##### Department of Mathematics,

University of California San Diego

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### Colloquium Seminar

## Dr. Lijun Ding

#### University of Wisconsin, Madison

## Optimization for statistical learning with low dimensional structure: regularity and conditioning

##### Abstract:

Many statistical learning problems, where one aims to recover an underlying low-dimensional signal, are based on optimization, e.g., the linear programming approach for recovering a sparse vector. Existing work often either overlooked the high computational cost in solving the optimization problem, or required case-specific algorithm and analysis -- especially for nonconvex problems. This talk addresses the above two issues from a unified perspective of conditioning. In particular, we show that once the sample size exceeds the intrinsic dimension of the signal, (1) a broad range of convex problems and a set of key nonsmooth nonconvex problems are well-conditioned, (2) well-conditioning, in turn, inspires new algorithm designs and ensures the efficiency of many off-the-shelf optimization methods.

Host: Rayan Saab

### December 12, 2023

### 3:00 PM

APM 6402

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