Novel Statistical methods and applications in Quantum Computing, Biomedicine, and Networks for Big Data

With the rapid development of science and technology, large and complex data have been generated in many areas, such as social science, neuroscience, and biomedicine. The extraordinary amount of data revolutionize our conventional decision-making system. This new phenomenon poses significant challenges on current statistical research. Therefore, my primary research goals are to develop new theoretically justifiable and computationally efficient methods for tackling big data applications from a computational and modeling perspective. To achieve my goals, a novel non-oracular quantum adaptive search (QAS) method for the best subset selection problem is proposed as the first topic. QAS performs almost identically to the naive best subset selection method but reduces its computational complexity from $O(D)$ to $O(\sqrt{D}log_2{D})$, where $D=2^p$ is the total number of subset over $p$ covariates. The second topic focuses on a social network application. Drawing on the concepts of community and brokerage from network analysis, we argue that the network of nongovernmental organizations (NGOs) may reinforce power disparities and inequalities at the very same time that it improves access to global governance and provides social power. Finally, the third topic is about biomedicine. The novel statistical analysis is applied to the clinical research on Obstructive Sleep Apnea (OSA). We found that several soluble cytokine receptors are associated with OSA. These findings may facilitate developing new treatment/therapy for patients with OSA.