On the connection between Noise-Contrastive Estimation and Contrastive Divergence
Paper in proceeding, 2024

Noise-contrastive estimation (NCE) is a popular method for estimating unnormalised probabilistic models, such as energy-based models, which are effective for modelling complex data distributions. Unlike classical maximum likelihood (ML) estimation that relies on importance sampling (resulting in ML-IS) or MCMC (resulting in contrastive divergence, CD), NCE uses a proxy criterion to avoid the need for evaluating an often intractable normalisation constant. Despite apparent conceptual differences, we show that two NCE criteria, ranking NCE (RNCE) and conditional NCE (CNCE), can be viewed as ML estimation methods. Specifically, RNCE is equivalent to ML estimation combined with conditional importance sampling, and both RNCE and CNCE are special cases of CD. These findings bridge the gap between the two method classes and allow us to apply techniques from the ML-IS and CD literature to NCE, offering several advantageous extensions.

Author

Amanda Olmin

Linköping University

Jakob Lindqvist

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering

Lennart Svensson

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering

F. Lindsten

Linköping University

Proceedings of the 38th Conference on Uncertainty in Artificial Intelligence, UAI 2022

26403498 (eISSN)

Vol. 238 3016-3024

27th International Conference on Artificial Intelligence and Statistics, AISTATS 2024
Valencia, Spain,

Subject Categories

Electrical Engineering, Electronic Engineering, Information Engineering

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Latest update

6/10/2024