FMMI: Flow Matching Mutual Information Estimation

We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that transforms one into the other. This technique produces a computationally efficient and precise MI estimate that scales well to high dimensions and across a wide range of ground-truth MI values.

Curse of Slicing: Why Sliced Mutual Information is a Deceptive Measure of Statistical Dependence

Sliced Mutual Information (SMI) is widely used as a scalable alternative to mutual information for measuring non-linear statistical dependence. Despite its advantages, such as faster convergence, robustness to high dimensionality, and nullification only under statistical independence, we demonstrate that SMI is highly susceptible to data manipulation and exhibits counterintuitive behavior. Through extensive benchmarking and theoretical analysis, we show that SMI saturates easily, fails to detect increases in statistical dependence (even under linear transformations designed to enhance the extraction of information), prioritizes redundancy over informative content, and in some cases, performs worse than simpler dependence measures like the correlation coefficient.