THESIS
2014
xiv, 178 pages : illustrations ; 30 cm
Abstract
Modern data arising from various domains, such as audio, image and text, are often
high-dimensional and contain spurious features with various structures. In most cases, a
simple model is at a more favorable side than complicated ones, since it often provides
better generalization performance, together with intuitive interpretation.
The structured-sparsity-inducing regularizers are highly desirable in this case. In this
thesis, several extensions of existing sparse models are proposed, which can be used to
encourage feature selection in 1. groups; 2. hierarchy 3. graph; and 4. clusters.
As the resulted objectives are often challenging to optimize, due to the nonsmoothness
or even nonconvexity of the regularizers. To overcome this obstacle, I developed a set
of first-order algo...[
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Modern data arising from various domains, such as audio, image and text, are often
high-dimensional and contain spurious features with various structures. In most cases, a
simple model is at a more favorable side than complicated ones, since it often provides
better generalization performance, together with intuitive interpretation.
The structured-sparsity-inducing regularizers are highly desirable in this case. In this
thesis, several extensions of existing sparse models are proposed, which can be used to
encourage feature selection in 1. groups; 2. hierarchy 3. graph; and 4. clusters.
As the resulted objectives are often challenging to optimize, due to the nonsmoothness
or even nonconvexity of the regularizers. To overcome this obstacle, I developed a set
of first-order algorithms based on the proximal method for a wide range of structured
regularization problems, including convex and nonconvex objectives in both deterministic
or stochastic settings. Theoretically, these algorithms enjoy low per-iteration complexity
with convergence (rate) guarantee.
Experiments on a number of synthetic and real data sets demonstrate the advantage
of proposed models and the efficiency of developed algorithms.
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