Paul Grigas (Massachusetts Institute of Technology)'s paper, titled "A new perspective on boosting in linear regression via subgradient optimization and relatives" (jointly authored with Robert M. Freund and Rahul Mazumder) has been selected as the recipient of the 2015 INFORMS Optimization Society Student Paper Prize. This research lies at the intersection of optimization and statistics and presents a comprehensive analysis of some classical boosting algorithms in linear regression from the perspective of first-order methods in convex optimization. In the paper, the authors show that standard boosting schemes such as Forward Stagewise epsilon (or FS ) and least squares boosting (LS-(eps)) can be viewed as instances of subgradient-based first-order methods, when the objective is suitably chosen. Viewing such schemes through a convex optimization lens, the authors derive comprehensive convergence rate statements as well as obtain insights into the trade -off between statistical properties such as data fidelity and computation cost. Moreover, they show that Least Absolute Shrinkage and Selection Operator (LASSO) can be viewed as a minor modification of the FS scheme. They substantiate many of their insights through detailed numerics on real and on synthetic data. Collectively, this paper paves the way for a novel unified understanding of various regression methods via first-order techniques. In summary, the committee felt that this paper refines and clarifies the relationship between well-studied regression schemes and first-order convex optimization algorithms in a novel and elegant way. We expect this work to endure and to continue to guide the development of optimization algorithms for statistical applications.
Ruoyu Sun (Stanford University), for his paper "Guaranteed matrix completion via non-convex factorization", co-authored with Zhi-Quan Luo.
Shimrit Shtern (Technion - Israel Institute of Technology), for her paper "A semi-definite programming approach for robust tracking", co-authored with Aharon Ben-Tal.
Mohit Tawarmalani (chair), Fatma Kılınç-Karzan, Warren Powell, Uday Shanbhag