{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:B3B7Q5CVCBJK4SWPJYD4VHY5NV","short_pith_number":"pith:B3B7Q5CV","schema_version":"1.0","canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","source":{"kind":"arxiv","id":"1905.12091","version":1},"attestation_state":"computed","paper":{"title":"Approximate Guarantees for Dictionary Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Aditya Bhaskara, Wai Ming Tai","submitted_at":"2019-05-28T21:11:27Z","abstract_excerpt":"In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\\mathbb{R}^d$), and the goal is to find a \"basis\" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \\times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \\ll n$), and $Y$ has columns that are $k$-sparse (typically $k \\ll d$). Most of the known theor"},"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":"1905.12091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T21:11:27Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3621e1aef4b49d24321735faf41f1bfec48029cafb084bda4328266300533b49","abstract_canon_sha256":"933a1b5052bbe6f9256704cd424d2a9a0a4f10d00817ecf37a732614f7d71069"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:48.988496Z","signature_b64":"GKBNiN/t+kxN15FFQEXyhJRufR5UouXffUu7Nf3XrPL9nD7mpNCNl4fX/tZ13o4gzk2UNwuQQ03VoueVFjpaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","last_reissued_at":"2026-05-17T23:44:48.987839Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:48.987839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Guarantees for Dictionary Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Aditya Bhaskara, Wai Ming Tai","submitted_at":"2019-05-28T21:11:27Z","abstract_excerpt":"In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\\mathbb{R}^d$), and the goal is to find a \"basis\" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \\times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \\ll n$), and $Y$ has columns that are $k$-sparse (typically $k \\ll d$). Most of the known theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12091","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":"1905.12091","created_at":"2026-05-17T23:44:48.987925+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12091v1","created_at":"2026-05-17T23:44:48.987925+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12091","created_at":"2026-05-17T23:44:48.987925+00:00"},{"alias_kind":"pith_short_12","alias_value":"B3B7Q5CVCBJK","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"B3B7Q5CVCBJK4SWP","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"B3B7Q5CV","created_at":"2026-05-18T12:33:12.712433+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/B3B7Q5CVCBJK4SWPJYD4VHY5NV","json":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV.json","graph_json":"https://pith.science/api/pith-number/B3B7Q5CVCBJK4SWPJYD4VHY5NV/graph.json","events_json":"https://pith.science/api/pith-number/B3B7Q5CVCBJK4SWPJYD4VHY5NV/events.json","paper":"https://pith.science/paper/B3B7Q5CV"},"agent_actions":{"view_html":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV","download_json":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV.json","view_paper":"https://pith.science/paper/B3B7Q5CV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12091&json=true","fetch_graph":"https://pith.science/api/pith-number/B3B7Q5CVCBJK4SWPJYD4VHY5NV/graph.json","fetch_events":"https://pith.science/api/pith-number/B3B7Q5CVCBJK4SWPJYD4VHY5NV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/action/storage_attestation","attest_author":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/action/author_attestation","sign_citation":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/action/citation_signature","submit_replication":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/action/replication_record"}},"created_at":"2026-05-17T23:44:48.987925+00:00","updated_at":"2026-05-17T23:44:48.987925+00:00"}