{ "schemaVersion": "1.6", "slug": "robust-gaussian-inverse-estimation", "title": "Quantitative robust estimation for Gaussian inverse problems", "shortTitle": "Spectrum-matched robustness", "url": "https://evidencepress.org/releases/robust-gaussian-inverse-estimation/", "oneLine": "A spectral linear estimator attains asymptotically optimal normalized robust risk with a uniform additive guarantee, and anisotropic jitter can implement it at population level.", "abstract": "This unrefereed candidate studies Gaussian inverse problems under samplewise norm-bounded attacks. It proves asymptotic optimality of a proposed spectral estimator among linear estimators and a uniform finite-dimensional additive risk-regret bound. When the minimizing dual parameter is positive, population linear least squares trained with anisotropic Gaussian input jitter implements the estimator exactly. Under positive-noise active-estimation hypotheses, isotropic jitter suffices exactly for a flat positive spectrum. A rational two-band certificate gives a strict anisotropic advantage. The result does not address finite-sample training, nonlinear estimators, risk ratios or empirical performance.", "datePublished": "2026-10-18", "dateModified": "2026-10-18", "version": "1.0.0", "doi": "10.5281/zenodo.23447009", "doiUrl": "https://doi.org/10.5281/zenodo.23447009", "conceptDoi": null, "pdfUrl": "https://github.com/ipitchford/robust-gaussian-inverse-estimation/releases/download/v1.0.0/paper.pdf", "altPdfUrl": null, "altPdfLabel": null, "zenodoUrl": "https://zenodo.org/records/23447009", "repoUrl": "https://github.com/ipitchford/robust-gaussian-inverse-estimation", "releaseUrl": "https://github.com/ipitchford/robust-gaussian-inverse-estimation/releases/tag/v1.0.0", "markdownUrl": "https://evidencepress.org/releases/robust-gaussian-inverse-estimation/index.md", "bibtexUrl": "https://evidencepress.org/releases/robust-gaussian-inverse-estimation/cite.bib", "audioUrl": "https://evidencepress.org/assets/audio/robust-gaussian-inverse-estimation.mp3", "imageUrl": "https://evidencepress.org/assets/og/robust-gaussian-inverse-estimation.png?v=3e2e2f93c1", "coverArtUrl": "https://evidencepress.org/assets/art/robust-gaussian-inverse-estimation.svg?v=85baed53cc", "media": [ { "type": "audio", "url": "https://evidencepress.org/assets/audio/robust-gaussian-inverse-estimation.mp3", "name": "Plain-English audio briefing", "description": "Communication aid; not additional research evidence.", "transcriptUrl": "https://evidencepress.org/assets/audio/robust-gaussian-inverse-estimation.txt" } ], "authors": [ "Anonymous" ], "license": "CC0-1.0", "status": "unrefereed-candidate", "verification": { "peerReviewed": false, "independentlyReproduced": false, "formallyVerified": false, "internallyReplayed": true, "detail": "Unrefereed AI-assisted candidate. Written proofs and producer-side finite replay do not establish external peer review, unaffiliated reproduction, formal verification or empirical estimator performance." }, "assurance": [ { "dimension": "availability", "label": "Availability and archiving", "question": "Is the evidence package publicly retrievable from an archive under a persistent identifier?", "state": "passed", "evidenceUrl": "https://zenodo.org/records/23447009", "note": "GitHub and Zenodo preserve the exact frozen release assets; availability is not correctness or peer review." }, { "dimension": "internalReplay", "label": "Internal replay", "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?", "state": "passed", "note": "Finite and exact certificate checks replay in normal and optimized-wrapper modes. Written asymptotic arguments are not machine proofs.", "evidenceUrl": "https://github.com/ipitchford/robust-gaussian-inverse-estimation/blob/v1.0.0/REPLAY.md" }, { "dimension": "independentRerun", "label": "Independent rerun", "question": "Has someone else run the supplied implementation and obtained the stated result?", "state": "not-assessed", "note": "No unaffiliated rerun established." }, { "dimension": "independentReimplementation", "label": "Independent reimplementation", "question": "Has someone else reached the result from an independent implementation?", "state": "not-assessed", "note": "Coordinated checking is not unaffiliated reimplementation." }, { "dimension": "formalVerification", "label": "Formal verification", "question": "Is a formalised statement machine-checked, and over which trusted base?", "state": "not-assessed", "note": "No proof-assistant formalisation established." }, { "dimension": "specialistReview", "label": "Specialist review", "question": "Has a domain specialist assessed the argument?", "state": "not-assessed", "note": "Internal model assessment is not external specialist review." }, { "dimension": "editorialPeerReview", "label": "Editorial peer review", "question": "Has a journal or venue run peer review to a decision?", "state": "not-assessed", "note": "No journal editorial peer review established." }, { "dimension": "dataEnvironmentReproducibility", "label": "Data and environment reproducibility", "question": "Are data and computational environment pinned well enough to rebuild?", "state": "partial", "evidenceUrl": "https://github.com/ipitchford/robust-gaussian-inverse-estimation/blob/v1.0.0/ENVIRONMENT.md", "note": "Inputs, code and environment are archived; unaffiliated cross-environment replay is not established." } ], "provenance": { "aiGenerated": true, "aiAssisted": true, "generatedBy": [ "AI-assisted research workflow", "OpenAI Codex: checking, revision and publication" ], "humanRole": "Publication authority only; no human research contribution inferred from ownership.", "reviewStatus": "Supplied review and internal AI-assisted assessment; no external human specialist or editorial peer review established." }, "attributionBoundary": null, "problem": null, "orderedProductAverage": null, "corrections": [], "publicCorrections": [], "publicCorrectionIndexes": null, "pageStructureVersion": "2.0", "pageStructureVariant": "canonical-theorem", "pageStructureWaivers": [], "recordMaturity": "current", "metadataProvenance": "Prepared from the final version-1.0.0 manuscript, exact frozen archive, supplied review and internal five-role assessment on 18 October 2026. Research commit b9b67b7c4340d7715dde4f533c0aa1f01b36a1d3; archive SHA-256 ee229749400c471dcb8d4f7e5a5dc2b36146becb43d03cffde71c33803482590.", "grandfatheredAtSchemaVersion": null, "keywords": [ "inverse problems", "robust estimation", "Gaussian models", "spectral estimators", "anisotropic jitter" ], "keyResults": [ "The proposed spectral estimator is asymptotically optimal among linear estimators for normalized robust risk under samplewise norm-bounded attacks.", "A uniform finite-dimensional theorem bounds its additive risk regret; it is not a risk-ratio guarantee.", "When the minimizing dual parameter is positive, anisotropic Gaussian input jitter implements the estimator exactly through population linear least squares.", "Under positive-noise active-estimation hypotheses, isotropic jitter suffices exactly for a flat positive spectrum; a rational two-band witness gives a strict gap otherwise." ], "reviews": [], "evidencePackage": "Self-contained analytic manuscript, exact rational two-band certificate, finite numerical checks, normal and optimized-wrapper internal replay, semantic negative controls, bounded source comparison and private internal AI-assisted assessment. No finite-sample learning experiment is claimed.", "openProblems": [], "mathObjects": [], "relatedWorks": [ { "citation": "Guan and Davenport, Distributionally Robust Gaussian Inverse Problems: source framework and proposed spectral rule.", "url": "https://arxiv.org/abs/2412.14407", "doi": "10.48550/arXiv.2412.14407" }, { "citation": "Standard Tikhonov and spectral regularisation literature supplies the inverse-problem background; the claimed contribution is the quantitative robust-risk and jitter characterisation in this model.", "url": "https://doi.org/10.1137/1.9781611971232", "doi": "10.1137/1.9781611971232" } ], "claimAssurance": null, "operatingModel": { "version": "1.0", "workId": "ep-work:robust-gaussian-inverse-estimation", "attemptIds": [ "ep-attempt:robust-gaussian-inverse-estimation-publication" ], "aims": [ "science" ], "artifactRoles": [ "research-output", "communication" ], "lineageId": null, "accelerationPrimitives": [ "structural-compression", "certificate-first", "adversarial-controls", "assurance-vector", "agent-readable-research-object" ], "decisionObject": { "type": "certificate", "description": "A spectral linear estimator, uniform additive regret bound and population jitter implementation with a strict two-band separation.", "scope": "Gaussian inverse model, samplewise norm-bounded attack and linear estimators; not finite-sample or nonlinear optimality." }, "bottleneckTargeted": [ "assurance", "publication" ], "semanticBridge": { "state": "explicit", "description": "The singular spectrum diagonalises the population linear risk; the robust dual rule maps to coordinatewise input-jitter variances when the minimizing dual parameter is positive.", "remainingRisks": [ "No finite-sample training theorem or experiment.", "No nonlinear-estimator comparison.", "Bounded source search is not proof of priority." ] }, "humanJudgmentGates": [ "Publication is authorised; practical estimator selection and external specialist scrutiny remain open." ], "parentLinks": [ { "relation": "depends-on-claim", "workId": null, "legacyReleaseSlug": null, "externalUrl": "https://arxiv.org/abs/2412.14407", "inheritedClaim": "Gaussian inverse-problem robust-risk framework and proposed spectral rule.", "inheritedAssuranceCeiling": "Preprint-level antecedent; reuse is not independent validation." } ], "assuranceTarget": { "dimensions": [ "independentRerun", "specialistReview", "formalVerification", "priorityAssessment" ], "nextAction": "Obtain unaffiliated proof reconstruction, then derive finite-sample learning guarantees before any empirical interpretation.", "claimCeiling": "Unrefereed population-level linear-estimator theory with finite and exact producer checks; no finite-sample, nonlinear, risk-ratio, empirical, formal-verification or exhaustive-priority claim." }, "impactClaims": [ { "id": "robust-inverse-no-impact", "aim": "science", "outcome": "Inspectable population-level robust-estimation theorem and boundary certificate", "setting": "AI-assisted theoretical research", "status": "NO_IMPACT_EVIDENCE", "designClass": "none", "comparator": "None registered.", "estimand": "No causal research-speed or estimator-performance effect estimated.", "evidenceRefs": [], "registeredDesignRef": null, "independentAssessment": null } ] }, "researchMetrics": { "schemaVersion": "1.0", "policyUrl": "https://evidencepress.org/api/research-metrics-policy.json", "outcomePolicyUrl": "https://evidencepress.org/api/v2/research-metrics-policy.json", "workLedgerUrl": "https://evidencepress.org/api/work-ledger.json", "claimCeiling": "These records describe scoped workflow inputs and outcomes. 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