Nonconvex Approaches in Data Science

Applied Math And Analysis Seminar

Yifei Lou (UT Dallas)

Friday, August 3, 2018 -
3:00pm to 4:00pm
Physics 119

Although "big data" is ubiquitous in data science, one often faces challenges of "small data," as the amount of data that can be taken or transmitted is limited by technical or economic constraints. To retrieve useful information from the insufficient amount of data, additional assumptions on the signal of interest are required, e.g. sparsity (having only a few non-zero elements). Conventional methods favor incoherent systems, in which any two measurements are as little correlated as possible. In reality, however, many problems are coherent. I will present a nonconvex approach that works particularly well in the coherent regime. I will also address computational aspects in the nonconvex optimization. Various numerical experiments have demonstrated advantages of the proposed method over the state-of-the-art. Applications, ranging from super-resolution to low-rank approximation, will be discussed.

Last updated: 2019/02/17 - 2:17pm