Convex Programming for Statistical Estimation: A New Perspective
Date/Time:20 Jan 2020 15:00
Venue: S17 #04-06 SR1
Speaker: Sohail Bahmani, Georgia Institute of Technology
Convex Programming for Statistical Estimation: A New Perspective
A critical aspect of statistical procedures in many engineering and scientific applications is their computational efficiency. Convex programming provides a versatile framework to design computationally tractable algorithms for many statistical tasks such as regression, classification, and variable selection. The estimation procedures based on convex programming are traditionally designed independent of the statistical model. We will discuss new approaches that use the statistical model to design estimators with convex formulations. These approaches can be applied in a broader set of problems and be computationally favourable.
In particular, we consider a broad class of parametric regression problems where the signal is observed through random nonlinear functions with a difference of convex (DC) form. This general statistical model includes familiar special cases such as phase retrieval/quadratic regression and blind deconvolution/bilinear regression. Given the DC decomposition of the observation functions as well as an approximate solution, we formulate a convex program as an estimator that operates in the natural space of the signal. In the mentioned special cases, the proposed approach is computationally superior to the methods based on semidefinite/sum-of-squares relaxation—tailored for polynomial observation functions—and can compete with the non-convex methods. Under some regularity assumptions, the proposed convex estimators achieve a desirable sample complexity.
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