Curse of Slicing: Why Sliced Mutual Information is a Deceptive Measure of Statistical Dependence
This work exposes critical flaws in a widely used dependence measure, impacting researchers and practitioners in statistics and machine learning who rely on SMI for scalable analysis.
The paper demonstrates that Sliced Mutual Information (SMI), a scalable measure for non-linear statistical dependence, is deceptive due to susceptibility to data manipulation, saturation, and failure to detect increased dependence, often underperforming simpler measures like correlation.
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.