{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:R6UNCJIAME4F7K3DPCRE73LGLX","short_pith_number":"pith:R6UNCJIA","canonical_record":{"source":{"id":"1511.09159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-30T05:02:02Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"d1de7117d1f6aad73bab7030aed5837091455e8956f47bdf41b713614df53058","abstract_canon_sha256":"26936a4615090d77fb6b1cb91e470b15bd2937dd5d8da3d267071a8212712616"},"schema_version":"1.0"},"canonical_sha256":"8fa8d1250061385fab6378a24fed665df8fb354173e0b97f8369226aa0542f43","source":{"kind":"arxiv","id":"1511.09159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09159","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09159v1","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09159","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"R6UNCJIAME4F","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R6UNCJIAME4F7K3D","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R6UNCJIA","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:R6UNCJIAME4F7K3DPCRE73LGLX","target":"record","payload":{"canonical_record":{"source":{"id":"1511.09159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-30T05:02:02Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"d1de7117d1f6aad73bab7030aed5837091455e8956f47bdf41b713614df53058","abstract_canon_sha256":"26936a4615090d77fb6b1cb91e470b15bd2937dd5d8da3d267071a8212712616"},"schema_version":"1.0"},"canonical_sha256":"8fa8d1250061385fab6378a24fed665df8fb354173e0b97f8369226aa0542f43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:40.926069Z","signature_b64":"EMKu4ZVbKzo7dBtXoLxwOvCharzpvA34hEeizs09nWH86p/2kF4O6GigwNEHwdZk9bA3aJqfsmCIODcuEELgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fa8d1250061385fab6378a24fed665df8fb354173e0b97f8369226aa0542f43","last_reissued_at":"2026-05-18T01:25:40.925520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:40.925520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.09159","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":"2026-05-18T01:25:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmCWnSI8CYo6RW0WOdk7zgU7rcBf75V0IfP3SzfMMHV4UUMWILsldh99SQwJu3JrTNm/774uwvI8Ve7+bnNYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:20:01.454759Z"},"content_sha256":"00b083a00518945030368122f93dcd68d2a5fdf6b4618d5fb4223c898789cf3d","schema_version":"1.0","event_id":"sha256:00b083a00518945030368122f93dcd68d2a5fdf6b4618d5fb4223c898789cf3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:R6UNCJIAME4F7K3DPCRE73LGLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proximal gradient method for huberized support vector machine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"Amit Chakraborty, Ioannis Akrotirianakis, Yangyang Xu","submitted_at":"2015-11-30T05:02:02Z","abstract_excerpt":"The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with $\\ell_1$-regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the Proximal Gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09159","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":"2026-05-18T01:25:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4kfBG0uR2YTXPJyZXv0N28yMT6M/lH3zYvi7nWuSKVapjyAeLBJTth+Zzs3U8VtsNd/loR9en7qIs3J78gKGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:20:01.455370Z"},"content_sha256":"439ff8eeaaba40a852d892536bebc94d54c2fad9e4f7f57ad6633c39d51b5bb4","schema_version":"1.0","event_id":"sha256:439ff8eeaaba40a852d892536bebc94d54c2fad9e4f7f57ad6633c39d51b5bb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6UNCJIAME4F7K3DPCRE73LGLX/bundle.json","state_url":"https://pith.science/pith/R6UNCJIAME4F7K3DPCRE73LGLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6UNCJIAME4F7K3DPCRE73LGLX/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":"2026-06-12T04:20:01Z","links":{"resolver":"https://pith.science/pith/R6UNCJIAME4F7K3DPCRE73LGLX","bundle":"https://pith.science/pith/R6UNCJIAME4F7K3DPCRE73LGLX/bundle.json","state":"https://pith.science/pith/R6UNCJIAME4F7K3DPCRE73LGLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6UNCJIAME4F7K3DPCRE73LGLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:R6UNCJIAME4F7K3DPCRE73LGLX","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":"26936a4615090d77fb6b1cb91e470b15bd2937dd5d8da3d267071a8212712616","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-30T05:02:02Z","title_canon_sha256":"d1de7117d1f6aad73bab7030aed5837091455e8956f47bdf41b713614df53058"},"schema_version":"1.0","source":{"id":"1511.09159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09159","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09159v1","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09159","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"R6UNCJIAME4F","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R6UNCJIAME4F7K3D","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R6UNCJIA","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:439ff8eeaaba40a852d892536bebc94d54c2fad9e4f7f57ad6633c39d51b5bb4","target":"graph","created_at":"2026-05-18T01:25:40Z","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":"The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with $\\ell_1$-regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the Proximal Gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show tha","authors_text":"Amit Chakraborty, Ioannis Akrotirianakis, Yangyang Xu","cross_cats":["cs.LG","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-30T05:02:02Z","title":"Proximal gradient method for huberized support vector machine"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09159","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":"sha256:00b083a00518945030368122f93dcd68d2a5fdf6b4618d5fb4223c898789cf3d","target":"record","created_at":"2026-05-18T01:25:40Z","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":"26936a4615090d77fb6b1cb91e470b15bd2937dd5d8da3d267071a8212712616","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-11-30T05:02:02Z","title_canon_sha256":"d1de7117d1f6aad73bab7030aed5837091455e8956f47bdf41b713614df53058"},"schema_version":"1.0","source":{"id":"1511.09159","kind":"arxiv","version":1}},"canonical_sha256":"8fa8d1250061385fab6378a24fed665df8fb354173e0b97f8369226aa0542f43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fa8d1250061385fab6378a24fed665df8fb354173e0b97f8369226aa0542f43","first_computed_at":"2026-05-18T01:25:40.925520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:40.925520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EMKu4ZVbKzo7dBtXoLxwOvCharzpvA34hEeizs09nWH86p/2kF4O6GigwNEHwdZk9bA3aJqfsmCIODcuEELgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:40.926069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00b083a00518945030368122f93dcd68d2a5fdf6b4618d5fb4223c898789cf3d","sha256:439ff8eeaaba40a852d892536bebc94d54c2fad9e4f7f57ad6633c39d51b5bb4"],"state_sha256":"5bcfd617b5f713d60dd0523835bbcd04ac6edaeb1e0bacd0e933dde6cf26a23f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K78ttZurCnfBZINZQfvLs+7WBy1pt1hEW1XsUtNVxg6WYqnElGCDfJzTj60hHK4v77PpApmYf6fOYNn5NRuFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:20:01.458489Z","bundle_sha256":"6c5a7ffc11acb69b5824450b5da991f0850abef6442536f5492a29b8dd35891c"}}