{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:2MZXWXBXTHUBGY575UPEKBP5CR","short_pith_number":"pith:2MZXWXBX","schema_version":"1.0","canonical_sha256":"d3337b5c3799e81363bfed1e4505fd1450f68a4a419821a3ee7e7b4014739307","source":{"kind":"arxiv","id":"2303.06992","version":1},"attestation_state":"computed","paper":{"title":"Improving Mutual Information Estimation with Annealed and Energy-Based Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alireza Makhzani, Greg Ver Steeg, Marzyeh Ghassemi, Rob Brekelmans, Roger Grosse, Sicong Huang","submitted_at":"2023-03-13T10:47:24Z","abstract_excerpt":"Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves estimating a potentially high-dimensional log partition function. In this work, we present a unifying view of existing MI bounds from the perspective of importance sampling, and propose three novel bounds based on this approach. Since accurate estimation of MI without density information requires a sample size exponential in the true MI, we assume either 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":"2303.06992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-13T10:47:24Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d4c811518eb2daf876fb1c5554f02192cf7d852de9cf3e879d72b4ba7949039d","abstract_canon_sha256":"a2f86e00e4d91d83bebb141ebb51dfd9f5ec824d144b85fe6085ef97306af2ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:12:13.460322Z","signature_b64":"3h2YoWLwEerlyacAlWbX5jSjE5JzW0Dtkc9mAg76wEQsEnrK8yMdEd9Vzna/YTjqoWi6SWzJUa/0x2+sfw7SCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3337b5c3799e81363bfed1e4505fd1450f68a4a419821a3ee7e7b4014739307","last_reissued_at":"2026-07-05T08:12:13.459904Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:12:13.459904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improving Mutual Information Estimation with Annealed and Energy-Based Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alireza Makhzani, Greg Ver Steeg, Marzyeh Ghassemi, Rob Brekelmans, Roger Grosse, Sicong Huang","submitted_at":"2023-03-13T10:47:24Z","abstract_excerpt":"Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves estimating a potentially high-dimensional log partition function. In this work, we present a unifying view of existing MI bounds from the perspective of importance sampling, and propose three novel bounds based on this approach. Since accurate estimation of MI without density information requires a sample size exponential in the true MI, we assume either a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06992","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/2303.06992/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":"2303.06992","created_at":"2026-07-05T08:12:13.459957+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.06992v1","created_at":"2026-07-05T08:12:13.459957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06992","created_at":"2026-07-05T08:12:13.459957+00:00"},{"alias_kind":"pith_short_12","alias_value":"2MZXWXBXTHUB","created_at":"2026-07-05T08:12:13.459957+00:00"},{"alias_kind":"pith_short_16","alias_value":"2MZXWXBXTHUBGY57","created_at":"2026-07-05T08:12:13.459957+00:00"},{"alias_kind":"pith_short_8","alias_value":"2MZXWXBX","created_at":"2026-07-05T08:12:13.459957+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/2MZXWXBXTHUBGY575UPEKBP5CR","json":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR.json","graph_json":"https://pith.science/api/pith-number/2MZXWXBXTHUBGY575UPEKBP5CR/graph.json","events_json":"https://pith.science/api/pith-number/2MZXWXBXTHUBGY575UPEKBP5CR/events.json","paper":"https://pith.science/paper/2MZXWXBX"},"agent_actions":{"view_html":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR","download_json":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR.json","view_paper":"https://pith.science/paper/2MZXWXBX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.06992&json=true","fetch_graph":"https://pith.science/api/pith-number/2MZXWXBXTHUBGY575UPEKBP5CR/graph.json","fetch_events":"https://pith.science/api/pith-number/2MZXWXBXTHUBGY575UPEKBP5CR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR/action/storage_attestation","attest_author":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR/action/author_attestation","sign_citation":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR/action/citation_signature","submit_replication":"https://pith.science/pith/2MZXWXBXTHUBGY575UPEKBP5CR/action/replication_record"}},"created_at":"2026-07-05T08:12:13.459957+00:00","updated_at":"2026-07-05T08:12:13.459957+00:00"}