{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OWUXPKKUQPZ5NVMOLB24NGAZAS","short_pith_number":"pith:OWUXPKKU","schema_version":"1.0","canonical_sha256":"75a977a95483f3d6d58e5875c6981904b416c7bd04c4d3df350704d3b19cdd96","source":{"kind":"arxiv","id":"1608.05749","version":1},"attestation_state":"computed","paper":{"title":"Solving a Mixture of Many Random Linear Equations by Tensor Decomposition and Alternating Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Constantine Caramanis, Sujay Sanghavi, Xinyang Yi","submitted_at":"2016-08-19T22:10:46Z","abstract_excerpt":"We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample corresponds to which model) are not observed. We give a tractable algorithm for the mixed linear equation problem, and show that under some technical conditions, our algorithm is guaranteed to solve the problem exactly with sample complexity linear in the dimension, and polynomial in $k$, the number of components. Previous approaches have requir"},"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":"1608.05749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-19T22:10:46Z","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"3d03503fdba4c398aeff57974e07b77cac3e00dbcf94a0b38941699fc2ed8ace","abstract_canon_sha256":"67a4b96bfe15e81aa9e6d3d14acb6f438258f50bdb8cae90d5739fc502650704"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:23.333119Z","signature_b64":"PYiOLQMvFkE5AJZUHibaTrINKXlfSPk4YXnAaGOlpLRKeBQ/JEEwNyE/NKL1kjq6osQwChfkc8f5G15MtLHyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75a977a95483f3d6d58e5875c6981904b416c7bd04c4d3df350704d3b19cdd96","last_reissued_at":"2026-05-18T01:08:23.332511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:23.332511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving a Mixture of Many Random Linear Equations by Tensor Decomposition and Alternating Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Constantine Caramanis, Sujay Sanghavi, Xinyang Yi","submitted_at":"2016-08-19T22:10:46Z","abstract_excerpt":"We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample corresponds to which model) are not observed. We give a tractable algorithm for the mixed linear equation problem, and show that under some technical conditions, our algorithm is guaranteed to solve the problem exactly with sample complexity linear in the dimension, and polynomial in $k$, the number of components. Previous approaches have requir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05749","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":""},"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":"1608.05749","created_at":"2026-05-18T01:08:23.332597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.05749v1","created_at":"2026-05-18T01:08:23.332597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05749","created_at":"2026-05-18T01:08:23.332597+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWUXPKKUQPZ5","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWUXPKKUQPZ5NVMO","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWUXPKKU","created_at":"2026-05-18T12:30:36.002864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.06959","citing_title":"Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05842","citing_title":"Expectation Maximization (EM) Converges for General Agnostic Mixtures","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS","json":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS.json","graph_json":"https://pith.science/api/pith-number/OWUXPKKUQPZ5NVMOLB24NGAZAS/graph.json","events_json":"https://pith.science/api/pith-number/OWUXPKKUQPZ5NVMOLB24NGAZAS/events.json","paper":"https://pith.science/paper/OWUXPKKU"},"agent_actions":{"view_html":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS","download_json":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS.json","view_paper":"https://pith.science/paper/OWUXPKKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.05749&json=true","fetch_graph":"https://pith.science/api/pith-number/OWUXPKKUQPZ5NVMOLB24NGAZAS/graph.json","fetch_events":"https://pith.science/api/pith-number/OWUXPKKUQPZ5NVMOLB24NGAZAS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS/action/storage_attestation","attest_author":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS/action/author_attestation","sign_citation":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS/action/citation_signature","submit_replication":"https://pith.science/pith/OWUXPKKUQPZ5NVMOLB24NGAZAS/action/replication_record"}},"created_at":"2026-05-18T01:08:23.332597+00:00","updated_at":"2026-05-18T01:08:23.332597+00:00"}