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arXiv · 2210.00189

Pitfalls of Gaussians as a noise distribution in NCE

Holden Lee·Chirag Pabbaraju·Anish Sevekari·Andrej Risteski
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Abstract

Noise Contrastive Estimation (NCE) is a popular approach for learning probability density functions parameterized up to a constant of proportionality. The main idea is to design a classification problem for distinguishing training data from samples from an easy-to-sample noise distribution $q$, in a manner that avoids having to calculate a partition function. It is well-known that the choice of $q$ can severely impact the computational and statistical efficiency of NCE. In practice, a common choice for $q$ is a Gaussian which matches the mean and covariance of the data. In this paper, we show that such a choice can result in an exponentially bad (in the ambient dimension) conditioning of the Hessian of the loss, even for very simple data distributions. As a consequence, both the statistical and algorithmic complexity for such a choice of $q$ will be problematic in practice, suggesting that more complex noise distributions are essential to the success of NCE.

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Holden Lee, Chirag Pabbaraju, Anish Sevekari, Andrej Risteski. 2022-10-01. Pitfalls of Gaussians as a noise distribution in NCE. https://arxiv.org/abs/2210.00189

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