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2019 Estimation from nonlinear observations via convex programming with application to bilinear regression
Sohail Bahmani
Electron. J. Statist. 13(1): 1978-2011 (2019). DOI: 10.1214/19-EJS1567

Abstract

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of nonlinear regression problems that involve difference of convex(DC) nonlinearities. The proposed method can be viewed as a significant extension of the “anchored regression” method formulated and analyzed in [10] for regression with convex nonlinearities. Our main assumption, in addition to other mild statistical and computational assumptions, is availability of a certain approximation oracle for the average of the gradients of the observation functions at a ground truth. Under this assumption and using a PAC-Bayesian analysis we show that the proposed estimator produces an accurate estimate with high probability. As a concrete example, we study the proposed framework in the bilinear regression problem with Gaussian factors and quantify a sufficient sample complexity for exact recovery. Furthermore, we describe a computationally tractable scheme that provably produces the required approximation oracle in the considered bilinear regression problem.

Citation

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Sohail Bahmani. "Estimation from nonlinear observations via convex programming with application to bilinear regression." Electron. J. Statist. 13 (1) 1978 - 2011, 2019. https://doi.org/10.1214/19-EJS1567

Information

Received: 1 June 2018; Published: 2019
First available in Project Euclid: 19 June 2019

zbMATH: 07080066
MathSciNet: MR3964268
Digital Object Identifier: 10.1214/19-EJS1567

Subjects:
Primary: 62F10, 90C25
Secondary: 62P30

JOURNAL ARTICLE
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Vol.13 • No. 1 • 2019
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