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Refining one's hypotheses in the light of data is a common scientificpractice; however, the dependency on the data introduces selection bias and canlead to specious statistical analysis. An approach for addressing this is viaconditioning on the selection procedure to account for how we have used thedata to generate our hypotheses, and prevent information to be used again afterselection. Many selective inference (a.k.a. post-selection inference)algorithms typically take this approach but will "over-condition" for sake oftractability. While this practice yields well calibrated statistic tests withcontrolled false positive rates (FPR), it can incur a major loss in power. Inour work, we extend two recent proposals for selecting features using theMaximum Mean Discrepancy and Hilbert Schmidt Independence Criterion tocondition on the minimal conditioning event. We show how recent advances inmultiscale bootstrap makes conditioning on the minimal selection event possibleand demonstrate our proposal over a range of synthetic and real worldexperiments. Our results show that our proposed test is indeed more powerful inmost scenarios.

More Powerful Selective Kernel Tests for Feature Selection