The investigator develops new regularization and optimization techniques for high dimensional data that arise from frontiers of biological, medical and scientific research. Four interrelated research topics are proposed for investigation. First, the functional sparse inference for functional magnetic resonance imaging data in neuroscience is proposed for more accurate localization of brain areas in response to the time-varying stimuli. Second, the investigator develops curvature-based shape analysis for high-dimensional space curves with applications to comparing biological shapes, detecting key anatomical regions which exhibit shape difference, and classifying functional data objects. Third, the investigator studies unified theory and methodology for regularized parametric and nonparametric estimators under a general class of loss functions. Fourth, a high-dimensional pseudo logistic regression and classification approach is proposed which simultaneously combines the strengths of both support vector machine and traditional logistic regression.
High-dimensional data sets and streams arising from bioinformatics, environment, financial markets, and signal and image processing pose numerous challenges to conventional statistical methods. A major goal of the proposal is to make methodological and theoretical contributions to the important and challenging regularization approach in the analysis of high-dimensional data, like spatio-temporal fMRI brain images, functional data objects and gene expression profiles. These new developments allow scientists to analyze high-dimensional data with efficient dimension reduction and increased interpretability. In addition, the investigator will integrate new computational tools and mathematical theories with those in sciences and engineering. Dissemination of these developments will enhance new knowledge discoveries and prudent policy making, and strengthen interdisciplinary collaborations. The research will also serve an educational purpose through multi-disciplinary courses on the contemporary state-of-the-art data mining and machine learning, and benefit the training and learning of undergraduate, graduate students and underrepresented minorities.
