{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DU5UNJ57DIQBZEELT4WODQHUX4","short_pith_number":"pith:DU5UNJ57","canonical_record":{"source":{"id":"1607.01417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-05T21:04:08Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"966882cbe8bbc1487b939b1c766bd5b3e49e03bb689fa4ef42482f099b78841e","abstract_canon_sha256":"86b546945d0525c5ca5f47ef5d28023d0caf8ee792b6f11fed07f14562fd02f2"},"schema_version":"1.0"},"canonical_sha256":"1d3b46a7bf1a201c908b9f2ce1c0f4bf2d99fb6571e85f08da0b473dce03bbe2","source":{"kind":"arxiv","id":"1607.01417","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01417","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01417v2","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01417","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"DU5UNJ57DIQB","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DU5UNJ57DIQBZEEL","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DU5UNJ57","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DU5UNJ57DIQBZEELT4WODQHUX4","target":"record","payload":{"canonical_record":{"source":{"id":"1607.01417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-05T21:04:08Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"966882cbe8bbc1487b939b1c766bd5b3e49e03bb689fa4ef42482f099b78841e","abstract_canon_sha256":"86b546945d0525c5ca5f47ef5d28023d0caf8ee792b6f11fed07f14562fd02f2"},"schema_version":"1.0"},"canonical_sha256":"1d3b46a7bf1a201c908b9f2ce1c0f4bf2d99fb6571e85f08da0b473dce03bbe2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:48.408471Z","signature_b64":"eDdtyZI1nZiYYDV844EI/95RqZHJIN7Z9uW2LXi4eDXfTTnU6DZAFZcESkt5SMhvHR6HQWW84y+btDVKob1IDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d3b46a7bf1a201c908b9f2ce1c0f4bf2d99fb6571e85f08da0b473dce03bbe2","last_reissued_at":"2026-05-18T00:37:48.407848Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:48.407848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.01417","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":"2026-05-18T00:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QxP20Z9FyDdtaE/tYPc3ToLOP3SAO8917MPhsv2nT4P85zQSLovWku+gXHlTg5CDguwhJyh2jaerVN1GYhNPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:12:04.957689Z"},"content_sha256":"a89ebee7caa95a8b40de596f7d2adae8c7e7747525254ed2fe03266ac559423c","schema_version":"1.0","event_id":"sha256:a89ebee7caa95a8b40de596f7d2adae8c7e7747525254ed2fe03266ac559423c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DU5UNJ57DIQBZEELT4WODQHUX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms for Generalized Cluster-wise Linear Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Diego Klabjan, Loren Williams, Yan Jiang, Young Woong Park","submitted_at":"2016-07-05T21:04:08Z","abstract_excerpt":"Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation, and refer to it as generalized CLR. We propose an exact mathematical programming based approach relying on column generation, a column generation based heuristic algorithm that clusters predefined groups of entities, a metaheuristic gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01417","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":"2026-05-18T00:37:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9g3qEq+r0YxZ1LjBCoZ/ynEs5F72hW626yRtAutfuNjGw5vAed3eVL86ofvMDBbJhjKw265Jb+cDD34eaUCRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:12:04.958038Z"},"content_sha256":"ae52de5f726395f2787c27d61bc21f62c4a160dda29b9981f20f5918aed842d1","schema_version":"1.0","event_id":"sha256:ae52de5f726395f2787c27d61bc21f62c4a160dda29b9981f20f5918aed842d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DU5UNJ57DIQBZEELT4WODQHUX4/bundle.json","state_url":"https://pith.science/pith/DU5UNJ57DIQBZEELT4WODQHUX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DU5UNJ57DIQBZEELT4WODQHUX4/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":"2026-05-28T12:12:04Z","links":{"resolver":"https://pith.science/pith/DU5UNJ57DIQBZEELT4WODQHUX4","bundle":"https://pith.science/pith/DU5UNJ57DIQBZEELT4WODQHUX4/bundle.json","state":"https://pith.science/pith/DU5UNJ57DIQBZEELT4WODQHUX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DU5UNJ57DIQBZEELT4WODQHUX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DU5UNJ57DIQBZEELT4WODQHUX4","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":"86b546945d0525c5ca5f47ef5d28023d0caf8ee792b6f11fed07f14562fd02f2","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-05T21:04:08Z","title_canon_sha256":"966882cbe8bbc1487b939b1c766bd5b3e49e03bb689fa4ef42482f099b78841e"},"schema_version":"1.0","source":{"id":"1607.01417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01417","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01417v2","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01417","created_at":"2026-05-18T00:37:48Z"},{"alias_kind":"pith_short_12","alias_value":"DU5UNJ57DIQB","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DU5UNJ57DIQBZEEL","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DU5UNJ57","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:ae52de5f726395f2787c27d61bc21f62c4a160dda29b9981f20f5918aed842d1","target":"graph","created_at":"2026-05-18T00:37:48Z","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":"Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation, and refer to it as generalized CLR. We propose an exact mathematical programming based approach relying on column generation, a column generation based heuristic algorithm that clusters predefined groups of entities, a metaheuristic gene","authors_text":"Diego Klabjan, Loren Williams, Yan Jiang, Young Woong Park","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-05T21:04:08Z","title":"Algorithms for Generalized Cluster-wise Linear Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01417","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:a89ebee7caa95a8b40de596f7d2adae8c7e7747525254ed2fe03266ac559423c","target":"record","created_at":"2026-05-18T00:37:48Z","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":"86b546945d0525c5ca5f47ef5d28023d0caf8ee792b6f11fed07f14562fd02f2","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-05T21:04:08Z","title_canon_sha256":"966882cbe8bbc1487b939b1c766bd5b3e49e03bb689fa4ef42482f099b78841e"},"schema_version":"1.0","source":{"id":"1607.01417","kind":"arxiv","version":2}},"canonical_sha256":"1d3b46a7bf1a201c908b9f2ce1c0f4bf2d99fb6571e85f08da0b473dce03bbe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d3b46a7bf1a201c908b9f2ce1c0f4bf2d99fb6571e85f08da0b473dce03bbe2","first_computed_at":"2026-05-18T00:37:48.407848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:48.407848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eDdtyZI1nZiYYDV844EI/95RqZHJIN7Z9uW2LXi4eDXfTTnU6DZAFZcESkt5SMhvHR6HQWW84y+btDVKob1IDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:48.408471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a89ebee7caa95a8b40de596f7d2adae8c7e7747525254ed2fe03266ac559423c","sha256:ae52de5f726395f2787c27d61bc21f62c4a160dda29b9981f20f5918aed842d1"],"state_sha256":"ca18ddf67bead58ea62e1934c7d69d993af2081e7592fd561d7a02ff2bc5abbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/hSdG9MAdUMZatJVpOA7LgS/efhnIFPBVGYgaKdzuoXzeYMIpKWW2n3/aMZdcxk8sxekc4hHPVAIePggm7/2Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:12:04.960110Z","bundle_sha256":"ee686a16ea60b9be8ea2164b241f899a65e5a9e8a8a375cdf9a92907f854ba51"}}