{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UEU4G2Z7QEQUYO4EVAIRDFRHEC","short_pith_number":"pith:UEU4G2Z7","canonical_record":{"source":{"id":"1702.08249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T12:03:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5524e7a66fa8992664475c0026c3488f23c2e2ceb3c5ce3f63c4ce17d53786f8","abstract_canon_sha256":"9fc9cf3d184cf8db0d6b738b95d078fe343e2dbd1d800af9ccbb7b3f49a5892f"},"schema_version":"1.0"},"canonical_sha256":"a129c36b3f81214c3b84a81111962720a4b82cdba73670825c13264186b630e9","source":{"kind":"arxiv","id":"1702.08249","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08249","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08249v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08249","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"UEU4G2Z7QEQU","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEU4G2Z7QEQUYO4E","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEU4G2Z7","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UEU4G2Z7QEQUYO4EVAIRDFRHEC","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T12:03:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5524e7a66fa8992664475c0026c3488f23c2e2ceb3c5ce3f63c4ce17d53786f8","abstract_canon_sha256":"9fc9cf3d184cf8db0d6b738b95d078fe343e2dbd1d800af9ccbb7b3f49a5892f"},"schema_version":"1.0"},"canonical_sha256":"a129c36b3f81214c3b84a81111962720a4b82cdba73670825c13264186b630e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:55.455361Z","signature_b64":"WTXpHkG0X2BaxMoBbq5hR2B6mF2+s9HNpulAZ8aijAWTQYlAPUNg1GRc9NFz54nPNUIafhIJWHFzF7wH2J0cDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a129c36b3f81214c3b84a81111962720a4b82cdba73670825c13264186b630e9","last_reissued_at":"2026-05-18T00:49:55.454567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:55.454567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08249","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8BvcYcYKBUy7rN8hrAglF1T3HEQvvldAXPG7F3lR6Boi5wLIvBVNpckq5NJaYHoWBZ1KISdlYWeUn2hR4anDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:37:38.248692Z"},"content_sha256":"9e74e21f6c9174d47ec1c6b9971ea21d28389e7fed2bc71d2ab76a652eb1b8b9","schema_version":"1.0","event_id":"sha256:9e74e21f6c9174d47ec1c6b9971ea21d28389e7fed2bc71d2ab76a652eb1b8b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UEU4G2Z7QEQUYO4EVAIRDFRHEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform Deviation Bounds for Unbounded Loss Functions like k-Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Andreas Krause, Mario Lucic, Olivier Bachem, S. Hamed Hassani","submitted_at":"2017-02-27T12:03:41Z","abstract_excerpt":"Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss functions which are *unbounded*. In our main application, this allows us to obtain bounds for $k$-Means clustering under weak assumptions on the underlying distribution. If the fourth moment is bounded, we prove a rate of $\\mathcal{O}\\left(m^{-\\frac12}\\right)$ compared to the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08249","kind":"arxiv","version":1},"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":"2026-05-18T00:49:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4aDugym1UXdZvtqJYGJb2ZlXCcRjnZaMYXxsJBXFPVfhx0n7THdCPFzkT6V8D0h6LAIU5G1YipAD9Jt0PtSsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:37:38.249393Z"},"content_sha256":"c0bf04642f2c2b5deb607b50555e95667770f688ed420260255dc03532aa2af0","schema_version":"1.0","event_id":"sha256:c0bf04642f2c2b5deb607b50555e95667770f688ed420260255dc03532aa2af0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC/bundle.json","state_url":"https://pith.science/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC/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":"2026-05-22T03:37:38Z","links":{"resolver":"https://pith.science/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC","bundle":"https://pith.science/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC/bundle.json","state":"https://pith.science/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEU4G2Z7QEQUYO4EVAIRDFRHEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UEU4G2Z7QEQUYO4EVAIRDFRHEC","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":"9fc9cf3d184cf8db0d6b738b95d078fe343e2dbd1d800af9ccbb7b3f49a5892f","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T12:03:41Z","title_canon_sha256":"5524e7a66fa8992664475c0026c3488f23c2e2ceb3c5ce3f63c4ce17d53786f8"},"schema_version":"1.0","source":{"id":"1702.08249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08249","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08249v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08249","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"UEU4G2Z7QEQU","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UEU4G2Z7QEQUYO4E","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UEU4G2Z7","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:c0bf04642f2c2b5deb607b50555e95667770f688ed420260255dc03532aa2af0","target":"graph","created_at":"2026-05-18T00:49:55Z","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":"Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss functions which are *unbounded*. In our main application, this allows us to obtain bounds for $k$-Means clustering under weak assumptions on the underlying distribution. If the fourth moment is bounded, we prove a rate of $\\mathcal{O}\\left(m^{-\\frac12}\\right)$ compared to the pr","authors_text":"Andreas Krause, Mario Lucic, Olivier Bachem, S. Hamed Hassani","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T12:03:41Z","title":"Uniform Deviation Bounds for Unbounded Loss Functions like k-Means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08249","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":"sha256:9e74e21f6c9174d47ec1c6b9971ea21d28389e7fed2bc71d2ab76a652eb1b8b9","target":"record","created_at":"2026-05-18T00:49:55Z","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":"9fc9cf3d184cf8db0d6b738b95d078fe343e2dbd1d800af9ccbb7b3f49a5892f","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-02-27T12:03:41Z","title_canon_sha256":"5524e7a66fa8992664475c0026c3488f23c2e2ceb3c5ce3f63c4ce17d53786f8"},"schema_version":"1.0","source":{"id":"1702.08249","kind":"arxiv","version":1}},"canonical_sha256":"a129c36b3f81214c3b84a81111962720a4b82cdba73670825c13264186b630e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a129c36b3f81214c3b84a81111962720a4b82cdba73670825c13264186b630e9","first_computed_at":"2026-05-18T00:49:55.454567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:55.454567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WTXpHkG0X2BaxMoBbq5hR2B6mF2+s9HNpulAZ8aijAWTQYlAPUNg1GRc9NFz54nPNUIafhIJWHFzF7wH2J0cDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:55.455361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e74e21f6c9174d47ec1c6b9971ea21d28389e7fed2bc71d2ab76a652eb1b8b9","sha256:c0bf04642f2c2b5deb607b50555e95667770f688ed420260255dc03532aa2af0"],"state_sha256":"f6662636081663bbfa441692a2e82040c681d13f914ac838fa2868b7f11f4535"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gW8KXRc1zmKtlyDSahS5b5ZOPVaa8NCjEqweFfTuqaXSey14S2x8gF1NdRPBNkhup8Cml9iiGCSaWldyEtbJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:37:38.253288Z","bundle_sha256":"e7e1fb12935b4a38cdfa95eb9b5a3fdf2107f1bd1dc73d78101c5ac207534b74"}}