Past Event: PhD Dissertation Defense

Yijun Dong Dissertation: Randomized Dimension Reduction with Statistical Guarantees

Yijun Dong, Ph.D. student in Computational Science, Engineering, and Mathematics at the Oden Institute of UT Austin, co-advised by Prof. Per-Gunnar Martinsson and Prof. Rachel Ward

Abstract

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model complexity, as well as the non-negligible workload of data pre-processing, also bring formidable costs to such successes in both computation and data aggregation. As the deceleration of Moore’s Law slackens the cost reduction of computation from the hardware level, fast heuristics for expensive classical routines and efficient algorithms for exploiting limited data are increasingly indispensable for pushing the limit of algorithm potency. This thesis explores some of such algorithms for fast execution and efficient data utilization. 

From the computational efficiency perspective, we design and analyze fast randomized low-rank decomposition algorithms for large matrices based on “matrix sketching”, which can be regarded as a dimension reduction strategy in the data space. These include the randomized pivoting-based interpolative and CUR decompositions and the randomized subspace approximations.

From the sample efficiency perspective, we focus on learning algorithms with various incorporations of data augmentation that improve generalization and distributional robustness provably. Specifically, we start by presenting a sample complexity analysis for data augmentation consistency regularization where we view sample efficiency from the lens of dimension reduction in the function space. Then, we introduce an adaptively weighted data augmentation consistency regularization algorithm for distributionally robust optimization with applications in medical image segmentation.

 

Biography

Yijun Dong is a Ph.D. student in Computational Science, Engineering, and Mathematics at the Oden Institute of UT Austin, co-advised by Prof. Per-Gunnar Martinsson and Prof. Rachel Ward. Her primary research interests lie in randomized numerical linear algebra and statistical learning theory; while her thesis focuses on randomized pivoting-based matrix skeleton selection, randomized subspace approximation, as well as data augmentation for generalization and distributionally robust optimization.