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Graph-based sparse learning: models, algorithms, and applications

Description

Sparse learning is a powerful tool to generate models of high-dimensional data with high interpretability, and it has many important applications in areas such as bioinformatics, medical image processing, and

Sparse learning is a powerful tool to generate models of high-dimensional data with high interpretability, and it has many important applications in areas such as bioinformatics, medical image processing, and computer vision. Recently, the a priori structural information has been shown to be powerful for improving the performance of sparse learning models. A graph is a fundamental way to represent structural information of features. This dissertation focuses on graph-based sparse learning. The first part of this dissertation aims to integrate a graph into sparse learning to improve the performance. Specifically, the problem of feature grouping and selection over a given undirected graph is considered. Three models are proposed along with efficient solvers to achieve simultaneous feature grouping and selection, enhancing estimation accuracy. One major challenge is that it is still computationally challenging to solve large scale graph-based sparse learning problems. An efficient, scalable, and parallel algorithm for one widely used graph-based sparse learning approach, called anisotropic total variation regularization is therefore proposed, by explicitly exploring the structure of a graph. The second part of this dissertation focuses on uncovering the graph structure from the data. Two issues in graphical modeling are considered. One is the joint estimation of multiple graphical models using a fused lasso penalty and the other is the estimation of hierarchical graphical models. The key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which reduces the size of the optimization problem, dramatically reducing the computational cost.

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Created

Date Created
  • 2014

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Novel statistical models for complex data structures

Description

Rapid advance in sensor and information technology has resulted in both spatially and temporally data-rich environment, which creates a pressing need for us to develop novel statistical methods and the

Rapid advance in sensor and information technology has resulted in both spatially and temporally data-rich environment, which creates a pressing need for us to develop novel statistical methods and the associated computational tools to extract intelligent knowledge and informative patterns from these massive datasets. The statistical challenges for addressing these massive datasets lay in their complex structures, such as high-dimensionality, hierarchy, multi-modality, heterogeneity and data uncertainty. Besides the statistical challenges, the associated computational approaches are also considered essential in achieving efficiency, effectiveness, as well as the numerical stability in practice. On the other hand, some recent developments in statistics and machine learning, such as sparse learning, transfer learning, and some traditional methodologies which still hold potential, such as multi-level models, all shed lights on addressing these complex datasets in a statistically powerful and computationally efficient way. In this dissertation, we identify four kinds of general complex datasets, including "high-dimensional datasets", "hierarchically-structured datasets", "multimodality datasets" and "data uncertainties", which are ubiquitous in many domains, such as biology, medicine, neuroscience, health care delivery, manufacturing, etc. We depict the development of novel statistical models to analyze complex datasets which fall under these four categories, and we show how these models can be applied to some real-world applications, such as Alzheimer's disease research, nursing care process, and manufacturing.

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Created

Date Created
  • 2012