  In this article, we study feature attributions of Machine Learning (ML)
models originating from linear game values and coalitional values defined as
operators on appropriate functional spaces. The main focus is on random games
based on the conditional and marginal expectations. The first part of our work
formulates a stability theory for these explanation operators by establishing
certain bounds for both marginal and conditional explanations. The differences
between the two games are then elucidated, such as showing that the marginal
explanations can become discontinuous on some naturally-designed domains, while
the conditional explanations remain stable. In the second part of our work,
group explanation methodologies are devised based on game values with coalition
structure, where the features are grouped based on dependencies. We show
analytically that grouping features this way has a stabilizing effect on the
marginal operator on both group and individual levels, and allows for the
unification of marginal and conditional explanations. Our results are verified
in a number of numerical experiments where an information-theoretic measure of
dependence is used for grouping.
