Statistical Estimation from Dependent and Adversarial Data

Abstract

This thesis studies learning and estimation from data that is not independent, but rather falls into one of the following categories: (1) Data with strong correlations, such as social network correlations and data over a spatial domain or a temporal domain; and (2) Adversarial time series data, where the algorithm can possibly influence future data points in an adversarial manner. I will define mathematical models and learning problems that aim to capture these scenarios and describe polynomial-time algorithms to solve them. For (1), I will define the learning problem as a problem of learning Ising models and present algorithms to learning Ising models under different contexts. For (2), I will use the formulation of adversarial streaming algorithms by Ben-Eliezer and Yogev [2020] and present a tight analysis.