Min-Marginal Power Indices for Multi-Objective Feature Selection

Game-theoretic feature selection scores each feature by its average marginal contribution across coalitions. An average shows whether a feature helps overall, but not whether, in some coalition, adding it turns an acceptable model into an unacceptable one. Building on minimum marginal aggregation, we define the Min-Marginal Power Index (MinPI) on a binary utility-threshold game. For a fixed quota, MinPI takes the value -1, 0, or +1 and labels each feature harmful, neutral, or decisive. A harmful label carries its own evidence, an evaluated coalition in which adding the feature drops utility below the quota, so no score cutoff is needed; finite-budget estimators keep this property but may miss harmful features. We use MinPI to propose feature removals, which are accepted only if they pass a validation gate, and to prefilter multi-objective search. On six benchmark datasets over five seeds, MinPI removed 12.5% of analyzed features with almost no loss of held-out utility. On Madelon and Abalone, where it removed the most, its removals cost far less held-out utility than random removals of the same size. Prefiltering increased the dataset-averaged hypervolume of multi-objective search in all five seeds. MinPI is therefore a conservative feature-deletion step whose gains are largest where the data contain many removable features.