Topics in sparse multivariate statistics
- In this thesis, we visit three topics in modern sparse multivariate analysis that has received and still continues to receive significant interest in applied statistics in recent years: (a) Sparse high dimensional regression (This work appears in our paper Mazumder et al 2010.); (b) Low-rank matrix completion \& collaborative filtering (This work appears in our paper Mazumder et al 2011) and (c) Sparse undirected gaussian graphical models. (This work appears in our papers Mazumder and Hastie 2012 and Mazumder and Hastie 2011). A main challenge in high dimensional multivariate analysis is in developing scalable and efficient algorithms for large scale problems that naturally arise in scientific and industrial applications. This thesis explores the computational challenges that arise in these problems. We develop and analyze statistically motivated algorithms for various models arising in the aforementioned areas. This enhances our understanding of algorithms, sheds novel insights on the statistical problems and leads to computational strategies that appear to outperform state of the art. A salient feature of this work lies in the exchange of ideas and machinery across the fields of statistics, machine learning, (convex) optimization and numerical linear algebra.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Statistics
|Statement of responsibility
|Submitted to the Department of Statistics.
|Thesis (Ph.D.)--Stanford University, 2012.
- © 2012 by Rahul Mazumder
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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