We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. The problem arises, for instance, when we would like to blame the change in the revenue of a search advertising campaign to changes in basic statistics such as impressions, clicks, cost-per-click, click-through-rates, etc. (Other applications occur in portfolio analysis and in e-commerce.) In the absence of an obvious way to perform attribution, we take an axiomatic approach. We show that there is a unique attribution method that satisfies three reasonable axioms (Additivity, Affine Scale Invariance and Anonymity) if and only if the characteristic function is multilinear. Happily, many practically relevant characteristic functions are multilinear. We also discuss the computational complexity of implementing the attribution scheme we identified.
Speaker's bio: Mukund Sundararajan is a Research Scientist at Google, Inc. His interests include foundations of market design, market analysis, electronic commerce and privacy. He holds a Ph.D. in Computer Science from Stanford.