An association measure for mixed-type variables

What the math gives to ML

The paper constructs a label-permutation-invariant association statistic between a real-valued variable and a nominal categorical variable by comparing conditional class-probability concentration with its marginal baseline. The transferable asset is not the asymptotic testing machinery itself, but the use of posterior vectors g(x) rather than arbitrary integer category encodings, together with invariance to category relabeling and monotone transformations of the scalar. A practical neural adaptation is an auxiliary regularizer that rewards a scalar bottleneck, score, or routing coordinate for retaining categorical information without imposing an artificial ordering on category IDs. This is most promising for representation learning and interpretable scalar bottlenecks, rather than as a replacement for standard supervised cross-entropy.