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This article is cited in 7 scientific papers (total in 7 papers)
Signal recovery by stochastic optimization
A. B. Juditskya, A. S. Nemirovskib a LJK, Université Grenoble Alpes, Saint-Martin-d’Hères, France
b ISyE, Georgia Institute of Technology, Atlanta, USA
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 $\|\cdot\|_2^2$ 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.
Keywords:
generalized linear models, statistical estimation problem, stochastic approximation, variational inequalities.
Received: 19.07.2018 Revised: 12.09.2018 Accepted: 08.11.2019
Citation:
A. B. Juditsky, A. S. Nemirovski, “Signal recovery by stochastic optimization”, Avtomat. i Telemekh., 2019, no. 10, 153–172; Autom. Remote Control, 80:10 (2019), 1878–1893
Linking options:
https://www.mathnet.ru/eng/at15369 https://www.mathnet.ru/eng/at/y2019/i10/p153
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Abstract page: | 242 | Full-text PDF : | 51 | References: | 25 | First page: | 15 |
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