Sparse learning problems, known as feature selection problems or variable selection problems, are a popular branch in the field of statistical learning. When faced with a dataset with only a few observations but a large number of features, we are interested in extracting the most useful features automatically by solving an optimization problem. In this dissertation, we start by introducing a novel penalty function as well as an iterative reweighted algorithm to solve the group sparsity problem, a special type of feature selection problems. The penalty function, named group LOG, shows a better ability to recover the ground-truth compared to other existing penalty functions in some datasets. Then, we propose a generalized formulation for a non-overlapping group sparsity problem that can be reduced to many existing works and provide the related algorithm by applying the alternating direction method of multipliers (ADMM) framework. In the end, we investigate a class of difference-of-convex (DC) programs that includes feature selection problems. Not only do we exhibit an exact algorithm for such problems, but we also design an inexact algorithm, which allows early termination in each iteration and justifies the stopping criteria in practice.
Operations Research and Engineering Management
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This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Ke, Chengyu, "Nonconvex optimization for statistical learning with structured sparsity" (2023). Operations Research and Engineering Management Theses and Dissertations. 22.
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