Learning with Asymmetry, High Dimension and Social Networks

Abstract

Yes or no is perhaps the most common answer we provide each day. Indeed, binary answers to well structured questions are the building blocks of our knowledge. I started my research career in drafting such answers in various circumstances within the domains of statistics and machine learning. From statisticians and computer scientists' point of view, classification is a well defined field. But more broadly, discretization is a powerful convention to help us understand the real-world social, economic and scientific situations. Also, the clean and tractable finite sample results from classification literature motivates me to investigate the explicit interplay among parameters in other fields. In this essay, I include my selected works regarding binary status in high dimensional statistics, statistical learning theory and social networks. In the first chapter, I introduce Regularized Optimal Affine Discriminant (ROAD), a high dimensional classification method explicitly using covariance information. In the second chapter, novel performance bounds of oracle type for asymmetric errors under the Neyman-Pearson context are derived. In the third chapter, I study the problem of information aggregation in social networks, where the focus is to determine aggregate learning status in any finite population network.