Prior-Invariant Max-Hellinger Forests For Skew-Insensitive Classification of Rare Events

Abstract

Severely imbalanced binary learning breaks down when class counts, boundary overlap, label corruption and probability error are treated as a single problem. This paper addresses the thesis objective of designing a Max-Hellinger node criterion, demonstrating its class-prior invariance for fixed branch-conditionals, and characterizing a bounded bagged forest constructed from this criterion. The PI-MHF framework incorporates class-conditional branch normalization, Max-Hellinger split selection, bounded recursive induction, bootstrap probability averaging, and calibration-only decision selection. Three algorithms define the architecture, and three propositions characterize bounded or invariant behavior under explicit finite-support assumptions. A seeded controlled experiment employs 10,000-observation Gaussian-mixture profiles at imbalance ratios of 10, 30, and 100, increasing overlap, training-label corruption (as recorded), clean held-out targets, and repeated seeds. PI-MHF achieves minority recall 0.746, MCC 0.374, and average precision 0.486 in the severe profile, and 0.531, 0.220, and 0.261 in the extreme profile. Comparator methods are superior on some endpoints, so the evidence supports a conditional mechanism claim, not a claim of universal superiority. The results show when the objective mechanism is helpful, where its safeguards retain information, and which failure modes need to be evaluated with recorded data.