TY - GEN AB - For high-dimensional data, two of the most important questions are the question of algorithmic optimality, which asks for the optimal algorithm within a certain class of computationally feasible procedures, and the question of statistical optimality, which asks for the optimal statistical procedure under a generating model. In this thesis the question of algorithmic optimality is investigated for the class of iterative thresholding algorithms on sparse and low rank structures under the framework of restricted optimality. The question of statistical optimality is investigated for the high-dimensional sparse changepoint detection problem and the contaminated density estimation problem under the minimax framework. AD - University of Chicago AU - Liu, Haoyang DA - 2020-08 DO - 10.6082/uchicago.2593 DO - doi ED - Rina F. Barber ED - Chao Gao ED - Mihai Anitescu ID - 2593 KW - Statistics KW - minimax KW - nonconvex KW - optimal L1 - https://knowledge.uchicago.edu/record/2593/files/Liu_uchicago_0330D_15373.pdf L2 - https://knowledge.uchicago.edu/record/2593/files/Liu_uchicago_0330D_15373.pdf L4 - https://knowledge.uchicago.edu/record/2593/files/Liu_uchicago_0330D_15373.pdf LA - eng LK - https://knowledge.uchicago.edu/record/2593/files/Liu_uchicago_0330D_15373.pdf N2 - For high-dimensional data, two of the most important questions are the question of algorithmic optimality, which asks for the optimal algorithm within a certain class of computationally feasible procedures, and the question of statistical optimality, which asks for the optimal statistical procedure under a generating model. In this thesis the question of algorithmic optimality is investigated for the class of iterative thresholding algorithms on sparse and low rank structures under the framework of restricted optimality. The question of statistical optimality is investigated for the high-dimensional sparse changepoint detection problem and the contaminated density estimation problem under the minimax framework. PB - University of Chicago PY - 2020-08 T1 - Algorithmic and Statistical Optimality for High-Dimensional Data TI - Algorithmic and Statistical Optimality for High-Dimensional Data UR - https://knowledge.uchicago.edu/record/2593/files/Liu_uchicago_0330D_15373.pdf Y1 - 2020-08 ER -