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Energy Discrepancies: A Score-Independent Loss for Energy-Based Models
Tobias Schröder · Zijing Ou · Jen Lim · Yingzhen Li · Sebastian Vollmer · Andrew Duncan

Tue Dec 12 03:15 PM -- 05:15 PM (PST) @ Great Hall & Hall B1+B2 #527

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that energy discrepancy approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum energy discrepancy estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.

Author Information

Tobias Schröder (Imperial College London)
Zijing Ou (Imperial College London)
Jen Lim (The University of Warwick)
Yingzhen Li (Imperial College London)

Yingzhen Li is a senior researcher at Microsoft Research Cambridge. She received her PhD from the University of Cambridge, and previously she has interned at Disney Research. She is passionate about building reliable machine learning systems, and her approach combines both Bayesian statistics and deep learning. Her contributions to the approximate inference field include: (1) algorithmic advances, such as variational inference with different divergences, combining variational inference with MCMC and approximate inference with implicit distributions; (2) applications of approximate inference, such as uncertainty estimation in Bayesian neural networks and algorithms to train deep generative models. She has served as area chairs at NeurIPS/ICML/ICLR/AISTATS on related research topics, and she is a co-organizer of the AABI2020 symposium, a flagship event of approximate inference.

Sebastian Vollmer (DFKI)
Andrew Duncan (Imperial College London)

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