Signal Recovery by Stochastic Optimization
- Authors: Juditsky A.B.1, Nemirovski A.S.2
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Affiliations:
- LJK, Université Grenoble Alpes
- ISyE, Georgia Institute of Technology
- Issue: Vol 80, No 10 (2019)
- Pages: 1878-1893
- Section: Topical Issue
- URL: https://journal-vniispk.ru/0005-1179/article/view/151197
- DOI: https://doi.org/10.1134/S0005117919100084
- ID: 151197
Cite item
Abstract
We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimation problem is reduced to the problem of solving a stochastic monotone Variational Inequality (VI). The solution to the stochastic VI can be found in a computationally efficient way, and in the case when the VI is strongly monotone we derive finite-time upper bounds on the expected ‖ · ‖22 error converging to 0 at the rate O(1/K) as the number K of observation grows. Our structural assumptions are essentially weaker than those necessary to ensure convexity of the optimization problem resulting from Maximum Likelihood estimation. In hindsight, the approach we promote can be traced back directly to the ideas behind the Rosenblatt’s perceptron algorithm.
About the authors
A. B. Juditsky
LJK, Université Grenoble Alpes
Author for correspondence.
Email: aanatoli.juditsky@univ-grenoble-alpes.fr
France, Saint-Martin-d’Hères
A. S. Nemirovski
ISyE, Georgia Institute of Technology
Email: aanatoli.juditsky@univ-grenoble-alpes.fr
United States, Atlanta, Georgia
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