Regularization methods and algorithms for noisy output signals and high-dimensional input vectors
- Input-output models with high-dimensional input vectors arise in many applications, such as microarray technology and portfolio risk management, where the dimensionality of the input vectors far exceeds the sample size. Noise in the output signals further complicates the fitting of these models. There has been a large literature to address the computational and statistical difficulties in fitting these models by using regularization methods. After a brief review of the regularization methods in the literature, we develop a new hybrid of L1 and L2 penalties and demonstrate its advantages over a previous proposal, the elastic net, to combine the L1 and L2 penalties. The statistical theory underlying the hybrid penalty is used to show when and how it can provide improvement over existing methods. We use recent advances in convex optimization to implement the proposed method and carry out simulation studies to compare its performance with other methods.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Management Science and Engineering
|Lai, T. L
|Lai, T. L
|Statement of responsibility
|Submitted to the Department of Management Science and Engineering.
|Thesis (Ph.D.)--Stanford University, 2012.
- © 2012 by Hongsong Yuan
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
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