Novel statistical models for complex data structures
Jing Li, Shuai Huang · 2012
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 lay in their complex structures, such as high-dimensionality, hierarchy, multi-modality, heterogeneity and 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 in a statistically powerful and computationally efficient way. In this dissertation, we identify four kinds of general complex 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 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.