##### Department of Mathematics,

University of California San Diego

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### Final Defense

## Yuchao Liu

#### UCSD

## Detection and Localization of a Submatrix: Theory, Methods and Algorithms

##### Abstract:

We consider the problem of detecting and localizing an submatrix with larger-than-usual entries inside a large, noisy matrix. This problem arises from analysis of data in genetics, bioinformatics, and social sciences. We consider that entries of the data matrix are independently following distributions from a natural exponential family, which generalizes the common Gaussian assumptions in the literature. Distribution-free methods of detection and size-adaptive methods of both detection and localization problems are studied with their asymptotic behaviors illustrated.

Advisor: Ery Arias-Castro

### March 2, 2018

### 9:00 AM

### AP&M 5829

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