{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MCSKIT3U3XHFZNGKB4Q5TM3QTC","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":"dadc4890e8c67502015b0fb25ce036dd396edfeaa9d3487ec241e911f23887b0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-16T17:34:45Z","title_canon_sha256":"1a80db0339aec5d15924cd54afee81fc5fe4c791c48f07b786f181e458eb8fd5"},"schema_version":"1.0","source":{"id":"1210.4846","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4846","created_at":"2026-05-18T03:42:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4846v1","created_at":"2026-05-18T03:42:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4846","created_at":"2026-05-18T03:42:55Z"},{"alias_kind":"pith_short_12","alias_value":"MCSKIT3U3XHF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MCSKIT3U3XHFZNGK","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MCSKIT3U","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:59ef40002affadb30088006c3bda615e7f425aab328f9f58ccf16ec2627db0f7","target":"graph","created_at":"2026-05-18T03:42:55Z","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":"In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a new dual-tree based variational approach for approximating the transition matrix and efficiently performing the random walk is proposed. The approach exploits a connection between kernel density estimation, mixture modeling, and random walk on graphs in an optimization of the transition matrix for the data graph that ties together edge transitions probabilit","authors_text":"Bo Thiesson, Milos Hauskrecht, Saeed Amizadeh","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-16T17:34:45Z","title":"Variational Dual-Tree Framework for Large-Scale Transition Matrix Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4846","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":"sha256:8c3902a25932be64410b95c21d3095ab1b2077645f66492e0297741ae7d62571","target":"record","created_at":"2026-05-18T03:42:55Z","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":"dadc4890e8c67502015b0fb25ce036dd396edfeaa9d3487ec241e911f23887b0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-16T17:34:45Z","title_canon_sha256":"1a80db0339aec5d15924cd54afee81fc5fe4c791c48f07b786f181e458eb8fd5"},"schema_version":"1.0","source":{"id":"1210.4846","kind":"arxiv","version":1}},"canonical_sha256":"60a4a44f74ddce5cb4ca0f21d9b37098a2490097dd1b298995c753d23141347e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60a4a44f74ddce5cb4ca0f21d9b37098a2490097dd1b298995c753d23141347e","first_computed_at":"2026-05-18T03:42:55.524993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:55.524993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4afvjzwXH1KV4dbpIenzi8F4Y3H+mLa6W49rbbZiLDD1NVntwL0lFlcbPCu+V5MjICCVrlfpFeo0lOK+FFrADA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:55.525787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4846","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c3902a25932be64410b95c21d3095ab1b2077645f66492e0297741ae7d62571","sha256:59ef40002affadb30088006c3bda615e7f425aab328f9f58ccf16ec2627db0f7"],"state_sha256":"bb0eb7f26a760706281eca93c402c0cb6704c7ad3b40f1bc146f458a98885870"}