Estimation from Indirect Observations Under Stochastic Uncertainty in Observation Matrix

Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines—the much-studied linear estimate originating from Kuks and Olman (Iswestija Akademija Nauk Estonskoj SSR 20:480–482, 1971) and polyhedral estimate introduced in Juditsky and Nemirovski...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 205; no. 3; p. 56
Main Authors Bekri, Yannis, Juditsky, Anatoli, Nemirovski, Arkadi
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2025
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convex analysis
Convexity
Engineering
Estimates
Inverse problems
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Parameter estimation
Recovery
Risk
Robustness
Statistical inference
Theory of Computation
Uncertainty
Statistical linear inverse problems
90C90
Robust estimation
Observation matrix uncertainty
62F35
62G35
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Summary:Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines—the much-studied linear estimate originating from Kuks and Olman (Iswestija Akademija Nauk Estonskoj SSR 20:480–482, 1971) and polyhedral estimate introduced in Juditsky and Nemirovski (Electron J Stat 14(1):458–502, 2020). It was shown in Juditsky and Nemirovski (Statistical inference via convex optimization, Princeton University Press, Princeton, 2020) that risk of these estimates can be tightly upper-bounded for a wide range of a priori information about the model through solving a convex optimization problem, leading to a computationally efficient implementation of nearly optimal estimates of these types. The subject of the present paper is design and analysis of linear and polyhedral estimates which are robust with respect to the stochastic uncertainty in the observation matrix. In this setting, we show how to bound the estimation risk by the optimal value of an efficiently solvable convex optimization problem; “presumably good” estimates are then obtained through optimization of the risk bounds with respect to estimate parameters.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02678-5