{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:52VHQI7LDTHBHP2VMO2GWGB7OE","short_pith_number":"pith:52VHQI7L","canonical_record":{"source":{"id":"1805.08836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-22T19:55:37Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"19e4a8c3aee4798eb5da08e26b8a60106f18f37479f6c10a8fe96c9fcbe87544","abstract_canon_sha256":"9b68c72bba23831f94c3f705fa41110618e63c685437e4dab32f67539d3b6433"},"schema_version":"1.0"},"canonical_sha256":"eeaa7823eb1cce13bf5563b46b183f712be27ab59f36079d2e8b26d02e8818e1","source":{"kind":"arxiv","id":"1805.08836","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08836","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08836v2","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08836","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"pith_short_12","alias_value":"52VHQI7LDTHB","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"52VHQI7LDTHBHP2V","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"52VHQI7L","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:52VHQI7LDTHBHP2VMO2GWGB7OE","target":"record","payload":{"canonical_record":{"source":{"id":"1805.08836","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-22T19:55:37Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"19e4a8c3aee4798eb5da08e26b8a60106f18f37479f6c10a8fe96c9fcbe87544","abstract_canon_sha256":"9b68c72bba23831f94c3f705fa41110618e63c685437e4dab32f67539d3b6433"},"schema_version":"1.0"},"canonical_sha256":"eeaa7823eb1cce13bf5563b46b183f712be27ab59f36079d2e8b26d02e8818e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:09.963338Z","signature_b64":"sbNBlJt/sM/57EdSXiw1g2bRP1RcSDA4lVEDNH2G+69Ea/85VENNHy5tk+gXvUNDCC3AakuGxp68eklh3T1tDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeaa7823eb1cce13bf5563b46b183f712be27ab59f36079d2e8b26d02e8818e1","last_reissued_at":"2026-05-18T00:02:09.962659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:09.962659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.08836","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":"2026-05-18T00:02:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AwIIlKLidT8C73pZhHgiEV44xCIumuFuB5D5fSgwGhqw2WR3VGd5GR5Nh5FQQ+dvU7rniaWTyQCJJxZDwJnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:28:12.011726Z"},"content_sha256":"0f426a445aeb9521930eace3265875db17d4347e4c6439ef60644db270b915d4","schema_version":"1.0","event_id":"sha256:0f426a445aeb9521930eace3265875db17d4347e4c6439ef60644db270b915d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:52VHQI7LDTHBHP2VMO2GWGB7OE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonparametric Density Estimation under Adversarial Losses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Ananya Uppal, Barnab\\'as P\\'oczos, Boyue Li, Chun-Liang Li, Manzil Zaheer, Shashank Singh","submitted_at":"2018-05-22T19:55:37Z","abstract_excerpt":"We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called \"adversarial losses\", which, besides classical $\\mathcal{L}^p$ losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08836","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":"2026-05-18T00:02:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipJCF82PD0ZFJlAiopyD3oodCuZUPIdOoJ+1ZqhIVW3XH4n4ElslQEyZiQdd0fJZup154LnMMagQcp3DbV/5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:28:12.012079Z"},"content_sha256":"3646627a22fe8f71fa78ca739e6d54e03bb0a8d1eab4c3336bcdf307ea4bba42","schema_version":"1.0","event_id":"sha256:3646627a22fe8f71fa78ca739e6d54e03bb0a8d1eab4c3336bcdf307ea4bba42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52VHQI7LDTHBHP2VMO2GWGB7OE/bundle.json","state_url":"https://pith.science/pith/52VHQI7LDTHBHP2VMO2GWGB7OE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52VHQI7LDTHBHP2VMO2GWGB7OE/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":"2026-06-23T06:28:12Z","links":{"resolver":"https://pith.science/pith/52VHQI7LDTHBHP2VMO2GWGB7OE","bundle":"https://pith.science/pith/52VHQI7LDTHBHP2VMO2GWGB7OE/bundle.json","state":"https://pith.science/pith/52VHQI7LDTHBHP2VMO2GWGB7OE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52VHQI7LDTHBHP2VMO2GWGB7OE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:52VHQI7LDTHBHP2VMO2GWGB7OE","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":"9b68c72bba23831f94c3f705fa41110618e63c685437e4dab32f67539d3b6433","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-22T19:55:37Z","title_canon_sha256":"19e4a8c3aee4798eb5da08e26b8a60106f18f37479f6c10a8fe96c9fcbe87544"},"schema_version":"1.0","source":{"id":"1805.08836","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08836","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08836v2","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08836","created_at":"2026-05-18T00:02:09Z"},{"alias_kind":"pith_short_12","alias_value":"52VHQI7LDTHB","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"52VHQI7LDTHBHP2V","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"52VHQI7L","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:3646627a22fe8f71fa78ca739e6d54e03bb0a8d1eab4c3336bcdf307ea4bba42","target":"graph","created_at":"2026-05-18T00:02:09Z","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 study minimax convergence rates of nonparametric density estimation under a large class of loss functions called \"adversarial losses\", which, besides classical $\\mathcal{L}^p$ losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs bas","authors_text":"Ananya Uppal, Barnab\\'as P\\'oczos, Boyue Li, Chun-Liang Li, Manzil Zaheer, Shashank Singh","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-22T19:55:37Z","title":"Nonparametric Density Estimation under Adversarial Losses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08836","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":"sha256:0f426a445aeb9521930eace3265875db17d4347e4c6439ef60644db270b915d4","target":"record","created_at":"2026-05-18T00:02:09Z","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":"9b68c72bba23831f94c3f705fa41110618e63c685437e4dab32f67539d3b6433","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-05-22T19:55:37Z","title_canon_sha256":"19e4a8c3aee4798eb5da08e26b8a60106f18f37479f6c10a8fe96c9fcbe87544"},"schema_version":"1.0","source":{"id":"1805.08836","kind":"arxiv","version":2}},"canonical_sha256":"eeaa7823eb1cce13bf5563b46b183f712be27ab59f36079d2e8b26d02e8818e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeaa7823eb1cce13bf5563b46b183f712be27ab59f36079d2e8b26d02e8818e1","first_computed_at":"2026-05-18T00:02:09.962659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:09.962659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sbNBlJt/sM/57EdSXiw1g2bRP1RcSDA4lVEDNH2G+69Ea/85VENNHy5tk+gXvUNDCC3AakuGxp68eklh3T1tDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:09.963338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08836","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f426a445aeb9521930eace3265875db17d4347e4c6439ef60644db270b915d4","sha256:3646627a22fe8f71fa78ca739e6d54e03bb0a8d1eab4c3336bcdf307ea4bba42"],"state_sha256":"2ae3c11323e89749634fd5dc5a65e1a340c5306a910d61dbba6f93767d93874e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8eTUeEDrRrvvO0ZbSce/a9gKWEs2ENjG/F27Am2eK1fCHllQ+K9S2mVr4GehWkixCya2Md/bQicXKQQBTI1JDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:28:12.014286Z","bundle_sha256":"b406e45634106d1a0a034615ea06dcb12ba2de558323cdc8b280b5dd70889ca7"}}