{"paper":{"title":"Adalina: Adaptive Linear Approximation for the Shapley Value and Beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A linear-space algorithm approximates Shapley values and semi-values with O(n/ε² log(1/δ)) queries while minimizing mean squared error for any utility.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bryan Kian Hsiang Low, Weida Li, Yaoliang Yu","submitted_at":"2026-04-09T16:38:14Z","abstract_excerpt":"The Shapley value, and its broader family of semi-values, has received much attention in various attribution problems. A fundamental and long-standing challenge is their efficient approximation, since exact computation generally requires an exponential number of utility queries in the number of players $n$. To meet the challenges of large-scale applications, we explore the limits of efficiently approximating semi-values under a $\\Theta(n)$ space constraint. Building upon a vector concentration inequality, we establish a theoretical framework that enables sharper query complexities for existing"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our algorithm requires O(n/ε² log(1/δ)) utility queries to ensure P(‖φ̂ - φ‖₂ ≥ ε) ≤ δ for all commonly used semi-values... our algorithm allows explicit minimization of the mean square error for each specific utility function... the first adaptive, linear-time, linear-space randomized algorithm, Adalina, that theoretically achieves improved mean square error.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The framework relies on a vector concentration inequality to derive the query bounds under a Θ(n) space constraint; if this inequality does not apply tightly to the semi-value estimators, the claimed complexities may not hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces Adalina, the first adaptive linear-time linear-space randomized algorithm for semi-value approximation with provable O(n/ε² log(1/δ)) query complexity and explicit MSE minimization.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A linear-space algorithm approximates Shapley values and semi-values with O(n/ε² log(1/δ)) queries while minimizing mean squared error for any utility.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9db8bb4ef4ad8cc365ada60f2b615f6e2a9d3fa5e417f4a809fdee9de7ed670b"},"source":{"id":"2604.08438","kind":"arxiv","version":2},"verdict":{"id":"31e2cd17-38a6-4b6f-adaf-f1867d94ab23","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:33:07.174134Z","strongest_claim":"Our algorithm requires O(n/ε² log(1/δ)) utility queries to ensure P(‖φ̂ - φ‖₂ ≥ ε) ≤ δ for all commonly used semi-values... our algorithm allows explicit minimization of the mean square error for each specific utility function... the first adaptive, linear-time, linear-space randomized algorithm, Adalina, that theoretically achieves improved mean square error.","one_line_summary":"Introduces Adalina, the first adaptive linear-time linear-space randomized algorithm for semi-value approximation with provable O(n/ε² log(1/δ)) query complexity and explicit MSE minimization.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The framework relies on a vector concentration inequality to derive the query bounds under a Θ(n) space constraint; if this inequality does not apply tightly to the semi-value estimators, the claimed complexities may not hold.","pith_extraction_headline":"A linear-space algorithm approximates Shapley values and semi-values with O(n/ε² log(1/δ)) queries while minimizing mean squared error for any utility."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.08438/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"cd1c453c5550d309211a649a1a515afd899c700c0c8f7dd1bb3875a4c21fa07c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}