2026-09-20T06:57:27Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/121209 2023-12-11 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

Yang, Yun Yang, Yun Chen, Xiaohui Liang, Feng Zhu, Ruoqing 2023-08 application/pdf en text Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2025-08-01 The student, Yifan Chen, accepted the attached license on 2023-07-06 at 20:10. The student, Yifan Chen, submitted this Dissertation for approval on 2023-07-06 at 20:11. This Dissertation was approved for publication on 2023-07-12 at 07:03. DSpace SAF Submission Ingestion Package generated from Vireo submission #19473 on 2023-12-04 at 17:30:32 This dissertation investigates the improvement and the application of subsampling sketching, a dimension reduction technique, in various statistical contexts. Firstly, we propose a framework, accumulative sketching, which encompasses Gaussian sketching and subsampling sketching as special cases, for approximate matrix multiplication (AMM). Theoretical analysis and empirical experiments demonstrate that our approach achieves a balance between computational efficiency and statistical accuracy, enhancing tasks such as generalized linear regression, randomized SVD, and kernel ridge regression. Furthermore, we develop efficient algorithms for accurately approximating statistical leverage scores in kernel ridge regression, resulting in significant improvements in efficiency of subsampling sketching compared to existing methods. We extend this technique to empirical risk minimization in reproducing kernel Hilbert spaces (RKHS), ensuring the adaptation maintains the minimax-optimal error rate of kernel estimators. Overall, our research offers potent tools for efficiently computing large-scale matrices via subsampling sketches in various settings while still preserving the statistical accuracy. Text eng https://hdl.handle.net/2142/121209 Copyright 2023 Yifan Chen Efficient matrix computations via subsampling sketches Chen, Yifan 2023-07-12 Sketching Approximate Matrix Multiplication Randomized Algorithms Kernel Methods Importance Sampling Ph.D. Dissertation Statistics University of Illinois at Urbana-Champaign Statistics