Axiomatic Characterization of Data-Driven Influence Measures for Classification
This provides a theoretical framework for feature influence analysis in classification, though it is incremental as it builds on existing axiomatic approaches with a focus on data-driven methods.
The paper tackles the problem of quantifying how individual features influence classification outcomes for specific datapoints, introducing a family of monotone influence measures (MIM) derived from axioms, which are provably sound and data-driven without querying the classifier.
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.