2020/10/05 by Ruizhi Liao, Daniel Moyer, Liao, Ruizhi +5 · 2 citations
Computer Science · #Adversarial Robustness in Machine Learning #Anomaly Detection Techniques and Applications #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2010.01766
openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual information. Although showing promise for this difficult problem, the variational methods have been theoretically and empirically proven to have serious statistical limitations: 1) many methods struggle to produce accurate estimates when the underlying mutual information is either low or high; 2) the resulting estimators may suffer from high variance. Our approach is based on training a classifier that provides the probability that a data sample pair is drawn from the joint distribution rather than from the product of its marginal distributions. Moreover, we establish a direct connection between mutual information and the average log odds estimate produced by the classifier on a test set, leading to a simple and accurate estimator of mutual information. We show theoretically that our method and other variational approaches are equivalent when they achieve their optimum, while our method sidesteps the variational bound. Empirical results demonstrate high accuracy of our approach and the advantages of our estimator in the context of representation learning. Our demo is available at https://github.com/RayRuizhiLiao/demimiestimator.