{"paper":{"title":"Functional uniqueness and stability of Gaussian priors in optimal L1 estimation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alex Dytso, Leighton Barnes","submitted_at":"2025-11-21T00:21:25Z","abstract_excerpt":"We study when optimal Bayesian estimators under Gaussian noise are approximately linear, and what this implies about the underlying prior distribution. Consider the classical model \\(Y = X + Z\\), where \\(Z\\) is Gaussian and independent of \\(X\\). It is well known that under squared-error loss, the conditional mean \\(\\mathbb{E}[X|Y]\\) is a linear function of \\(Y\\) if and only if the prior is Gaussian. Much less is understood under absolute-error loss, where the optimal estimator is the conditional median and standard orthogonality-based tools no longer apply.\n  Recent work has established that, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.16864","kind":"arxiv","version":2},"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/2511.16864/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"}