Accelerating NCE Convergence with Adaptive Normalizing Constant Computation

Anish Sevekari, Rishal Aggarwal, Maria Chikina, David Koes

Keywords: Noise Contraastive Estimation, Density Estimation, Partition function Estimation, Bennett Acceptance Ration, Generative Modelling

TL;DR: Compute the optimal value of the partition function at each gradient descent step of NCE to obtain better performance.

Abstract: Noise Contrastive Estimation (NCE) is a widely used method for training generative models, typically used as an alternative to Maximum Likelihood Estimation (MLE) when exact computations of probability are hard. NCE trains generative models by discriminating between data and appropriately chosen noise distributions. Although NCE is statistically consistent, it suffers from slow convergence and high variance when there is small overlap between the noise and data distributions. Both these problems are related to the flatness of the NCE loss landscape. We propose an innovative approach to circumvent slow convergence rates by quick inference of the optimal normalizing constant at every gradient step. This allows the rest of the parameters to have more freedom during NCE optimization. We analyze the use of both binary search and the Bennett Acceptance Ratio (BAR) for quick computation of the normalizing constant and show improved performance for both methods on convex and non-convex settings.

Submission Number: 126