Contrastive Predictive Coding Done Right for Mutual Information Estimation
This work addresses a foundational issue in machine learning for researchers using mutual information estimation, but it is incremental as it modifies an existing method without broad practical impact.
The paper tackled the problem of using InfoNCE for mutual information estimation by showing it is not a valid estimator and introducing InfoNCE-anchor, a modified version that reduces bias and achieves more accurate MI estimates, though it does not improve downstream task performance in representation learning.
The InfoNCE objective, originally introduced for contrastive representation learning, has become a popular choice for mutual information (MI) estimation, despite its indirect connection to MI. In this paper, we demonstrate why InfoNCE should not be regarded as a valid MI estimator, and we introduce a simple modification, which we refer to as InfoNCE-anchor, for accurate MI estimation. Our modification introduces an auxiliary anchor class, enabling consistent density ratio estimation and yielding a plug-in MI estimator with significantly reduced bias. Beyond this, we generalize our framework using proper scoring rules, which recover InfoNCE-anchor as a special case when the log score is employed. This formulation unifies a broad spectrum of contrastive objectives, including NCE, InfoNCE, and $f$-divergence variants, under a single principled framework. Empirically, we find that InfoNCE-anchor with the log score achieves the most accurate MI estimates; however, in self-supervised representation learning experiments, we find that the anchor does not improve the downstream task performance. These findings corroborate that contrastive representation learning benefits not from accurate MI estimation per se, but from the learning of structured density ratios.