{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:36OC2UOBCRWIWQ7AQ5L5J27P7A","short_pith_number":"pith:36OC2UOB","canonical_record":{"source":{"id":"1402.2365","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-11T04:09:53Z","cross_cats_sorted":["math.OC","stat.TH"],"title_canon_sha256":"7fe9c40869c48364d624a471a8d4f4352ee77005c6dd7389fb5cf263df66860c","abstract_canon_sha256":"b2e1d45356e159fbaa2e2433c7e712f37ee96192035650d0378f7f1cea1d5fa5"},"schema_version":"1.0"},"canonical_sha256":"df9c2d51c1146c8b43e08757d4ebeff82ce3dc51fb646497682f7245d3e18b30","source":{"kind":"arxiv","id":"1402.2365","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2365","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2365v4","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2365","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"36OC2UOBCRWI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"36OC2UOBCRWIWQ7A","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"36OC2UOB","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:36OC2UOBCRWIWQ7AQ5L5J27P7A","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2365","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-11T04:09:53Z","cross_cats_sorted":["math.OC","stat.TH"],"title_canon_sha256":"7fe9c40869c48364d624a471a8d4f4352ee77005c6dd7389fb5cf263df66860c","abstract_canon_sha256":"b2e1d45356e159fbaa2e2433c7e712f37ee96192035650d0378f7f1cea1d5fa5"},"schema_version":"1.0"},"canonical_sha256":"df9c2d51c1146c8b43e08757d4ebeff82ce3dc51fb646497682f7245d3e18b30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.562373Z","signature_b64":"8Cr4a95xpcGJuYidfImtXmWFp6WybMKSVOk+ViQqln1xcJ1k0D5nIUx1vtm/AQu8JjPcy+klKWbqt3DWXVSIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df9c2d51c1146c8b43e08757d4ebeff82ce3dc51fb646497682f7245d3e18b30","last_reissued_at":"2026-05-18T00:57:38.561827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.561827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2365","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/B0rR/oTxYUOS0OMwLwEc7HbXmaGw4XfI/6NlHznvpm7PCBB0YtJ+cW1+Hqol1FWWhQ33zNWl50LvgxjT8jBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:52:07.389759Z"},"content_sha256":"6c16ec85a7953a675d5d9f4139265f62b499038407d53b74f6398231533eed74","schema_version":"1.0","event_id":"sha256:6c16ec85a7953a675d5d9f4139265f62b499038407d53b74f6398231533eed74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:36OC2UOBCRWIWQ7AQ5L5J27P7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On perturbed proximal gradient algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Eric Moulines, Gersende Fort, Yves F. Atchade","submitted_at":"2014-02-11T04:09:53Z","abstract_excerpt":"We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo batch size under which convergence is guaranteed: both increasing batch size and constant batch size are considered. We also derive non-asymptotic bounds for an averaged version. Our results cover both the cases of biased and unbiased Monte Carlo approximation. To support our findings, we discuss the inference of a sparse generalized linear model with random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2365","kind":"arxiv","version":4},"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":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xDhUz1lGTARTSFxBEXjroVqGcy0HBG0C5QqhcBqaT3uc+pcZfXW/eciyZJdCtULfFAOrRt/OtZAKHOhUDScGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:52:07.390480Z"},"content_sha256":"724d02d12f52bfdf13b6df79c64d98e09130c0f6cd50612e1dccfa53a0425e6b","schema_version":"1.0","event_id":"sha256:724d02d12f52bfdf13b6df79c64d98e09130c0f6cd50612e1dccfa53a0425e6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A/bundle.json","state_url":"https://pith.science/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A/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":"2026-05-27T20:52:07Z","links":{"resolver":"https://pith.science/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A","bundle":"https://pith.science/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A/bundle.json","state":"https://pith.science/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/36OC2UOBCRWIWQ7AQ5L5J27P7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:36OC2UOBCRWIWQ7AQ5L5J27P7A","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":"b2e1d45356e159fbaa2e2433c7e712f37ee96192035650d0378f7f1cea1d5fa5","cross_cats_sorted":["math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-11T04:09:53Z","title_canon_sha256":"7fe9c40869c48364d624a471a8d4f4352ee77005c6dd7389fb5cf263df66860c"},"schema_version":"1.0","source":{"id":"1402.2365","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2365","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2365v4","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2365","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"36OC2UOBCRWI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"36OC2UOBCRWIWQ7A","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"36OC2UOB","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:724d02d12f52bfdf13b6df79c64d98e09130c0f6cd50612e1dccfa53a0425e6b","target":"graph","created_at":"2026-05-18T00:57:38Z","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":"We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo batch size under which convergence is guaranteed: both increasing batch size and constant batch size are considered. We also derive non-asymptotic bounds for an averaged version. Our results cover both the cases of biased and unbiased Monte Carlo approximation. To support our findings, we discuss the inference of a sparse generalized linear model with random ","authors_text":"Eric Moulines, Gersende Fort, Yves F. Atchade","cross_cats":["math.OC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-11T04:09:53Z","title":"On perturbed proximal gradient algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2365","kind":"arxiv","version":4},"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":"sha256:6c16ec85a7953a675d5d9f4139265f62b499038407d53b74f6398231533eed74","target":"record","created_at":"2026-05-18T00:57:38Z","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":"b2e1d45356e159fbaa2e2433c7e712f37ee96192035650d0378f7f1cea1d5fa5","cross_cats_sorted":["math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-02-11T04:09:53Z","title_canon_sha256":"7fe9c40869c48364d624a471a8d4f4352ee77005c6dd7389fb5cf263df66860c"},"schema_version":"1.0","source":{"id":"1402.2365","kind":"arxiv","version":4}},"canonical_sha256":"df9c2d51c1146c8b43e08757d4ebeff82ce3dc51fb646497682f7245d3e18b30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df9c2d51c1146c8b43e08757d4ebeff82ce3dc51fb646497682f7245d3e18b30","first_computed_at":"2026-05-18T00:57:38.561827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:38.561827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Cr4a95xpcGJuYidfImtXmWFp6WybMKSVOk+ViQqln1xcJ1k0D5nIUx1vtm/AQu8JjPcy+klKWbqt3DWXVSIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:38.562373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2365","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c16ec85a7953a675d5d9f4139265f62b499038407d53b74f6398231533eed74","sha256:724d02d12f52bfdf13b6df79c64d98e09130c0f6cd50612e1dccfa53a0425e6b"],"state_sha256":"6073efd11d565a807c67632c8022f11bf269932fc9f87c0403cc06cd04f73b6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EmeuH98Ul9vTZTPl2ZZplv8ZymMKscyur1fgtMdKJbyasO4qv/2H4HrtLKnhtLyL7AnwIyPlOmHOU6gH4inVBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:52:07.394461Z","bundle_sha256":"fde9a9a747cfa5d5a05bfa97105a57cf8d5c223a0868263d65bac40463fc1afc"}}