On the coalitional decomposition of parameters of interest

TL;DR

This paper develops conditions for unambiguous, interpretable decompositions of parameters like variance in black-box models with probabilistic inputs, improving upon existing methods under weaker assumptions.

Contribution

It introduces generalized conditions for decomposing parameters of interest, enabling clearer interpretation and recovering known decompositions with fewer assumptions.

Findings

Provides conditions for unambiguous decompositions

Enables recovery of known decompositions under weaker assumptions

Improves interpretability of parameter contributions

Abstract

Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs). In this paper, we produce conditions for obtaining unambiguous and interpretable decompositions of very general parameters of interest. This allows to recover known decompositions, holding under weaker assumptions than stated in the literature.