CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information

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Authors Lawrence Carin, Shuyang Dai, Weituo Hao, Zhe Gan, Pengyu Cheng, Jiachang Liu
Journal/Conference Name ICML 2020 1
Paper Category
Paper Abstract 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
Date of publication 2020
Code Programming Language Jupyter Notebook

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