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  -