ABSTRACT Title of dissertation: STATISTICAL MODELS AND OPTIMIZATION ALGORITHMS FOR HIGH-DIMENSIONAL COMPUTER VISION PROBLEMS

Data-driven and computational approaches are showing signicant promise in solving several challenging problems in various elds such as bioinformatics, nance and many branches of engineering. In this dissertation, we explore the potential of these approaches, specically statistical data models and optimization algorithms, for solving several challenging problems in computer vision. In doing so, we con-tribute to the literatures of both statistical data models and computer vision. In the context of statistical data models, we propose principled approaches for solving robust regression problems, both linear and kernel, and missing data matrix factor-ization problem. In computer vision, we propose statistically optimal and ecient algorithms for solving the remote face recognition and structure from motion (SfM) problems. The goal of robust regression is to estimate the functional relation between two variables from a given data set which might be contaminated with outliers. Under the reasonable assumption that there are fewer outliers than inliers in a dataset, we formulate the robust linear regression problem as a sparse learning problem