{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:J4KHC36VJTWDXDCAFYGHJUFPX6","short_pith_number":"pith:J4KHC36V","schema_version":"1.0","canonical_sha256":"4f14716fd54cec3b8c402e0c74d0afbfa60e6c10bba1fe555d6d020c0c4c9441","source":{"kind":"arxiv","id":"1111.5950","version":3},"attestation_state":"computed","paper":{"title":"Non-Linear Transformations of Gaussians and Gaussian-Mixtures with implications on Estimation and Information Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Paolo Banelli","submitted_at":"2011-11-25T11:26:25Z","abstract_excerpt":"This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression analysis of the NLT output and derives sufficient general conditions to establish when the input-output regression coefficient is equal to the \\emph{partial} regression coefficient of the output with respect to a (additive) part of the input. A special case is represented by zero-mean Gaussian inputs, obtained as the sum of other zero-mean Gaussian random variabl"},"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":"1111.5950","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-11-25T11:26:25Z","cross_cats_sorted":["math.IT","math.PR","math.ST","stat.TH"],"title_canon_sha256":"a089d40c57cf685fc1ba66b4e751e7fa7b704bf2ac25f22addd51ab5eb1eecb8","abstract_canon_sha256":"f2b7401c72cbe3837aa7c603486d0eaf996a80022be98455177913e42188d1a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:00.406678Z","signature_b64":"wmQHIYr28znPXrQ36xWYCAwYXC6sf7DK8Tj0AYyXTgVQkOFTowrDteA24PEiJVrJzGBgxJmTK0lYSL6w9K/5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f14716fd54cec3b8c402e0c74d0afbfa60e6c10bba1fe555d6d020c0c4c9441","last_reissued_at":"2026-05-18T03:26:00.405860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:00.405860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Linear Transformations of Gaussians and Gaussian-Mixtures with implications on Estimation and Information Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Paolo Banelli","submitted_at":"2011-11-25T11:26:25Z","abstract_excerpt":"This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression analysis of the NLT output and derives sufficient general conditions to establish when the input-output regression coefficient is equal to the \\emph{partial} regression coefficient of the output with respect to a (additive) part of the input. A special case is represented by zero-mean Gaussian inputs, obtained as the sum of other zero-mean Gaussian random variabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5950","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":""},"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":"1111.5950","created_at":"2026-05-18T03:26:00.405993+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.5950v3","created_at":"2026-05-18T03:26:00.405993+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5950","created_at":"2026-05-18T03:26:00.405993+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4KHC36VJTWD","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4KHC36VJTWDXDCA","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4KHC36V","created_at":"2026-05-18T12:26:32.869790+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/J4KHC36VJTWDXDCAFYGHJUFPX6","json":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6.json","graph_json":"https://pith.science/api/pith-number/J4KHC36VJTWDXDCAFYGHJUFPX6/graph.json","events_json":"https://pith.science/api/pith-number/J4KHC36VJTWDXDCAFYGHJUFPX6/events.json","paper":"https://pith.science/paper/J4KHC36V"},"agent_actions":{"view_html":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6","download_json":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6.json","view_paper":"https://pith.science/paper/J4KHC36V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.5950&json=true","fetch_graph":"https://pith.science/api/pith-number/J4KHC36VJTWDXDCAFYGHJUFPX6/graph.json","fetch_events":"https://pith.science/api/pith-number/J4KHC36VJTWDXDCAFYGHJUFPX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6/action/storage_attestation","attest_author":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6/action/author_attestation","sign_citation":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6/action/citation_signature","submit_replication":"https://pith.science/pith/J4KHC36VJTWDXDCAFYGHJUFPX6/action/replication_record"}},"created_at":"2026-05-18T03:26:00.405993+00:00","updated_at":"2026-05-18T03:26:00.405993+00:00"}