Statistical Learning and Modeling: Methodology and Algorithm

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My research program focuses on developing new statistical tools to analyze, model, and interpret complex systems such as human dynamics and high-dimensional multimodal data arising from medical research. This research lies at the intersection of modern statistical learning and "traditional" statistical ideas. This proposed research has two research directions: (1) Develop efficient statistical models and algorithms for describing, analyzing and interpreting human behaviour data, such as e-mail communication, emergency calls etc.; (2) Develop automated statistical learning tools for analyzing high dimensional multimodal data. The ultimate goal of the first research direction is to propose a flexible model, which does not require domain knowledge and is interpretable. The short term objectives we want to accomplish over the next five years include: (1) Extend the current nonparametric self-exciting point process, i.e., a model incorporates both spatial and temporal information besides modeling exciting and bursts phenomena, to have a branch coefficient function depending on location and time in order to satisfy real world conditions; (2) An Expectation Maximization based local log likelihood estimation will be proposed to reduce computational cost in estimating background and triggering functions in nonparametric self-exciting point processes; (3) Further, a short-term forecast algorithm for nonparametric self-exciting point processes will be developed to predict the time and number of the occurrence of future events. To overcome the difficulties in analyzing high-dimensional multimodal data from multiple sources, in the second research direction, we propose to develop a hybrid approach that interactively combines methods from statistics, computational topology and deep learning. The proposed research includes three short-term objectives: (1) Analysis of craniofacial morphology in 3D facial imaging; (2) Analysis of multivariate time series; (3) Joint analysis of structured and unstructured to structured data. The methods developed in the first research direction can be easily adapted and applied to other areas such as social networks and terrorist data. The new model developed in the second research direction will potentially enhance the diagnostic accuracy of Obstructive Sleep Apnea patients and lead to the development of new tools to analyze high-dimensional multimodal datasets arising in other research areas.