{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KPJZ2JSPWYWYTPMM6UTKPA6357","short_pith_number":"pith:KPJZ2JSP","canonical_record":{"source":{"id":"1702.08402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T17:48:46Z","cross_cats_sorted":[],"title_canon_sha256":"32c255fc709c08aeeb453659d3942feb0dfda3353cd1badb650f4d1a3e6ae818","abstract_canon_sha256":"b95451783073f838941e825f6dd8c79ab6128612a2331272dd7b4ef55ab46a54"},"schema_version":"1.0"},"canonical_sha256":"53d39d264fb62d89bd8cf526a783dbefc058cdf11eebefb0990c4380ad8fe25e","source":{"kind":"arxiv","id":"1702.08402","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08402","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08402v2","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08402","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"KPJZ2JSPWYWY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KPJZ2JSPWYWYTPMM","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KPJZ2JSP","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KPJZ2JSPWYWYTPMM6UTKPA6357","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T17:48:46Z","cross_cats_sorted":[],"title_canon_sha256":"32c255fc709c08aeeb453659d3942feb0dfda3353cd1badb650f4d1a3e6ae818","abstract_canon_sha256":"b95451783073f838941e825f6dd8c79ab6128612a2331272dd7b4ef55ab46a54"},"schema_version":"1.0"},"canonical_sha256":"53d39d264fb62d89bd8cf526a783dbefc058cdf11eebefb0990c4380ad8fe25e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:52.524143Z","signature_b64":"uoBbyFMTMeQ0J/v+6bvhHTC/xOMoG+rQQWe+OzmwIJHkSJVKrGLFDUJkT+p8c+KlNpZZ3RdHUb8WElsdkEDaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53d39d264fb62d89bd8cf526a783dbefc058cdf11eebefb0990c4380ad8fe25e","last_reissued_at":"2026-05-18T00:33:52.523569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:52.523569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08402","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":"2026-05-18T00:33:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sW2jW78/q6JC2Z6M6QcOMQJibjjEOWYHns/5aleUB0vLEEMdTlGOWpIhRoIsSeQ3eGzqBX5o/MPdYZqoVAObDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:43:42.824885Z"},"content_sha256":"1f500aecccc53e7342b01249d74d164e67625f32b98a82afc82d576784dd4050","schema_version":"1.0","event_id":"sha256:1f500aecccc53e7342b01249d74d164e67625f32b98a82afc82d576784dd4050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KPJZ2JSPWYWYTPMM6UTKPA6357","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Markus Heinonen, Sami Remes, Samuel Kaski","submitted_at":"2017-02-27T17:48:46Z","abstract_excerpt":"We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08402","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":"2026-05-18T00:33:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0vyIlMKXJCfPztl9qIWRXD0wOf/6u1cvIITjAq/E/F133wfs5QhsI/oJwig3hBZ+vtEUoDJ3FeMck51XdLchBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:43:42.825436Z"},"content_sha256":"0f2f1b360db1823f7fc065d18ceca0ade2097bb15625c373f04f5509a4554e25","schema_version":"1.0","event_id":"sha256:0f2f1b360db1823f7fc065d18ceca0ade2097bb15625c373f04f5509a4554e25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPJZ2JSPWYWYTPMM6UTKPA6357/bundle.json","state_url":"https://pith.science/pith/KPJZ2JSPWYWYTPMM6UTKPA6357/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPJZ2JSPWYWYTPMM6UTKPA6357/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":"2026-06-03T02:43:42Z","links":{"resolver":"https://pith.science/pith/KPJZ2JSPWYWYTPMM6UTKPA6357","bundle":"https://pith.science/pith/KPJZ2JSPWYWYTPMM6UTKPA6357/bundle.json","state":"https://pith.science/pith/KPJZ2JSPWYWYTPMM6UTKPA6357/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPJZ2JSPWYWYTPMM6UTKPA6357/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KPJZ2JSPWYWYTPMM6UTKPA6357","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":"b95451783073f838941e825f6dd8c79ab6128612a2331272dd7b4ef55ab46a54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T17:48:46Z","title_canon_sha256":"32c255fc709c08aeeb453659d3942feb0dfda3353cd1badb650f4d1a3e6ae818"},"schema_version":"1.0","source":{"id":"1702.08402","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08402","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08402v2","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08402","created_at":"2026-05-18T00:33:52Z"},{"alias_kind":"pith_short_12","alias_value":"KPJZ2JSPWYWY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KPJZ2JSPWYWYTPMM","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KPJZ2JSP","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:0f2f1b360db1823f7fc065d18ceca0ade2097bb15625c373f04f5509a4554e25","target":"graph","created_at":"2026-05-18T00:33:52Z","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":"We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent si","authors_text":"Markus Heinonen, Sami Remes, Samuel Kaski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T17:48:46Z","title":"A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08402","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":"sha256:1f500aecccc53e7342b01249d74d164e67625f32b98a82afc82d576784dd4050","target":"record","created_at":"2026-05-18T00:33:52Z","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":"b95451783073f838941e825f6dd8c79ab6128612a2331272dd7b4ef55ab46a54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T17:48:46Z","title_canon_sha256":"32c255fc709c08aeeb453659d3942feb0dfda3353cd1badb650f4d1a3e6ae818"},"schema_version":"1.0","source":{"id":"1702.08402","kind":"arxiv","version":2}},"canonical_sha256":"53d39d264fb62d89bd8cf526a783dbefc058cdf11eebefb0990c4380ad8fe25e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53d39d264fb62d89bd8cf526a783dbefc058cdf11eebefb0990c4380ad8fe25e","first_computed_at":"2026-05-18T00:33:52.523569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:52.523569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uoBbyFMTMeQ0J/v+6bvhHTC/xOMoG+rQQWe+OzmwIJHkSJVKrGLFDUJkT+p8c+KlNpZZ3RdHUb8WElsdkEDaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:52.524143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08402","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f500aecccc53e7342b01249d74d164e67625f32b98a82afc82d576784dd4050","sha256:0f2f1b360db1823f7fc065d18ceca0ade2097bb15625c373f04f5509a4554e25"],"state_sha256":"633b31e2b707d6c4ee7ba3f1046c8c41851fa363a2878e8d0d4e94e2cfb56590"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2/xLXHhAyoYXhBieYnMiO5AFwSWdUP5+D2Lhi6Ne3RF6kCGUf3imNPoXCKm5QApSMD38HWAv9M8kZRL6zKVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:43:42.828020Z","bundle_sha256":"8dfc82b97370c039a302e4a86edf737b721392f49211696c1627be54c3d304b0"}}