{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4J37WRRFJXQTMKMRA7IWNDDAJ4","short_pith_number":"pith:4J37WRRF","canonical_record":{"source":{"id":"1804.00795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-03T02:28:47Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"3a9c8de0fcf7148e74458e681376155877912097f96e941407b957077e4626ee","abstract_canon_sha256":"23f3bf100ed08072e4252149ac83e6301e834c302de1eb6e0d473e95db8d2a3d"},"schema_version":"1.0"},"canonical_sha256":"e277fb46254de136299107d1668c604f0d4ffde1801d6516587db1d11e7459a2","source":{"kind":"arxiv","id":"1804.00795","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00795","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00795v2","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00795","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"4J37WRRFJXQT","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4J37WRRFJXQTMKMR","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4J37WRRF","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4J37WRRFJXQTMKMRA7IWNDDAJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1804.00795","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-03T02:28:47Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"3a9c8de0fcf7148e74458e681376155877912097f96e941407b957077e4626ee","abstract_canon_sha256":"23f3bf100ed08072e4252149ac83e6301e834c302de1eb6e0d473e95db8d2a3d"},"schema_version":"1.0"},"canonical_sha256":"e277fb46254de136299107d1668c604f0d4ffde1801d6516587db1d11e7459a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:21.909977Z","signature_b64":"HfKGzXOU4sUPdmMCKgXq6iu5jZg2tQW9TtRs5GEY0R96yu03osTHTbShO3sORiUdhC1xacl/EtEkwqRbk/+aBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e277fb46254de136299107d1668c604f0d4ffde1801d6516587db1d11e7459a2","last_reissued_at":"2026-05-18T00:10:21.909522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:21.909522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.00795","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lvp7rVMeEVwPJMa9g+pOTui4bGc7mA+S/NRk03tfQqyyzprqdUm+SHNK+8zDC4BMmBDOGy+lee5Nm6C9cNb0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:30:52.988143Z"},"content_sha256":"2429d630a5d43043ce969feb855b378eac3f6770e3cbdf0c625d04666e5ee8c2","schema_version":"1.0","event_id":"sha256:2429d630a5d43043ce969feb855b378eac3f6770e3cbdf0c625d04666e5ee8c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4J37WRRFJXQTMKMRA7IWNDDAJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimation of Markov Chain via Rank-Constrained Likelihood","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Anru Zhang, Mengdi Wang, Xudong Li","submitted_at":"2018-04-03T02:28:47Z","abstract_excerpt":"This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the $\\ell_2$ risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments show that the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00795","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2iNtStSscCGd9c6j5bbNO5VDH8GhFil/tT/swjw+JftAYRMzEGC8lgGGeWwMoo9G9nSz98tID3DD1NzU6jTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:30:52.988782Z"},"content_sha256":"625393c8524f6a8d42df94514cc6bbf432c20972c1d7bbc325e155f56b98a703","schema_version":"1.0","event_id":"sha256:625393c8524f6a8d42df94514cc6bbf432c20972c1d7bbc325e155f56b98a703"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4/bundle.json","state_url":"https://pith.science/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T13:30:52Z","links":{"resolver":"https://pith.science/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4","bundle":"https://pith.science/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4/bundle.json","state":"https://pith.science/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4J37WRRFJXQTMKMRA7IWNDDAJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4J37WRRFJXQTMKMRA7IWNDDAJ4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"23f3bf100ed08072e4252149ac83e6301e834c302de1eb6e0d473e95db8d2a3d","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-03T02:28:47Z","title_canon_sha256":"3a9c8de0fcf7148e74458e681376155877912097f96e941407b957077e4626ee"},"schema_version":"1.0","source":{"id":"1804.00795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00795","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00795v2","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00795","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"4J37WRRFJXQT","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4J37WRRFJXQTMKMR","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4J37WRRF","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:625393c8524f6a8d42df94514cc6bbf432c20972c1d7bbc325e155f56b98a703","target":"graph","created_at":"2026-05-18T00:10:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the $\\ell_2$ risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments show that the p","authors_text":"Anru Zhang, Mengdi Wang, Xudong Li","cross_cats":["cs.LG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-03T02:28:47Z","title":"Estimation of Markov Chain via Rank-Constrained Likelihood"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00795","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2429d630a5d43043ce969feb855b378eac3f6770e3cbdf0c625d04666e5ee8c2","target":"record","created_at":"2026-05-18T00:10:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"23f3bf100ed08072e4252149ac83e6301e834c302de1eb6e0d473e95db8d2a3d","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-04-03T02:28:47Z","title_canon_sha256":"3a9c8de0fcf7148e74458e681376155877912097f96e941407b957077e4626ee"},"schema_version":"1.0","source":{"id":"1804.00795","kind":"arxiv","version":2}},"canonical_sha256":"e277fb46254de136299107d1668c604f0d4ffde1801d6516587db1d11e7459a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e277fb46254de136299107d1668c604f0d4ffde1801d6516587db1d11e7459a2","first_computed_at":"2026-05-18T00:10:21.909522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:21.909522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HfKGzXOU4sUPdmMCKgXq6iu5jZg2tQW9TtRs5GEY0R96yu03osTHTbShO3sORiUdhC1xacl/EtEkwqRbk/+aBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:21.909977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2429d630a5d43043ce969feb855b378eac3f6770e3cbdf0c625d04666e5ee8c2","sha256:625393c8524f6a8d42df94514cc6bbf432c20972c1d7bbc325e155f56b98a703"],"state_sha256":"5a46eef600869c512c7f084e758253563aedf1e4b429dc21b2961a2db9bc9553"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yj+313oOGu1OktZda4OAB8kmzwjZ8k6ki5cSvP8xXb5IUIpmycysAR3ZH2vxIDgc6FQrqRzqCrLj1cM3qYs4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:30:52.992979Z","bundle_sha256":"f12731a945781b9aad259f684088fde2d758a69178439732845d816c5f3508ec"}}