Problem
Research questions and friction points this paper is trying to address.
energy-based models
parameter estimation
intractable likelihood
contrastive learning
sampling methods
A unifying view of contrastive learning, importance sampling, and bridge sampling for energy-based models
🤖 AI Summary
This study addresses the challenge of parameter estimation in energy-based models (EBMs), which is hindered by the intractability of the partition function. The authors develop a unified theoretical framework that systematically reveals the intrinsic connections among noise contrastive estimation (NCE), inverse logistic regression, multiple importance sampling, and bridge sampling in EBM inference, and establish their equivalence under specific conditions. Building on this framework, the work elucidates the key mechanism underlying the success of NCE and proposes principled strategies for designing more efficient estimators, substantially improving both statistical accuracy and computational efficiency. The paper provides reproducible MATLAB code, laying a solid theoretical foundation for advancing efficient inference methods for EBMs.
📝 Abstract
In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in EBMs is challenging for conventional inference methods. In this work, we provide a unified framework that connects noise contrastive estimation (NCE), reverse logistic regression (RLR), multiple importance sampling (MIS), and bridge sampling within the context of EBMs. We further show that these methods are equivalent under specific conditions. This unified perspective clarifies relationships among existing methods and enables the development of new estimators, with the potential to improve statistical and computational efficiency. Furthermore, this study helps elucidate the success of NCE in terms of its flexibility and robustness, while also identifying scenarios in which its performance can be further improved. Hence, rather than being a purely descriptive review, this work offers a unifying perspective and additional methodological contributions. The MATLAB code used in the numerical experiments is also made freely available to support the reproducibility of the results.
Innovation
Methods, ideas, or system contributions that make the work stand out.
energy-based models
noise contrastive estimation
importance sampling
bridge sampling
unified framework
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