{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:7RKCKGSHUHFPRVC4RGTBURYTZO","short_pith_number":"pith:7RKCKGSH","schema_version":"1.0","canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","source":{"kind":"arxiv","id":"2110.14779","version":1},"attestation_state":"computed","paper":{"title":"Spectrahedral Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ML","stat.TH"],"primary_cat":"math.OC","authors_text":"Eliza O'Reilly, Venkat Chandrasekaran","submitted_at":"2021-10-27T21:21:19Z","abstract_excerpt":"Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data, i.e. a function that is the maximum eigenvalue of an affine matrix expression of the input. This method represents a significant generalization of polyhedral (also called max-affine) regression, in which a polyhedral function (a maximum of a fixed number of affine functions) is fit to the data. We prove bounds on how well spectrahedral functions can approxima"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2110.14779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-10-27T21:21:19Z","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"title_canon_sha256":"fb89c8c18eab2a4157c16b3e53182601ef8e0d7e67d4b00c3d68abc8b84f7204","abstract_canon_sha256":"22b77025e684ee28483cfb63e750a8e6720bd8ed2c4a8f481591834444b79fda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:27:06.284728Z","signature_b64":"WyhtQUzgkbpkeYJ484VjUpaRrV5q7FKn8gipeT/6Fhyxj90R8IAouGRuzYpz3zczByy9sFRkGbRf4y0cWus1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","last_reissued_at":"2026-07-05T03:27:06.284276Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:27:06.284276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectrahedral Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ML","stat.TH"],"primary_cat":"math.OC","authors_text":"Eliza O'Reilly, Venkat Chandrasekaran","submitted_at":"2021-10-27T21:21:19Z","abstract_excerpt":"Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data, i.e. a function that is the maximum eigenvalue of an affine matrix expression of the input. This method represents a significant generalization of polyhedral (also called max-affine) regression, in which a polyhedral function (a maximum of a fixed number of affine functions) is fit to the data. We prove bounds on how well spectrahedral functions can approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14779","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14779/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2110.14779","created_at":"2026-07-05T03:27:06.284338+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.14779v1","created_at":"2026-07-05T03:27:06.284338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14779","created_at":"2026-07-05T03:27:06.284338+00:00"},{"alias_kind":"pith_short_12","alias_value":"7RKCKGSHUHFP","created_at":"2026-07-05T03:27:06.284338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7RKCKGSHUHFPRVC4","created_at":"2026-07-05T03:27:06.284338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7RKCKGSH","created_at":"2026-07-05T03:27:06.284338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07694","citing_title":"Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity","ref_index":73,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO","json":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO.json","graph_json":"https://pith.science/api/pith-number/7RKCKGSHUHFPRVC4RGTBURYTZO/graph.json","events_json":"https://pith.science/api/pith-number/7RKCKGSHUHFPRVC4RGTBURYTZO/events.json","paper":"https://pith.science/paper/7RKCKGSH"},"agent_actions":{"view_html":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO","download_json":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO.json","view_paper":"https://pith.science/paper/7RKCKGSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.14779&json=true","fetch_graph":"https://pith.science/api/pith-number/7RKCKGSHUHFPRVC4RGTBURYTZO/graph.json","fetch_events":"https://pith.science/api/pith-number/7RKCKGSHUHFPRVC4RGTBURYTZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/action/storage_attestation","attest_author":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/action/author_attestation","sign_citation":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/action/citation_signature","submit_replication":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/action/replication_record"}},"created_at":"2026-07-05T03:27:06.284338+00:00","updated_at":"2026-07-05T03:27:06.284338+00:00"}