{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:M5KNOUPW3SK5LHBUNEN2IBJ5O2","short_pith_number":"pith:M5KNOUPW","schema_version":"1.0","canonical_sha256":"6754d751f6dc95d59c34691ba4053d76a5d351a447550fb91206b7f62d67936c","source":{"kind":"arxiv","id":"2605.30055","version":1},"attestation_state":"computed","paper":{"title":"The Wasserstein cost of Importance Sampling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Michael Goldman, Simon Coste","submitted_at":"2026-05-28T15:07:45Z","abstract_excerpt":"Importance sampling (IS) consists in biasing samples from a distribution $f$ towards another distribution $g$. Concretely, given samples $X_i$ from $f$, the IS measure is $$\\hat{g}_n = \\frac{1}{Z_n}\\sum_{i=1}^n \\frac{g(X_i)}{f(X_i)} \\delta_{X_i},$$ with $Z_n = \\sum_{i=1}^n \\frac{g(X_i)}{f(X_i)}$. The random measure $\\hat{g}_n$ approximates $g$, and is used in many contexts ranging from Monte Carlo integration to Bayesian inference. We show that, in high dimension ($d \\geqslant 3$), the Wasserstein cost $W_p^p(\\hat{g}_n, g)$ has order $n^{-p/d}$ in expectation, i.e.\n  $$\\beta^{\\mathrm{low}}_{p,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.30055","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-28T15:07:45Z","cross_cats_sorted":["math.FA","math.ST","stat.TH"],"title_canon_sha256":"69bfa485ec0273b1040316d11cb1f737e4c7b376ca065658b55c316da8b4c5c2","abstract_canon_sha256":"48c4e0fc6324b6791c5366a0115bfe3887ca3f4760e05d43144560016b766600"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:08.675067Z","signature_b64":"/1jE1ZNWbqPa2CZozhZl1nqgCvoKeWfP1GU/LKZ8+ng9/fIoGOXTNowd0Icp7Y2yVhxXITqQEGWMQ44nSoH/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6754d751f6dc95d59c34691ba4053d76a5d351a447550fb91206b7f62d67936c","last_reissued_at":"2026-05-29T02:06:08.674601Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:08.674601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Wasserstein cost of Importance Sampling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Michael Goldman, Simon Coste","submitted_at":"2026-05-28T15:07:45Z","abstract_excerpt":"Importance sampling (IS) consists in biasing samples from a distribution $f$ towards another distribution $g$. Concretely, given samples $X_i$ from $f$, the IS measure is $$\\hat{g}_n = \\frac{1}{Z_n}\\sum_{i=1}^n \\frac{g(X_i)}{f(X_i)} \\delta_{X_i},$$ with $Z_n = \\sum_{i=1}^n \\frac{g(X_i)}{f(X_i)}$. The random measure $\\hat{g}_n$ approximates $g$, and is used in many contexts ranging from Monte Carlo integration to Bayesian inference. We show that, in high dimension ($d \\geqslant 3$), the Wasserstein cost $W_p^p(\\hat{g}_n, g)$ has order $n^{-p/d}$ in expectation, i.e.\n  $$\\beta^{\\mathrm{low}}_{p,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30055","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/2605.30055/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":"2605.30055","created_at":"2026-05-29T02:06:08.674684+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.30055v1","created_at":"2026-05-29T02:06:08.674684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30055","created_at":"2026-05-29T02:06:08.674684+00:00"},{"alias_kind":"pith_short_12","alias_value":"M5KNOUPW3SK5","created_at":"2026-05-29T02:06:08.674684+00:00"},{"alias_kind":"pith_short_16","alias_value":"M5KNOUPW3SK5LHBU","created_at":"2026-05-29T02:06:08.674684+00:00"},{"alias_kind":"pith_short_8","alias_value":"M5KNOUPW","created_at":"2026-05-29T02:06:08.674684+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/M5KNOUPW3SK5LHBUNEN2IBJ5O2","json":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2.json","graph_json":"https://pith.science/api/pith-number/M5KNOUPW3SK5LHBUNEN2IBJ5O2/graph.json","events_json":"https://pith.science/api/pith-number/M5KNOUPW3SK5LHBUNEN2IBJ5O2/events.json","paper":"https://pith.science/paper/M5KNOUPW"},"agent_actions":{"view_html":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2","download_json":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2.json","view_paper":"https://pith.science/paper/M5KNOUPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.30055&json=true","fetch_graph":"https://pith.science/api/pith-number/M5KNOUPW3SK5LHBUNEN2IBJ5O2/graph.json","fetch_events":"https://pith.science/api/pith-number/M5KNOUPW3SK5LHBUNEN2IBJ5O2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2/action/storage_attestation","attest_author":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2/action/author_attestation","sign_citation":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2/action/citation_signature","submit_replication":"https://pith.science/pith/M5KNOUPW3SK5LHBUNEN2IBJ5O2/action/replication_record"}},"created_at":"2026-05-29T02:06:08.674684+00:00","updated_at":"2026-05-29T02:06:08.674684+00:00"}