CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information
This addresses a key bottleneck in machine learning for tasks requiring MI minimization, offering a practical solution with broad applicability, though it builds incrementally on prior work focused on lower bounds.
The paper tackles the challenge of estimating and minimizing mutual information (MI) in high-dimensional spaces with only sample access, proposing a novel Contrastive Log-ratio Upper Bound (CLUB) for MI minimization. It demonstrates effectiveness in simulations and real-world tasks like domain adaptation and information bottleneck, showing reliable estimation and improved performance.
Mutual information (MI) minimization has gained considerable interests in various machine learning tasks. However, estimating and minimizing MI in high-dimensional spaces remains a challenging problem, especially when only samples, rather than distribution forms, are accessible. Previous works mainly focus on MI lower bound approximation, which is not applicable to MI minimization problems. In this paper, we propose a novel Contrastive Log-ratio Upper Bound (CLUB) of mutual information. We provide a theoretical analysis of the properties of CLUB and its variational approximation. Based on this upper bound, we introduce a MI minimization training scheme and further accelerate it with a negative sampling strategy. Simulation studies on Gaussian distributions show the reliable estimation ability of CLUB. Real-world MI minimization experiments, including domain adaptation and information bottleneck, demonstrate the effectiveness of the proposed method. The code is at https://github.com/Linear95/CLUB.