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In recent years, many Machine Learning (ML) explanation techniques have beendesigned using ideas from cooperative game theory. These game-theoreticexplainers suffer from high complexity, hindering their exact computation inpractical settings. In our work, we focus on a wide class of linear gamevalues, as well as coalitional values, for the marginal game based on a givenML model and predictor vector. By viewing these explainers as expectations overappropriate sample spaces, we design a novel Monte Carlo sampling algorithmthat estimates them at a reduced complexity that depends linearly on the sizeof the background dataset. We set up a rigorous framework for the statisticalanalysis and obtain error bounds for our sampling methods. The advantage ofthis approach is that it is fast, easily implementable, and model-agnostic.Furthermore, it has similar statistical accuracy as other known estimationtechniques that are more complex and model-specific. We provide rigorous proofsof statistical convergence, as well as numerical experiments whose resultsagree with our theoretical findings.

Approximation of group explainers with coalition structure using Monte Carlo sampling on the product space of coalitions and features