{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I6WPLRFJTRKV7INFR626R7UMDL","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":"e0a9be393f0715674ae89d3ec6f3fdf12abdf73b132559f063debfdfcdc374f5","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-30T06:57:56Z","title_canon_sha256":"65d43c0cac7712d1cff85deea381c6fdd8ed1332ec1363b9b09212389b65d15d"},"schema_version":"1.0","source":{"id":"1201.6115","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6115","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6115v3","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6115","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"I6WPLRFJTRKV","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I6WPLRFJTRKV7INF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I6WPLRFJ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:c8479ff56bb4d080334b51c6233e639f0facb4d23490f3bcadee17b829af00eb","target":"graph","created_at":"2026-05-18T03:51:23Z","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":"Let $(X,Y)\\in\\mathcal{X}\\times \\mathcal{Y}$ be a random couple with unknown distribution $P$. Let $\\GG$ be a class of measurable functions and $\\ell$ a loss function. The problem of statistical learning deals with the estimation of the Bayes: $$g^*=\\arg\\min_{g\\in\\GG}\\E_P \\ell(g(X),Y). $$ In this paper, we study this problem when we deal with a contaminated sample $(Z_1,Y_1),..., (Z_n,Y_n)$ of i.i.d. indirect observations. Each input $Z_i$, $i=1,...,n$ is distributed from a density $Af$, where $A$ is a known compact linear operator and $f$ is the density of the direct input $X$.\nWe derive fast ","authors_text":"S\\'ebastien Loustau (LAREMA)","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-30T06:57:56Z","title":"Statistical learning with indirect observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6115","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":"sha256:7cb9395e19f0dac0350eecb6ccbd453838af18a98f377497fbb692c1ea7983ad","target":"record","created_at":"2026-05-18T03:51:23Z","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":"e0a9be393f0715674ae89d3ec6f3fdf12abdf73b132559f063debfdfcdc374f5","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-30T06:57:56Z","title_canon_sha256":"65d43c0cac7712d1cff85deea381c6fdd8ed1332ec1363b9b09212389b65d15d"},"schema_version":"1.0","source":{"id":"1201.6115","kind":"arxiv","version":3}},"canonical_sha256":"47acf5c4a99c555fa1a58fb5e8fe8c1aee25ef69b44dbd0149c1af793292d627","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47acf5c4a99c555fa1a58fb5e8fe8c1aee25ef69b44dbd0149c1af793292d627","first_computed_at":"2026-05-18T03:51:23.508265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:23.508265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i5uI/2XxQubRkrcDluVu45ZobOnIawFOu0lPAc1b8qm8KlTK+IoLOn+hYvak2iRhBOlCZqSsADn4N/usyZ86CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:23.509056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6115","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cb9395e19f0dac0350eecb6ccbd453838af18a98f377497fbb692c1ea7983ad","sha256:c8479ff56bb4d080334b51c6233e639f0facb4d23490f3bcadee17b829af00eb"],"state_sha256":"085de9e026dcde761bf730efdfc0454168beed6d6b747771bd6b634f8c0d62b3"}