{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KTT3FUGN7JFEFQGBSNI2M3JE2M","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":"4bf2659b03b62e3db7d13f5d50227ac7425315aea3a94ceedc0077f2d92a7fc8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-24T00:12:28Z","title_canon_sha256":"768275789655e4632095f07a54519ba76b4af449a4571b8bbacf3cd3b771c32c"},"schema_version":"1.0","source":{"id":"1809.08705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08705","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08705v1","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08705","created_at":"2026-05-18T00:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"KTT3FUGN7JFE","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KTT3FUGN7JFEFQGB","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KTT3FUGN","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:4dd21e992b994fde81581ace871c42e4a55468457beb40172a4c4dd2765acb4f","target":"graph","created_at":"2026-05-18T00:05:03Z","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":"Finite mixture models are among the most popular statistical models used in different data science disciplines. Despite their broad applicability, inference under these models typically leads to computationally challenging non-convex problems. While the Expectation-Maximization (EM) algorithm is the most popular approach for solving these non-convex problems, the behavior of this algorithm is not well understood. In this work, we focus on the case of mixture of Laplacian (or Gaussian) distribution. We start by analyzing a simple equally weighted mixture of two single dimensional Laplacian dist","authors_text":"Babak Barazandeh, Meisam Razaviyayn","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-24T00:12:28Z","title":"On the Behavior of the Expectation-Maximization Algorithm for Mixture Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08705","kind":"arxiv","version":1},"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":"sha256:3571fbe21abf3a7ea2b5e80a467ddb6daf7e02794456c6062f9b1e68f54b8c9e","target":"record","created_at":"2026-05-18T00:05:03Z","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":"4bf2659b03b62e3db7d13f5d50227ac7425315aea3a94ceedc0077f2d92a7fc8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-09-24T00:12:28Z","title_canon_sha256":"768275789655e4632095f07a54519ba76b4af449a4571b8bbacf3cd3b771c32c"},"schema_version":"1.0","source":{"id":"1809.08705","kind":"arxiv","version":1}},"canonical_sha256":"54e7b2d0cdfa4a42c0c19351a66d24d334ffe6492f9eb7016e2b3cc64ace5b23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54e7b2d0cdfa4a42c0c19351a66d24d334ffe6492f9eb7016e2b3cc64ace5b23","first_computed_at":"2026-05-18T00:05:03.777229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:03.777229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XL3HgHsVLACdM9x9zuaoToM8jSCjJTMMuscQewFtAJSLFp1c9SUSvflVX9pypkIQPEDiS6PpE3Gv4A8iDHqtDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:03.777638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3571fbe21abf3a7ea2b5e80a467ddb6daf7e02794456c6062f9b1e68f54b8c9e","sha256:4dd21e992b994fde81581ace871c42e4a55468457beb40172a4c4dd2765acb4f"],"state_sha256":"fa178aa0068231bef193c981ac168ae5c6fd1a5db03abf821c8c1f60021b6ae2"}