{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HABPNZHJ6ZDXUMH7IBUNOG7U2C","short_pith_number":"pith:HABPNZHJ","canonical_record":{"source":{"id":"2412.10615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-12-13T23:41:27Z","cross_cats_sorted":["cs.SY","stat.ML"],"title_canon_sha256":"ccdee5d933efed6352879fe4b9d887b14102481c89b0ca2091abaf3a16ebfb84","abstract_canon_sha256":"533f464cf84b77e7d82f73c83c22fa7715dcb5477a1b96aac78737d86832b966"},"schema_version":"1.0"},"canonical_sha256":"3802f6e4e9f6477a30ff4068d71bf4d09c56454f4c65fd74f143838e256bbf9b","source":{"kind":"arxiv","id":"2412.10615","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.10615","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"2412.10615v2","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.10615","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"HABPNZHJ6ZDX","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"pith_short_16","alias_value":"HABPNZHJ6ZDXUMH7","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"pith_short_8","alias_value":"HABPNZHJ","created_at":"2026-07-05T11:13:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HABPNZHJ6ZDXUMH7IBUNOG7U2C","target":"record","payload":{"canonical_record":{"source":{"id":"2412.10615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-12-13T23:41:27Z","cross_cats_sorted":["cs.SY","stat.ML"],"title_canon_sha256":"ccdee5d933efed6352879fe4b9d887b14102481c89b0ca2091abaf3a16ebfb84","abstract_canon_sha256":"533f464cf84b77e7d82f73c83c22fa7715dcb5477a1b96aac78737d86832b966"},"schema_version":"1.0"},"canonical_sha256":"3802f6e4e9f6477a30ff4068d71bf4d09c56454f4c65fd74f143838e256bbf9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:16.918054Z","signature_b64":"MobOsj7ltrywlJFL9yq1WpMPZDqnz8fjEnRlVTg5Da+2V2aeCmmJbiS6h4wNsT+IvaB5QXck9CyJRVj5XA/mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3802f6e4e9f6477a30ff4068d71bf4d09c56454f4c65fd74f143838e256bbf9b","last_reissued_at":"2026-07-05T11:13:16.917511Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:16.917511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.10615","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":"2026-07-05T11:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bLKYpp/9L/sw7C3JpUTC/Xe5JG3zUb5BaEmsvoecooHf+1pjMqdo7g/3CyZYAHBiGzBG1KSdhYgxseilTa9QDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:34:48.523523Z"},"content_sha256":"f7d54b69fa7a99c82872605f15c2a48786f8a80ac7754d88db0c0c649c363bb8","schema_version":"1.0","event_id":"sha256:f7d54b69fa7a99c82872605f15c2a48786f8a80ac7754d88db0c0c649c363bb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HABPNZHJ6ZDXUMH7IBUNOG7U2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","stat.ML"],"primary_cat":"eess.SY","authors_text":"Maryann Rui, Munther Dahleh","submitted_at":"2024-12-13T23:41:27Z","abstract_excerpt":"We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response parameters of the mixture models. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10615","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.10615/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZDF0XCoXQSNEKTGtlZH3S+oKuEyU+t0UXhiI56JHy4WQ1u4JaOi0mHouQDngi2mkRBQhHxjzBsvCPAgY30ECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:34:48.524107Z"},"content_sha256":"11d30de736a2307c5927c9cb7adcc8b2ec9f0b3fd0a7b71e81ec04d821e7c814","schema_version":"1.0","event_id":"sha256:11d30de736a2307c5927c9cb7adcc8b2ec9f0b3fd0a7b71e81ec04d821e7c814"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C/bundle.json","state_url":"https://pith.science/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C/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":"2026-08-07T23:34:48Z","links":{"resolver":"https://pith.science/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C","bundle":"https://pith.science/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C/bundle.json","state":"https://pith.science/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HABPNZHJ6ZDXUMH7IBUNOG7U2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HABPNZHJ6ZDXUMH7IBUNOG7U2C","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":"533f464cf84b77e7d82f73c83c22fa7715dcb5477a1b96aac78737d86832b966","cross_cats_sorted":["cs.SY","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-12-13T23:41:27Z","title_canon_sha256":"ccdee5d933efed6352879fe4b9d887b14102481c89b0ca2091abaf3a16ebfb84"},"schema_version":"1.0","source":{"id":"2412.10615","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.10615","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"2412.10615v2","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.10615","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"HABPNZHJ6ZDX","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"pith_short_16","alias_value":"HABPNZHJ6ZDXUMH7","created_at":"2026-07-05T11:13:16Z"},{"alias_kind":"pith_short_8","alias_value":"HABPNZHJ","created_at":"2026-07-05T11:13:16Z"}],"graph_snapshots":[{"event_id":"sha256:11d30de736a2307c5927c9cb7adcc8b2ec9f0b3fd0a7b71e81ec04d821e7c814","target":"graph","created_at":"2026-07-05T11:13:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.10615/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response parameters of the mixture models. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexit","authors_text":"Maryann Rui, Munther Dahleh","cross_cats":["cs.SY","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-12-13T23:41:27Z","title":"Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10615","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:f7d54b69fa7a99c82872605f15c2a48786f8a80ac7754d88db0c0c649c363bb8","target":"record","created_at":"2026-07-05T11:13:16Z","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":"533f464cf84b77e7d82f73c83c22fa7715dcb5477a1b96aac78737d86832b966","cross_cats_sorted":["cs.SY","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2024-12-13T23:41:27Z","title_canon_sha256":"ccdee5d933efed6352879fe4b9d887b14102481c89b0ca2091abaf3a16ebfb84"},"schema_version":"1.0","source":{"id":"2412.10615","kind":"arxiv","version":2}},"canonical_sha256":"3802f6e4e9f6477a30ff4068d71bf4d09c56454f4c65fd74f143838e256bbf9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3802f6e4e9f6477a30ff4068d71bf4d09c56454f4c65fd74f143838e256bbf9b","first_computed_at":"2026-07-05T11:13:16.917511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:16.917511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MobOsj7ltrywlJFL9yq1WpMPZDqnz8fjEnRlVTg5Da+2V2aeCmmJbiS6h4wNsT+IvaB5QXck9CyJRVj5XA/mBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:16.918054Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.10615","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7d54b69fa7a99c82872605f15c2a48786f8a80ac7754d88db0c0c649c363bb8","sha256:11d30de736a2307c5927c9cb7adcc8b2ec9f0b3fd0a7b71e81ec04d821e7c814"],"state_sha256":"f2456ea2cb3bcbffe66e7f5121370785c64c2ddf0784d3580257bbabce45b280"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OZAtGXz9DIsg1T2sXSSJAWSntVSB9qC8oT4l1VLRNxBnbzYV3WSWAxt17rNFOm+rmrQaBQqAJCzK52x09AUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:34:48.529205Z","bundle_sha256":"e3d12bd20e52d74f24385ca924181707e93406514c46a0f0682d1a004dbdd1fc"}}