Events Calendar

AI SEMINAR

Speaker: Mahdi Soltanolkotabi, Assistant Professor at USC

Talk Title: Finding low-complexity models without the shackles of convexity

Series: AI Seminar

Abstract: In many applications, one wishes to estimate a large number of parameters from highly incomplete data samples. Low-dimensional models such as sparsity, low-rank, etc provide a principled approach for addressing the challenges posed by such high-dimensional data. The last decade has witnessed a flurry of activity in understanding when and how it is possible to find low complexity models via convex relaxations. However, the computational cost of such convex schemes can be prohibitive. In fact, in this talk I will argue that over insistence on convex methods has stymied progress in many application domains. I will discuss my ongoing research efforts to unshackle such problems from the confines of convexity opening the door for new applications.

I will discuss three concrete problems characterized by incomplete information about a low-complexity object of interest. The first is the century-old phase retrieval problem where one wishes to recover a signal from magnitude only measurements--phase information is completely missing. The second is a problem in data analysis, where we observe only a few incomplete linear measurements from a data matrix (e.g. a few entries) and wish to reliably infer all of the entries of the matrix. The third problem involves the recovery of a structured image from highly compressed information--most measurements are missing. To retrieve seemingly lost information I will present novel non-convex algorithms for these problems. Surprisingly, despite the lack of convexity these algorithms can provably converge to the global optimum and hence impute the missing information precisely.



Biography: Mahdi Soltanolkotabi completed his Ph.D. in electrical engineering at Stanford University in 2014. He was a postdoctoral researcher in the Algorithms, Machines, and People AMP lab and the EECS and Statistics departments at UC Berkeley during the 2014-2015 academic year. His research focuses on design and mathematical understanding of computationally efficient algorithms for optimization, high dimensional statistics, machine learning, signal processing and computational imaging. Recently, a main focus of his research has been on developing and analyzing algorithms for non-convex optimization with provable guarantees of convergence to the global optimum.

WILL NOT BE WEBCASTED

Host: Emilio Ferrara

Location: Information Science Institute (ISI) - 1135 - 11th fl Large CR

Audiences: Everyone Is Invited

Contact: Alma Nava / Information Sciences Institute