{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6CASU6QV6HOOD7GDU6YK2LO6U2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b1f69f622e4322360d22d30979e47d1b268c32432f45fb8f10e1a74b142ce62b","cross_cats_sorted":["cs.DS","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-08T18:06:32Z","title_canon_sha256":"70eeb1e2705e0dd88de94529333eb6ffa6abdcc09505af38b66f95d2734b4086"},"schema_version":"1.0","source":{"id":"2102.04401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.04401","created_at":"2026-07-05T02:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"2102.04401v1","created_at":"2026-07-05T02:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.04401","created_at":"2026-07-05T02:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"6CASU6QV6HOO","created_at":"2026-07-05T02:13:32Z"},{"alias_kind":"pith_short_16","alias_value":"6CASU6QV6HOOD7GD","created_at":"2026-07-05T02:13:32Z"},{"alias_kind":"pith_short_8","alias_value":"6CASU6QV","created_at":"2026-07-05T02:13:32Z"}],"graph_snapshots":[{"event_id":"sha256:9ff3bc712d6cb355d3334131ee9c026abbef62d65c87d2374e73806fa6761eeb","target":"graph","created_at":"2026-07-05T02:13:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.04401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of agnostic learning under the Gaussian distribution. We develop a method for finding hard families of examples for a wide class of problems by using LP duality. For Boolean-valued concept classes, we show that the $L^1$-regression algorithm is essentially best possible, and therefore that the computational difficulty of agnostically learning a concept class is closely related to the polynomial degree required to approximate any function from the class in $L^1$-norm. Using this characterization along with additional analytic tools, we obtain optimal SQ lower bounds for agn","authors_text":"Daniel M. Kane, Ilias Diakonikolas, Nikos Zarifis, Thanasis Pittas","cross_cats":["cs.DS","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-08T18:06:32Z","title":"The Optimality of Polynomial Regression for Agnostic Learning under Gaussian Marginals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.04401","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:79efc0a5254a3e57cbab128bb44c3c7968645852935eab4b9dc0bf4e1892655f","target":"record","created_at":"2026-07-05T02:13:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b1f69f622e4322360d22d30979e47d1b268c32432f45fb8f10e1a74b142ce62b","cross_cats_sorted":["cs.DS","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-08T18:06:32Z","title_canon_sha256":"70eeb1e2705e0dd88de94529333eb6ffa6abdcc09505af38b66f95d2734b4086"},"schema_version":"1.0","source":{"id":"2102.04401","kind":"arxiv","version":1}},"canonical_sha256":"f0812a7a15f1dce1fcc3a7b0ad2ddea6839ae23880c3067b036a54b36d26a461","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0812a7a15f1dce1fcc3a7b0ad2ddea6839ae23880c3067b036a54b36d26a461","first_computed_at":"2026-07-05T02:13:32.892639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:13:32.892639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gFFgO3fh3fLXh9EEmSQG+7FZV+1nKiVGEf08unw3qZ2Hf9nWwJw4u3pMTFpQWKA97yf2Erd8jW69QB1km+DhCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:13:32.893086Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.04401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79efc0a5254a3e57cbab128bb44c3c7968645852935eab4b9dc0bf4e1892655f","sha256:9ff3bc712d6cb355d3334131ee9c026abbef62d65c87d2374e73806fa6761eeb"],"state_sha256":"f85c950766c5704e049d3db33015399486f2ec78fefc16d7e3d56df459d29d69"}