{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4AZOSLSFR66LG525LJ4CYHMKR5","short_pith_number":"pith:4AZOSLSF","canonical_record":{"source":{"id":"1806.10648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-06-27T19:10:56Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"d803a3b35cd6da232aa4d01c6964fde9674d5cee78586d1be3f1250544040254","abstract_canon_sha256":"a78c60644c52e84656ae442d005d14a450951b79df33dddb0b807913fa5c89d2"},"schema_version":"1.0"},"canonical_sha256":"e032e92e458fbcb3775d5a782c1d8a8f6441f7247e08ebdaab486a0045b47aaf","source":{"kind":"arxiv","id":"1806.10648","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10648","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10648v2","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10648","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"pith_short_12","alias_value":"4AZOSLSFR66L","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AZOSLSFR66LG525","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AZOSLSF","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4AZOSLSFR66LG525LJ4CYHMKR5","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10648","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-06-27T19:10:56Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"d803a3b35cd6da232aa4d01c6964fde9674d5cee78586d1be3f1250544040254","abstract_canon_sha256":"a78c60644c52e84656ae442d005d14a450951b79df33dddb0b807913fa5c89d2"},"schema_version":"1.0"},"canonical_sha256":"e032e92e458fbcb3775d5a782c1d8a8f6441f7247e08ebdaab486a0045b47aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:38.599692Z","signature_b64":"PnPmIfLVMizx77+7IMS2TQ99LtNjyzrX3v25aJgjWu3vIgDivWU69/MVC7+t2NfqoWqHrfDCOdhfIBkKfAPsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e032e92e458fbcb3775d5a782c1d8a8f6441f7247e08ebdaab486a0045b47aaf","last_reissued_at":"2026-05-17T23:50:38.599263Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:38.599263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10648","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":"2026-05-17T23:50:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ln0Dl+pX5whm6fLCYMA/1zjR4MU3fP55UTeYKFX2EtqOW1wq0qeSHPUyl4eg7MJgE1QnrAMJxHiKOiK/kiZOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:22:29.672088Z"},"content_sha256":"c254090ac57362c3285daedd3952cf005df28e1b8366a366dfbc8a4b73b5079a","schema_version":"1.0","event_id":"sha256:c254090ac57362c3285daedd3952cf005df28e1b8366a366dfbc8a4b73b5079a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4AZOSLSFR66LG525LJ4CYHMKR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uncoupled isotonic regression via minimum Wasserstein deconvolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jonathan Weed, Philippe Rigollet","submitted_at":"2018-06-27T19:10:56Z","abstract_excerpt":"Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\\mathbb{E}[y_i]=f(x_i), i=1, \\ldots n$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart where one is given only the unordered sets $\\{x_1, \\ldots, x_n\\}$ and $\\{y_1, \\ldots, y_n\\}$. In this work, we leverage tools from optimal transport theory to derive minimax rates under weak moments conditions on $y_i$ and to give an e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10648","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":"2026-05-17T23:50:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xebl7ZQ5WXYJfsw+XxwgvV20x6QXmVUNiGbOVrTwzdp+AHDgyWvnkYGlDwOiQ7/sNqecIGDMvIX/gOnrzdzPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:22:29.672579Z"},"content_sha256":"4e51274cfdc8172a37348c837ae7bc3dff5cbb15c5eecd2ec6814b32f020cf49","schema_version":"1.0","event_id":"sha256:4e51274cfdc8172a37348c837ae7bc3dff5cbb15c5eecd2ec6814b32f020cf49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4AZOSLSFR66LG525LJ4CYHMKR5/bundle.json","state_url":"https://pith.science/pith/4AZOSLSFR66LG525LJ4CYHMKR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4AZOSLSFR66LG525LJ4CYHMKR5/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":"2026-08-18T07:22:29Z","links":{"resolver":"https://pith.science/pith/4AZOSLSFR66LG525LJ4CYHMKR5","bundle":"https://pith.science/pith/4AZOSLSFR66LG525LJ4CYHMKR5/bundle.json","state":"https://pith.science/pith/4AZOSLSFR66LG525LJ4CYHMKR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4AZOSLSFR66LG525LJ4CYHMKR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4AZOSLSFR66LG525LJ4CYHMKR5","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":"a78c60644c52e84656ae442d005d14a450951b79df33dddb0b807913fa5c89d2","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-06-27T19:10:56Z","title_canon_sha256":"d803a3b35cd6da232aa4d01c6964fde9674d5cee78586d1be3f1250544040254"},"schema_version":"1.0","source":{"id":"1806.10648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10648","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10648v2","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10648","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"pith_short_12","alias_value":"4AZOSLSFR66L","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AZOSLSFR66LG525","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AZOSLSF","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:4e51274cfdc8172a37348c837ae7bc3dff5cbb15c5eecd2ec6814b32f020cf49","target":"graph","created_at":"2026-05-17T23:50:38Z","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":"Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\\mathbb{E}[y_i]=f(x_i), i=1, \\ldots n$. While this problem is well understood both statistically and computationally, much less is known about its uncoupled counterpart where one is given only the unordered sets $\\{x_1, \\ldots, x_n\\}$ and $\\{y_1, \\ldots, y_n\\}$. In this work, we leverage tools from optimal transport theory to derive minimax rates under weak moments conditions on $y_i$ and to give an e","authors_text":"Jonathan Weed, Philippe Rigollet","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-06-27T19:10:56Z","title":"Uncoupled isotonic regression via minimum Wasserstein deconvolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10648","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:c254090ac57362c3285daedd3952cf005df28e1b8366a366dfbc8a4b73b5079a","target":"record","created_at":"2026-05-17T23:50:38Z","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":"a78c60644c52e84656ae442d005d14a450951b79df33dddb0b807913fa5c89d2","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-06-27T19:10:56Z","title_canon_sha256":"d803a3b35cd6da232aa4d01c6964fde9674d5cee78586d1be3f1250544040254"},"schema_version":"1.0","source":{"id":"1806.10648","kind":"arxiv","version":2}},"canonical_sha256":"e032e92e458fbcb3775d5a782c1d8a8f6441f7247e08ebdaab486a0045b47aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e032e92e458fbcb3775d5a782c1d8a8f6441f7247e08ebdaab486a0045b47aaf","first_computed_at":"2026-05-17T23:50:38.599263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:38.599263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PnPmIfLVMizx77+7IMS2TQ99LtNjyzrX3v25aJgjWu3vIgDivWU69/MVC7+t2NfqoWqHrfDCOdhfIBkKfAPsDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:38.599692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c254090ac57362c3285daedd3952cf005df28e1b8366a366dfbc8a4b73b5079a","sha256:4e51274cfdc8172a37348c837ae7bc3dff5cbb15c5eecd2ec6814b32f020cf49"],"state_sha256":"1e386c853d5b1d8eb69fbadd2ac8d409d4cc2db60971e80f6677547c0bdfc866"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dM/hz2z2x1roeynk26sb44T2Pf3PiYGjbb0kv3TzVOYwFf7LX265rum6CI1DtuLCeLRvRfI51mK/egfRDT4YCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:22:29.676780Z","bundle_sha256":"a64fde451c2cf66c5d1e512ca9e57ab2475927d20a18fd78420fc61ea172dc16"}}