Noise-contrastive estimation: A new estimation principle for unnormalized statistical models

M. Gutmann, A. Hyvärinen

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We present a new estimation principle for parameterized statistical models. The idea is to perform nonlinear logistic regression to discriminate between the observed data and some artificially generated noise, using the model log-density function in the regression nonlinearity. We show that this leads to a consistent (convergent) estimator of the parameters, and analyze the asymptotic variance. In particular, the method is shown to directly work for unnormalized models, i.e. models where the density function does not integrate to one. The normalization constant can be estimated just like any other parameter. For a tractable ICA model, we compare the method with other estimation methods that can be used to learn unnormalized models, including score matching, contrastive divergence, and maximum-likelihood where the normalization constant is estimated with importance sampling. Simulations show that noise-contrastive estimation offers the best trade-off between computational and statistical efficiency. The method is then applied to the modeling of natural images: We show that the method can successfully estimate a large-scale two-layer model and a Markov random field.
Original languageEnglish
Title of host publication Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS)
EditorsY.W. Teh, M. Titterington
PublisherJournal of Machine Learning Research - Proceedings Track
Number of pages8
Publication statusPublished - 2010

Publication series



Dive into the research topics of 'Noise-contrastive estimation: A new estimation principle for unnormalized statistical models'. Together they form a unique fingerprint.

Cite this