{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SLF75QKTPBK56E6GGFHJBENHG6","short_pith_number":"pith:SLF75QKT","schema_version":"1.0","canonical_sha256":"92cbfec1537855df13c6314e9091a737b5e3218b9b850715a69649c721456fe3","source":{"kind":"arxiv","id":"1604.03463","version":2},"attestation_state":"computed","paper":{"title":"The Matrix Generalized Inverse Gaussian Distribution: Properties and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Arindam Banerjee, Farideh Fazayeli","submitted_at":"2016-04-12T16:03:31Z","abstract_excerpt":"While the Matrix Generalized Inverse Gaussian ($\\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways of sampling from the distribution have not been carefully studied. In this paper, we show that the $\\mathcal{MGIG}$ is unimodal, and the mode can be obtained by solving an Algebraic Riccati Equation (ARE) equation [7]. Based on the property, we propose an importance sampling method for the $\\mathcal{MGIG}$ where the mode of the proposal distribution matches "},"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":"1604.03463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-04-12T16:03:31Z","cross_cats_sorted":[],"title_canon_sha256":"a68a28dbba03e0dd64a051ca58ff8631448867bb9c0d8b7409aff4de972c7780","abstract_canon_sha256":"26dfdbe78d914ed0ed73848a6bfffad1cb0f4dcb8b2823df36c9b9ec842a7549"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:23.997821Z","signature_b64":"kSE63VxvRbWZTxP2NJAWfIb57H0anopKItsCcfvfDT29koLPPegzUVXLsD797IwSa07Y3xPhAqH4KYiPEAd5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92cbfec1537855df13c6314e9091a737b5e3218b9b850715a69649c721456fe3","last_reissued_at":"2026-05-18T01:08:23.997148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:23.997148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Matrix Generalized Inverse Gaussian Distribution: Properties and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Arindam Banerjee, Farideh Fazayeli","submitted_at":"2016-04-12T16:03:31Z","abstract_excerpt":"While the Matrix Generalized Inverse Gaussian ($\\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways of sampling from the distribution have not been carefully studied. In this paper, we show that the $\\mathcal{MGIG}$ is unimodal, and the mode can be obtained by solving an Algebraic Riccati Equation (ARE) equation [7]. Based on the property, we propose an importance sampling method for the $\\mathcal{MGIG}$ where the mode of the proposal distribution matches "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03463","kind":"arxiv","version":2},"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":"1604.03463","created_at":"2026-05-18T01:08:23.997260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.03463v2","created_at":"2026-05-18T01:08:23.997260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03463","created_at":"2026-05-18T01:08:23.997260+00:00"},{"alias_kind":"pith_short_12","alias_value":"SLF75QKTPBK5","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SLF75QKTPBK56E6G","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SLF75QKT","created_at":"2026-05-18T12:30:44.179134+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/SLF75QKTPBK56E6GGFHJBENHG6","json":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6.json","graph_json":"https://pith.science/api/pith-number/SLF75QKTPBK56E6GGFHJBENHG6/graph.json","events_json":"https://pith.science/api/pith-number/SLF75QKTPBK56E6GGFHJBENHG6/events.json","paper":"https://pith.science/paper/SLF75QKT"},"agent_actions":{"view_html":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6","download_json":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6.json","view_paper":"https://pith.science/paper/SLF75QKT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.03463&json=true","fetch_graph":"https://pith.science/api/pith-number/SLF75QKTPBK56E6GGFHJBENHG6/graph.json","fetch_events":"https://pith.science/api/pith-number/SLF75QKTPBK56E6GGFHJBENHG6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6/action/storage_attestation","attest_author":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6/action/author_attestation","sign_citation":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6/action/citation_signature","submit_replication":"https://pith.science/pith/SLF75QKTPBK56E6GGFHJBENHG6/action/replication_record"}},"created_at":"2026-05-18T01:08:23.997260+00:00","updated_at":"2026-05-18T01:08:23.997260+00:00"}