{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VH24WSMJBJQWLRDWKHPVGSK3MM","short_pith_number":"pith:VH24WSMJ","canonical_record":{"source":{"id":"1904.06288","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-04-12T15:52:04Z","cross_cats_sorted":["cs.LG","stat.TH"],"title_canon_sha256":"8fd3b09825a8c0e87ce12543abc5b64fc028d58123f6df559e7ce561c61738a9","abstract_canon_sha256":"4cc8b0c175807761dd5a02151c897629bfc6f40b9a1c17f233194d4622c57a48"},"schema_version":"1.0"},"canonical_sha256":"a9f5cb49890a6165c47651df53495b632072d7e4df25a5275759791d1f98ef9e","source":{"kind":"arxiv","id":"1904.06288","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06288","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06288v3","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06288","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"VH24WSMJBJQW","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"VH24WSMJBJQWLRDW","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"VH24WSMJ","created_at":"2026-07-05T00:20:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VH24WSMJBJQWLRDWKHPVGSK3MM","target":"record","payload":{"canonical_record":{"source":{"id":"1904.06288","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-04-12T15:52:04Z","cross_cats_sorted":["cs.LG","stat.TH"],"title_canon_sha256":"8fd3b09825a8c0e87ce12543abc5b64fc028d58123f6df559e7ce561c61738a9","abstract_canon_sha256":"4cc8b0c175807761dd5a02151c897629bfc6f40b9a1c17f233194d4622c57a48"},"schema_version":"1.0"},"canonical_sha256":"a9f5cb49890a6165c47651df53495b632072d7e4df25a5275759791d1f98ef9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:20:13.999144Z","signature_b64":"pO5pZHljO7MEC82IIQt0xXtBPNc1OJs1jObbQDQwJ1s5Up5+lhTJd7i9bxaMJGeR39Xs7LdAheMyxN9WnXD9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9f5cb49890a6165c47651df53495b632072d7e4df25a5275759791d1f98ef9e","last_reissued_at":"2026-07-05T00:20:13.998764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:20:13.998764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.06288","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:20:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cWai5zP8GJDggg+Z/O1dPdtQSToYEXcdPEsijuaWBr9At5OoEMb+p8lb2UU6p/U+827nWPzP+7U0YPOTISxgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:44:49.515333Z"},"content_sha256":"2aa1525112c81aae1409bfa20b790fcd73982364880eb9e6f5db5393096ea8b8","schema_version":"1.0","event_id":"sha256:2aa1525112c81aae1409bfa20b790fcd73982364880eb9e6f5db5393096ea8b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VH24WSMJBJQWLRDWKHPVGSK3MM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Outlier-robust estimation of a sparse linear model using $\\ell_1$-penalized Huber's $M$-estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Arnak S. Dalalyan, Philip Thompson","submitted_at":"2019-04-12T15:52:04Z","abstract_excerpt":"We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\\ell_1$-penalized Huber's $M$-estimator based on $n$ samples attains the optimal rate of convergence $(s/n)^{1/2} + (o/n)$, up to a logarithmic factor. For more general design matrices, our results highlight the importance of two properties: the transfer principle and the incoherence property. These properties with suitable constants are shown to yield the optimal r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06288","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.06288/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:20:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tG8y8n8Oltl3zSUMOfvRn6nDfruvgO2OqSgiFL6tdDPZDwB/P6ZXo5UN+EC7oSX3cppTvujhKkoVjJE/Sxk9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:44:49.515700Z"},"content_sha256":"39eeac3a36da37929f334574b88433f7756b00c375df2ecaa3c65b4dfa2c2b20","schema_version":"1.0","event_id":"sha256:39eeac3a36da37929f334574b88433f7756b00c375df2ecaa3c65b4dfa2c2b20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VH24WSMJBJQWLRDWKHPVGSK3MM/bundle.json","state_url":"https://pith.science/pith/VH24WSMJBJQWLRDWKHPVGSK3MM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VH24WSMJBJQWLRDWKHPVGSK3MM/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":"2026-07-05T08:44:49Z","links":{"resolver":"https://pith.science/pith/VH24WSMJBJQWLRDWKHPVGSK3MM","bundle":"https://pith.science/pith/VH24WSMJBJQWLRDWKHPVGSK3MM/bundle.json","state":"https://pith.science/pith/VH24WSMJBJQWLRDWKHPVGSK3MM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VH24WSMJBJQWLRDWKHPVGSK3MM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VH24WSMJBJQWLRDWKHPVGSK3MM","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":"4cc8b0c175807761dd5a02151c897629bfc6f40b9a1c17f233194d4622c57a48","cross_cats_sorted":["cs.LG","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-04-12T15:52:04Z","title_canon_sha256":"8fd3b09825a8c0e87ce12543abc5b64fc028d58123f6df559e7ce561c61738a9"},"schema_version":"1.0","source":{"id":"1904.06288","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06288","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06288v3","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06288","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"VH24WSMJBJQW","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"VH24WSMJBJQWLRDW","created_at":"2026-07-05T00:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"VH24WSMJ","created_at":"2026-07-05T00:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:39eeac3a36da37929f334574b88433f7756b00c375df2ecaa3c65b4dfa2c2b20","target":"graph","created_at":"2026-07-05T00:20:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1904.06288/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the $\\ell_1$-penalized Huber's $M$-estimator based on $n$ samples attains the optimal rate of convergence $(s/n)^{1/2} + (o/n)$, up to a logarithmic factor. For more general design matrices, our results highlight the importance of two properties: the transfer principle and the incoherence property. These properties with suitable constants are shown to yield the optimal r","authors_text":"Arnak S. Dalalyan, Philip Thompson","cross_cats":["cs.LG","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-04-12T15:52:04Z","title":"Outlier-robust estimation of a sparse linear model using $\\ell_1$-penalized Huber's $M$-estimator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06288","kind":"arxiv","version":3},"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":"sha256:2aa1525112c81aae1409bfa20b790fcd73982364880eb9e6f5db5393096ea8b8","target":"record","created_at":"2026-07-05T00:20:13Z","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":"4cc8b0c175807761dd5a02151c897629bfc6f40b9a1c17f233194d4622c57a48","cross_cats_sorted":["cs.LG","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-04-12T15:52:04Z","title_canon_sha256":"8fd3b09825a8c0e87ce12543abc5b64fc028d58123f6df559e7ce561c61738a9"},"schema_version":"1.0","source":{"id":"1904.06288","kind":"arxiv","version":3}},"canonical_sha256":"a9f5cb49890a6165c47651df53495b632072d7e4df25a5275759791d1f98ef9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9f5cb49890a6165c47651df53495b632072d7e4df25a5275759791d1f98ef9e","first_computed_at":"2026-07-05T00:20:13.998764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:20:13.998764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pO5pZHljO7MEC82IIQt0xXtBPNc1OJs1jObbQDQwJ1s5Up5+lhTJd7i9bxaMJGeR39Xs7LdAheMyxN9WnXD9CA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:20:13.999144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06288","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aa1525112c81aae1409bfa20b790fcd73982364880eb9e6f5db5393096ea8b8","sha256:39eeac3a36da37929f334574b88433f7756b00c375df2ecaa3c65b4dfa2c2b20"],"state_sha256":"3eb381df1e634721ab57c0394ae67acd6708c0124c3d9a2b538f1846d716b820"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qy/PyIhlpku5pic3iL5FGczkId+Nti0tl9BocbpQKHmUwZyhtS8ukbQaHcrl4VeMjr45csxN7NrCUhCikid/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T08:44:49.517718Z","bundle_sha256":"f7acd9956f19f9dec7fb499ab78af401142604c726f0c06ae979a9505d6586c1"}}