{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XKTTS3FHVNIBYDY7WBNE25ILN4","short_pith_number":"pith:XKTTS3FH","schema_version":"1.0","canonical_sha256":"baa7396ca7ab501c0f1fb05a4d750b6f01d44d86f11e84e275445acb427f99bc","source":{"kind":"arxiv","id":"1605.06420","version":4},"attestation_state":"computed","paper":{"title":"Quantifying the accuracy of approximate diffusions and Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.CO","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"James Zou, Jonathan H. Huggins","submitted_at":"2016-05-20T16:17:22Z","abstract_excerpt":"Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating these stochastic processes can be considerable, and many algorithms have been proposed to approximate the underlying Markov chain or diffusion. A fundamental question is how the computational savings trade off against the statistical error incurred due to approximations. This paper develops general results that address this question. We bound the Wasserstei"},"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":"1605.06420","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-20T16:17:22Z","cross_cats_sorted":["math.PR","stat.CO","stat.ML","stat.TH"],"title_canon_sha256":"aace54ff0dbdf12508e1e0a340fe2e6736d799c6f345eba44d9394b8ae56f3c0","abstract_canon_sha256":"98888ab8613882331aa3a36916243701c1f5cb7b1580c63a78992de7a84fd4d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:24.758577Z","signature_b64":"HdAkTvHReR8bEMxHxRS664RJv3oZNbQOQfdMbaf5VGdcD3Wwe8kbTxpEgtuidoBeAh0Gy1z6Ml6eqNF772ELCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baa7396ca7ab501c0f1fb05a4d750b6f01d44d86f11e84e275445acb427f99bc","last_reissued_at":"2026-05-18T00:36:24.757844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:24.757844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantifying the accuracy of approximate diffusions and Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.CO","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"James Zou, Jonathan H. Huggins","submitted_at":"2016-05-20T16:17:22Z","abstract_excerpt":"Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating these stochastic processes can be considerable, and many algorithms have been proposed to approximate the underlying Markov chain or diffusion. A fundamental question is how the computational savings trade off against the statistical error incurred due to approximations. This paper develops general results that address this question. We bound the Wasserstei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06420","kind":"arxiv","version":4},"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":"1605.06420","created_at":"2026-05-18T00:36:24.757974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.06420v4","created_at":"2026-05-18T00:36:24.757974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06420","created_at":"2026-05-18T00:36:24.757974+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKTTS3FHVNIB","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKTTS3FHVNIBYDY7","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKTTS3FH","created_at":"2026-05-18T12:30:51.357362+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/XKTTS3FHVNIBYDY7WBNE25ILN4","json":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4.json","graph_json":"https://pith.science/api/pith-number/XKTTS3FHVNIBYDY7WBNE25ILN4/graph.json","events_json":"https://pith.science/api/pith-number/XKTTS3FHVNIBYDY7WBNE25ILN4/events.json","paper":"https://pith.science/paper/XKTTS3FH"},"agent_actions":{"view_html":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4","download_json":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4.json","view_paper":"https://pith.science/paper/XKTTS3FH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.06420&json=true","fetch_graph":"https://pith.science/api/pith-number/XKTTS3FHVNIBYDY7WBNE25ILN4/graph.json","fetch_events":"https://pith.science/api/pith-number/XKTTS3FHVNIBYDY7WBNE25ILN4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4/action/storage_attestation","attest_author":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4/action/author_attestation","sign_citation":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4/action/citation_signature","submit_replication":"https://pith.science/pith/XKTTS3FHVNIBYDY7WBNE25ILN4/action/replication_record"}},"created_at":"2026-05-18T00:36:24.757974+00:00","updated_at":"2026-05-18T00:36:24.757974+00:00"}