Title:
Robust Statistical Inference Through the Lens of Optimization
Robust Statistical Inference Through the Lens of Optimization
Author(s)
Xie, Liyan
Advisor(s)
Xie, Yao
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Abstract
Statistical signal processing and hypothesis testing are fundamental problems in modern data science and engineering applications. This thesis mainly focuses on developing new theories and algorithms for three research problems in the area of robust statistical inference. The first problem we study is sequential change detection. We consider the subspace change for the covariance matrix of high-dimensional data sequences, which is a fundamental problem since subspace structure is commonly used for modeling high-dimensional data. We also consider a non-parametric setting that can be useful when the data distributions cannot be easily represented by simple parametric families, and the weighted L2 divergence is proposed to detect the change. The second problem we study is data-driven robust hypothesis testing when the true data-generating distributions are all unknown and we only have access to a limited number of training samples. A strong duality result is proved and used to find the robust optimal test by convex optimization. The third problem is parameter recovery for spatio-temporal models by solving variational inequalities, with an application example in modeling crime events.
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Date Issued
2021-05-20
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Text
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Dissertation