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Exact algorithms are known for unweighted KNN and for weighted KNN classification, but weighted KNN regression and soft-label prediction have resisted: the only exact method is an O(N^K) brute force, exponential in neighborhood size K. The obstruction: the weighted regression prediction is a ratio of two coalition-dependent sums, whose normalization denominator breaks the additive, threshold, and duplication structures the prior polynomial algorithms rely on. We close this gap. We give (i) the first pseudo-polynomial-time exact algorithm (polynomial in N and K at fixed lattice precision) for weighted KNN-regression Data Shapley, a counting dynamic program over the joint integer state (sum of w, s","title":"Exact and Certified Data Shapley for Weighted k-Nearest-Neighbor Regression and Soft-Label Prediction","url":"https://arxiv.org/abs/2607.11956","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.11956v1 Announce Type: cross \nAbstract: Data Shapley is the standard principled answer to which training points are worth what, and its k-nearest-neighbor (KNN) specialization is the version deployed in practice: the exact estimator shipped by toolkits such as pyDVL and OpenDataVal. Exact algorithms are known for unweighted KNN and for weighted KNN classification, but weighted KNN regression and soft-label prediction have resisted: the only exact method is an O(N^K) brute force, exponential in neighborhood size K. The obstruction: the weighted regression prediction is a ratio of two coalition-dependent sums, whose normalization denominator breaks the additive, threshold, and duplication structures the prior polynomial algorithms rely on. We close this gap. We give (i) the first pseudo-polynomial-time exact algorithm (polynomial in N and K at fixed lattice precision) for weighted KNN-regression Data Shapley, a counting dynamic program over the joint integer state (sum of w, s","title":"Exact and Certified Data Shapley for Weighted k-Nearest-Neighbor Regression and Soft-Label Prediction","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-15T04:44:03Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.11956"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:2fb3f2cffe1a433c01cce782ecd866e7992cfa70489d139ca24ee979a92f09b36f7c77107b9ef87aeded4bdbb67b6afa77ae9b5a8132a05983e8c8fad8ef9700","signer":"crovia.substrate","subject":{"observed_at":"2026-07-15T04:44:03Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.11956"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"85038ce1f231fd411aa60d0dd876316a6ff1114d764d87d86f90949104dc8a7a","leaf_index":316433,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"59c7ea41095042140e6a2f5bc25026a21fa3e71ae08973c1fcfdb5daebe89173","side":"left"},{"sibling":"b6bd09aeb0137e6b7f6f568cf9d805c33cc3514f8dea8be1fdd55a84de9354c2","side":"right"},{"sibling":"0bb069a931a010bd55f12bb98df9c3bc285aec7652500aa3c04fffc113e50936","side":"right"},{"sibling":"b0cc3bfef8972d1ffb2224e09a3eb595912d3d8eed43aa12ec0fbb3b1a1d50a1","side":"right"},{"sibling":"b28aaa2b8e3806e84380dfadb9c1a88a893c37e5d6f06ca9e13f3ece16110533","side":"left"},{"sibling":"3ea7a19ff8b61cc6962de915bdc45e55b7d3dffeff00132f56e415325dda195c","side":"right"},{"sibling":"7ea54d26dd378975e8412c96c63f11ce7eb04515c5676061d25695229e6c6c97","side":"right"},{"sibling":"c07de1952926cdb34af34c5c0baaf9021a0ab704be6665431e37a7c145fca4d5","side":"right"},{"sibling":"1c7f1bf97993e3a126824f8350788b168c4c13264fb03a73b3ede312035d3527","side":"right"},{"sibling":"84a7590e6b24dd07ed46597f19deb75d9ad247b4227b17f30857ec7cc0fc5c21","side":"right"},{"sibling":"c8d3d8cb0183b912107f9781ad2a1b6c0c9424906c5907c09deeb5bea9d7b571","side":"left"},{"sibling":"0cb62c0ada57a2406a6bcb100889d3e8b29a15efeed07adaff5bb90a5e80612a","side":"right"},{"sibling":"0b69289b25462ddd6166f6f49004cfc8ada0ab4f10adafe188347817bdd46e37","side":"left"},{"sibling":"1418b281cd985b5ed411ef25f2017a1826cc14919b6fad3934e6ceeec693699b","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"abe4a8c706e530484d1e96a8988cb09eab85928b2050985500ab289753fe3eec","side":"right"},{"sibling":"f436dccf82aa2c1eb7bfa3eb84316e116aaf64dc55cd9592597118f6cb0648f6","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":316730,"merkle_root":"a8e6e5be81ea6f5b5f2227422459bf39455fe9f0b6602b4d1ce6977dbfd78bc7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260715T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-15T05:38:24Z","sig_algorithm":"ed25519","signature":"df1678d268b5a07413e2ca6e748c3f40b6cfedea930a18d843489a4ab513da791bf0a886caab1b918d0989f8ebaaf3d0035ca2aa777913b1ad29979f1deb9a0c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_fadc45f74d2c42ffcde51a09f6cf77536e191751a02de53a3f293fb9346a78da"}}