{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KFEHW7MIZMHWSC7OVZWXCWCKBN","short_pith_number":"pith:KFEHW7MI","schema_version":"1.0","canonical_sha256":"51487b7d88cb0f690beeae6d71584a0b7338c2a682cf5eddb7d8d43b81d7fd4a","source":{"kind":"arxiv","id":"1108.4324","version":3},"attestation_state":"computed","paper":{"title":"Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Bernard Henri Fleury, Carles Navarro Manch\\'on, Dmitriy Shutin, Mihai-Alin Badiu, Niels Lovmand Pedersen","submitted_at":"2011-08-22T14:12:11Z","abstract_excerpt":"In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters "},"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":"1108.4324","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2011-08-22T14:12:11Z","cross_cats_sorted":[],"title_canon_sha256":"18bdfeaf499bb4f3dd5d7b00d229146837e107d95bb848ce1c276717c3782f91","abstract_canon_sha256":"e908ee9d2bbf5f2712acb0ea18d91f64df065e4407a6e7c42a8f1f97a35fed15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:59.346973Z","signature_b64":"DAj31Bpo4FHja5kFNBs3UnKouLw8UsNjMiwBBn8eiJrmcVvbrmqlNguIBodE+JkXA2ty/rCWG11qM8/2IpfnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51487b7d88cb0f690beeae6d71584a0b7338c2a682cf5eddb7d8d43b81d7fd4a","last_reissued_at":"2026-05-18T01:59:59.346354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:59.346354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Bernard Henri Fleury, Carles Navarro Manch\\'on, Dmitriy Shutin, Mihai-Alin Badiu, Niels Lovmand Pedersen","submitted_at":"2011-08-22T14:12:11Z","abstract_excerpt":"In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4324","kind":"arxiv","version":3},"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":"1108.4324","created_at":"2026-05-18T01:59:59.346441+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.4324v3","created_at":"2026-05-18T01:59:59.346441+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4324","created_at":"2026-05-18T01:59:59.346441+00:00"},{"alias_kind":"pith_short_12","alias_value":"KFEHW7MIZMHW","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"KFEHW7MIZMHWSC7O","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"KFEHW7MI","created_at":"2026-05-18T12:26:32.869790+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/KFEHW7MIZMHWSC7OVZWXCWCKBN","json":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN.json","graph_json":"https://pith.science/api/pith-number/KFEHW7MIZMHWSC7OVZWXCWCKBN/graph.json","events_json":"https://pith.science/api/pith-number/KFEHW7MIZMHWSC7OVZWXCWCKBN/events.json","paper":"https://pith.science/paper/KFEHW7MI"},"agent_actions":{"view_html":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN","download_json":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN.json","view_paper":"https://pith.science/paper/KFEHW7MI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.4324&json=true","fetch_graph":"https://pith.science/api/pith-number/KFEHW7MIZMHWSC7OVZWXCWCKBN/graph.json","fetch_events":"https://pith.science/api/pith-number/KFEHW7MIZMHWSC7OVZWXCWCKBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN/action/storage_attestation","attest_author":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN/action/author_attestation","sign_citation":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN/action/citation_signature","submit_replication":"https://pith.science/pith/KFEHW7MIZMHWSC7OVZWXCWCKBN/action/replication_record"}},"created_at":"2026-05-18T01:59:59.346441+00:00","updated_at":"2026-05-18T01:59:59.346441+00:00"}