{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ANTEEP4YGGVNRDV3YITPFAUQPI","short_pith_number":"pith:ANTEEP4Y","schema_version":"1.0","canonical_sha256":"0366423f9831aad88ebbc226f282907a373b53fc4a482ca434e404facbf6cb03","source":{"kind":"arxiv","id":"2607.07468","version":1},"attestation_state":"computed","paper":{"title":"Statistical inverse learning and $\\ell^1$-regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Abhishake Rastogi, Luca Ratti, Tapio Helin, Tatiana A. Bubba","submitted_at":"2026-07-08T14:32:08Z","abstract_excerpt":"We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\\ell^1$, and observations are generated through a possibly nonlinear forward operator $A:\\ell^1\\to H$, where $H$ is a vector-valued reproducing kernel Hilbert space. We propose an $\\ell^1$-regularized empirical risk minimizer and develop a theoretical analysis of its statistical properties.\n  Under mild assumptions, we establish almost-sure consistency and derive non-asymptotic high-probability convergence rates in bo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.07468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-07-08T14:32:08Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"e8ab75d53dfb253017e417e9b0d3152b320a9d59bd35dd00e4ec2b76820df433","abstract_canon_sha256":"d9949078ddf7df276b1c3a44e240f0007c6966563478f5e9031ad6e97f9d7625"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:25.766682Z","signature_b64":"GOqdfW5fxuF+BgSveiAYOeOxXQh0L3ZGq5sbol92Yn1EtPgfsYtF7pDeozeG7gubITiqCLaHEpezVm4z+bSMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0366423f9831aad88ebbc226f282907a373b53fc4a482ca434e404facbf6cb03","last_reissued_at":"2026-07-09T01:20:25.766272Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:25.766272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical inverse learning and $\\ell^1$-regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Abhishake Rastogi, Luca Ratti, Tapio Helin, Tatiana A. Bubba","submitted_at":"2026-07-08T14:32:08Z","abstract_excerpt":"We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning. The unknown is modeled as an element of $\\ell^1$, and observations are generated through a possibly nonlinear forward operator $A:\\ell^1\\to H$, where $H$ is a vector-valued reproducing kernel Hilbert space. We propose an $\\ell^1$-regularized empirical risk minimizer and develop a theoretical analysis of its statistical properties.\n  Under mild assumptions, we establish almost-sure consistency and derive non-asymptotic high-probability convergence rates in bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07468","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07468/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.07468","created_at":"2026-07-09T01:20:25.766338+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.07468v1","created_at":"2026-07-09T01:20:25.766338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07468","created_at":"2026-07-09T01:20:25.766338+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANTEEP4YGGVN","created_at":"2026-07-09T01:20:25.766338+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANTEEP4YGGVNRDV3","created_at":"2026-07-09T01:20:25.766338+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANTEEP4Y","created_at":"2026-07-09T01:20:25.766338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI","json":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI.json","graph_json":"https://pith.science/api/pith-number/ANTEEP4YGGVNRDV3YITPFAUQPI/graph.json","events_json":"https://pith.science/api/pith-number/ANTEEP4YGGVNRDV3YITPFAUQPI/events.json","paper":"https://pith.science/paper/ANTEEP4Y"},"agent_actions":{"view_html":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI","download_json":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI.json","view_paper":"https://pith.science/paper/ANTEEP4Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.07468&json=true","fetch_graph":"https://pith.science/api/pith-number/ANTEEP4YGGVNRDV3YITPFAUQPI/graph.json","fetch_events":"https://pith.science/api/pith-number/ANTEEP4YGGVNRDV3YITPFAUQPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI/action/storage_attestation","attest_author":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI/action/author_attestation","sign_citation":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI/action/citation_signature","submit_replication":"https://pith.science/pith/ANTEEP4YGGVNRDV3YITPFAUQPI/action/replication_record"}},"created_at":"2026-07-09T01:20:25.766338+00:00","updated_at":"2026-07-09T01:20:25.766338+00:00"}