{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:XM4E4JPWZS3R7QNJ6XPDWUTB4N","short_pith_number":"pith:XM4E4JPW","schema_version":"1.0","canonical_sha256":"bb384e25f6ccb71fc1a9f5de3b5261e35407ef03344dc8d3b3884853694571d3","source":{"kind":"arxiv","id":"1909.13384","version":1},"attestation_state":"computed","paper":{"title":"Optimal Sketching for Kronecker Product Regression and Low Rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Huaian Diao, Rajesh Jayaram, Wen Sun, Zhao Song","submitted_at":"2019-09-29T22:24:28Z","abstract_excerpt":"We study the Kronecker product regression problem, in which the design matrix is a Kronecker product of two or more matrices. Given $A_i \\in \\mathbb{R}^{n_i \\times d_i}$ for $i=1,2,\\dots,q$ where $n_i \\gg d_i$ for each $i$, and $b \\in \\mathbb{R}^{n_1 n_2 \\cdots n_q}$, let $\\mathcal{A} = A_1 \\otimes A_2 \\otimes \\cdots \\otimes A_q$. Then for $p \\in [1,2]$, the goal is to find $x \\in \\mathbb{R}^{d_1 \\cdots d_q}$ that approximately minimizes $\\|\\mathcal{A}x - b\\|_p$. Recently, Diao, Song, Sun, and Woodruff (AISTATS, 2018) gave an algorithm which is faster than forming the Kronecker product $\\mathc"},"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":"1909.13384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-09-29T22:24:28Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"72a7cef921ece9721ed0f01928c18945469d171150f0a9c3dbffa87873457b1c","abstract_canon_sha256":"21835be575c1e25da3997b56fa5691d6448f9f545f0762fdc93728dfd5ce292b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:08:09.758531Z","signature_b64":"T2QfgwwS1VE6oMA/sxuxoev/rBNM/9tWxGFzPrZP0NCTG85E7Q694W6T/92UcTM3X1+Y2FRY9SkjbcgblidXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb384e25f6ccb71fc1a9f5de3b5261e35407ef03344dc8d3b3884853694571d3","last_reissued_at":"2026-07-05T00:08:09.758040Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:08:09.758040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Sketching for Kronecker Product Regression and Low Rank Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Huaian Diao, Rajesh Jayaram, Wen Sun, Zhao Song","submitted_at":"2019-09-29T22:24:28Z","abstract_excerpt":"We study the Kronecker product regression problem, in which the design matrix is a Kronecker product of two or more matrices. Given $A_i \\in \\mathbb{R}^{n_i \\times d_i}$ for $i=1,2,\\dots,q$ where $n_i \\gg d_i$ for each $i$, and $b \\in \\mathbb{R}^{n_1 n_2 \\cdots n_q}$, let $\\mathcal{A} = A_1 \\otimes A_2 \\otimes \\cdots \\otimes A_q$. Then for $p \\in [1,2]$, the goal is to find $x \\in \\mathbb{R}^{d_1 \\cdots d_q}$ that approximately minimizes $\\|\\mathcal{A}x - b\\|_p$. Recently, Diao, Song, Sun, and Woodruff (AISTATS, 2018) gave an algorithm which is faster than forming the Kronecker product $\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.13384","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/1909.13384/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":"1909.13384","created_at":"2026-07-05T00:08:09.758099+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.13384v1","created_at":"2026-07-05T00:08:09.758099+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.13384","created_at":"2026-07-05T00:08:09.758099+00:00"},{"alias_kind":"pith_short_12","alias_value":"XM4E4JPWZS3R","created_at":"2026-07-05T00:08:09.758099+00:00"},{"alias_kind":"pith_short_16","alias_value":"XM4E4JPWZS3R7QNJ","created_at":"2026-07-05T00:08:09.758099+00:00"},{"alias_kind":"pith_short_8","alias_value":"XM4E4JPW","created_at":"2026-07-05T00:08:09.758099+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N","json":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N.json","graph_json":"https://pith.science/api/pith-number/XM4E4JPWZS3R7QNJ6XPDWUTB4N/graph.json","events_json":"https://pith.science/api/pith-number/XM4E4JPWZS3R7QNJ6XPDWUTB4N/events.json","paper":"https://pith.science/paper/XM4E4JPW"},"agent_actions":{"view_html":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N","download_json":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N.json","view_paper":"https://pith.science/paper/XM4E4JPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.13384&json=true","fetch_graph":"https://pith.science/api/pith-number/XM4E4JPWZS3R7QNJ6XPDWUTB4N/graph.json","fetch_events":"https://pith.science/api/pith-number/XM4E4JPWZS3R7QNJ6XPDWUTB4N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N/action/storage_attestation","attest_author":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N/action/author_attestation","sign_citation":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N/action/citation_signature","submit_replication":"https://pith.science/pith/XM4E4JPWZS3R7QNJ6XPDWUTB4N/action/replication_record"}},"created_at":"2026-07-05T00:08:09.758099+00:00","updated_at":"2026-07-05T00:08:09.758099+00:00"}