in previous stage so that the final latent space EBM prior can be naturally formed by product of ratios in different stages. The proposed method enables informative and much sharper prior than existing baselines, and can be trained efficiently. Our experiments demonstrate strong performances in image generation and reconstruction as well as anomaly detection.