Axiomatic Characterization of Data-Driven Influence Measures for Classification

We study the following problem: given a labeled dataset and a specific datapoint (x) over right arrow, how did the i-th feature influence the classification for (x) over right arrow? We identify a family of numerical influence measures - functions that, given a datapoint assign a numeric value phi(i)((x) over right arrow) to every feature i, corresponding to how altering i's value would influence the outcome for (x) over right arrow. This family, which we term monotone influence measures (MIM), is uniquely derived from a set of desirable properties, or axioms. The MIM family constitutes a provably sound methodology for measuring feature influence in classification domains; the values generated by MIM are based on the dataset alone, and do not make any queries to the classifier. While this requirement naturally limits the scope of our framework, we demonstrate its effectiveness on data.