A Characterization of Monotone Influence Measures for Data Classification

In this work we focus on the following question: how important was the i-th feature in determining the outcome for a given datapoint? We identify a family of influence measures; functions that, given a datapoint x, assign a value phi_i(x) to every feature i, which roughly corresponds to that i's importance in determining the outcome for x. This family is uniquely derived from a set of axioms: desirable properties that any reasonable influence measure should satisfy. Departing from prior work on influence measures, we assume no knowledge of - or access to - the underlying classifier labelling the dataset. In other words, our influence measures are based on the dataset alone, and do not make any queries to the classifier. While this requirement naturally limits the scope of explanations we provide, we show that it is effective on real datasets.