Density Estimation and Anomaly Detection in Large Social Networks

Abstract

Abstract : High-velocity streams of high-dimensional data pose significant big data analysis challenges across a range of applications and settings, including large-scale social network analysis. Online learning and online convex programming play a significant role in the rapid recovery of important or anomalous information from these large data streams. While recent advances in online learning have led to novel and rapidly converging algorithms, these methods are unable to adapt to non-stationary environments arising in real-world settings. This paper describes a dynamic mirror descent framework which addresses this challenge, yielding low theoretical regrets bounds and accurate, adaptive, and computationally efficient algorithms which are applicable to broad classes of problems. The methods are capable of learning and adapting to the underlying and possibly time-varying dynamics of a system or environment. Empirical results in the context of social network tracking, dynamic texture analysis, sequential compressed sensing of a dynamic scene, and tracking self-exciting point processes support the core theoretical findings.