2014 Theses Doctoral
Convex Optimization Algorithms and Recovery Theories for Sparse Models in Machine Learning
Sparse modeling is a rapidly developing topic that arises frequently in areas such as machine learning, data analysis and signal processing. One important application of sparse modeling is the recovery of a high-dimensional object from relatively low number of noisy observations, which is the main focuses of the Compressed Sensing, Matrix Completion(MC) and Robust Principal Component Analysis (RPCA) . However, the power of sparse models is hampered by the unprecedented size of the data that has become more and more available in practice. Therefore, it has become increasingly important to better harnessing the convex optimization techniques to take advantage of any underlying "sparsity" structure in problems of extremely large size.
This thesis focuses on two main aspects of sparse modeling. From the modeling perspective, it extends convex programming formulations for matrix completion and robust principal component analysis problems to the case of tensors, and derives theoretical guarantees for exact tensor recovery under a framework of strongly convex programming. On the optimization side, an efficient first-order algorithm with the optimal convergence rate has been proposed and studied for a wide range of problems of linearly constraint sparse modeling problems.
- Huang_columbia_0054D_11915.pdf binary/octet-stream 908 KB Download File
More About This Work
- Academic Units
- Industrial Engineering and Operations Research
- Thesis Advisors
- Goldfarb, Donald
- Ph.D., Columbia University
- Published Here
- July 7, 2014