{"paper":{"title":"PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression","license":"http://creativecommons.org/licenses/by/4.0/","headline":"PolySHAP shows that the paired sampling heuristic in KernelSHAP produces exactly the same Shapley approximations as fitting a second-degree polynomial.","cross_cats":["cs.LG"],"primary_cat":"cs.AI","authors_text":"Christopher Musco, Fabian Fumagalli, R. Teal Witter","submitted_at":"2026-01-26T15:47:45Z","abstract_excerpt":"Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has emerged as a leading method for avoiding this exponential cost. KernelSHAP approximates Shapley values by approximating the game as a linear function, which is fit using a small number of game evaluations for random feature subsets.\n  In this work, we extend KernelSHAP by approximating the game via higher degree polynomials, which capture non-linear interactions "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that paired sampling outputs exactly the same Shapley value approximations as second-order PolySHAP, without ever fitting a degree 2 polynomial. To the best of our knowledge, this finding provides the first strong theoretical justification for the excellent practical performance of the paired sampling heuristic.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the underlying cooperative game value function admits a useful low-degree polynomial approximation under the sampling distribution used for KernelSHAP-style estimation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"PolySHAP approximates Shapley values via polynomial regression and proves paired sampling equals its quadratic version, providing the first theoretical justification for that heuristic.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"PolySHAP shows that the paired sampling heuristic in KernelSHAP produces exactly the same Shapley approximations as fitting a second-degree polynomial.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3b87e386a29c35b620689411f500761762e7b57e6d20dea2032b05a1c53eb9a0"},"source":{"id":"2601.18608","kind":"arxiv","version":3},"verdict":{"id":"a598b375-7a5d-4235-aaac-0e4905a637bc","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:14:21.184479Z","strongest_claim":"We prove that paired sampling outputs exactly the same Shapley value approximations as second-order PolySHAP, without ever fitting a degree 2 polynomial. To the best of our knowledge, this finding provides the first strong theoretical justification for the excellent practical performance of the paired sampling heuristic.","one_line_summary":"PolySHAP approximates Shapley values via polynomial regression and proves paired sampling equals its quadratic version, providing the first theoretical justification for that heuristic.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the underlying cooperative game value function admits a useful low-degree polynomial approximation under the sampling distribution used for KernelSHAP-style estimation.","pith_extraction_headline":"PolySHAP shows that the paired sampling heuristic in KernelSHAP produces exactly the same Shapley approximations as fitting a second-degree polynomial."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8020b9188bd46df9dc350218c84d4e15f64dad05abd3b817cdb8bb828bff3a14"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}