Axiomatic Characterization of Data-Driven Influence Measures for
  Classification
  We study the following problem: given a labeled dataset and a specific
datapoint x, how did the i-th feature influence the classification for x? We
identify a family of numerical influence measures - functions that, given a
datapoint x, assign a numeric value phi_i(x) to every feature i, corresponding
to how altering i's value would influence the outcome for x. 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.
