{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EIUZYMRGB7LN37WOZOMELWM755","short_pith_number":"pith:EIUZYMRG","schema_version":"1.0","canonical_sha256":"22299c32260fd6ddfececb9845d99fef51b8995f6ef05b36abd72782e1c85037","source":{"kind":"arxiv","id":"2607.01895","version":1},"attestation_state":"computed","paper":{"title":"Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Francis Bach (SIERRA)","submitted_at":"2026-07-02T08:46:52Z","abstract_excerpt":"We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix. By affine invariance, the model is written as q $\\sim$ N(0, I), p $\\sim$ N($\\Delta$, I), with linear features, where $\\Delta$ is a mean vector. The variational estimator is the empirical Kullback-Leibler (KL) log-normalized fit with a squared L2-penalty on its nonconstant coefficient, and the spectral estimator recently introduced in [1] replaces a single variational problem by a continuum of ridge-regularized least-squares problems. We derive high-dimensional deterministic a"},"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":"2607.01895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-02T08:46:52Z","cross_cats_sorted":["math.OC","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"fbca1b3a9854ad0124bb3647a92c320e9997dd7269acb5f59294cb594c96d8b0","abstract_canon_sha256":"18d57f0b2038b2653b96302bc563d22effdaccab2f4c1abd70b63d6861d2ceaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:32.764649Z","signature_b64":"CsoEmoknEd4RmDzhMHxH3eiBzUFrb4YGahJc5vwI1tRNMuCpdUw+/2Tanq8GUKmHmXndm0nt+LktIr3qQpCdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22299c32260fd6ddfececb9845d99fef51b8995f6ef05b36abd72782e1c85037","last_reissued_at":"2026-07-03T01:17:32.764263Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:32.764263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.LG","authors_text":"Francis Bach (SIERRA)","submitted_at":"2026-07-02T08:46:52Z","abstract_excerpt":"We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix. By affine invariance, the model is written as q $\\sim$ N(0, I), p $\\sim$ N($\\Delta$, I), with linear features, where $\\Delta$ is a mean vector. The variational estimator is the empirical Kullback-Leibler (KL) log-normalized fit with a squared L2-penalty on its nonconstant coefficient, and the spectral estimator recently introduced in [1] replaces a single variational problem by a continuum of ridge-regularized least-squares problems. We derive high-dimensional deterministic a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01895","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/2607.01895/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":"2607.01895","created_at":"2026-07-03T01:17:32.764321+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.01895v1","created_at":"2026-07-03T01:17:32.764321+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01895","created_at":"2026-07-03T01:17:32.764321+00:00"},{"alias_kind":"pith_short_12","alias_value":"EIUZYMRGB7LN","created_at":"2026-07-03T01:17:32.764321+00:00"},{"alias_kind":"pith_short_16","alias_value":"EIUZYMRGB7LN37WO","created_at":"2026-07-03T01:17:32.764321+00:00"},{"alias_kind":"pith_short_8","alias_value":"EIUZYMRG","created_at":"2026-07-03T01:17:32.764321+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/EIUZYMRGB7LN37WOZOMELWM755","json":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755.json","graph_json":"https://pith.science/api/pith-number/EIUZYMRGB7LN37WOZOMELWM755/graph.json","events_json":"https://pith.science/api/pith-number/EIUZYMRGB7LN37WOZOMELWM755/events.json","paper":"https://pith.science/paper/EIUZYMRG"},"agent_actions":{"view_html":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755","download_json":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755.json","view_paper":"https://pith.science/paper/EIUZYMRG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.01895&json=true","fetch_graph":"https://pith.science/api/pith-number/EIUZYMRGB7LN37WOZOMELWM755/graph.json","fetch_events":"https://pith.science/api/pith-number/EIUZYMRGB7LN37WOZOMELWM755/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755/action/storage_attestation","attest_author":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755/action/author_attestation","sign_citation":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755/action/citation_signature","submit_replication":"https://pith.science/pith/EIUZYMRGB7LN37WOZOMELWM755/action/replication_record"}},"created_at":"2026-07-03T01:17:32.764321+00:00","updated_at":"2026-07-03T01:17:32.764321+00:00"}