Data-Efficient Quickest Change Detection with On-Off Observation Control

In this paper we extend the Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on-off observation control policy, that decides whether or not to take a given observation, along with the stopping time at which the change is declared, so as to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem, and using dynamic programming arguments, we obtain an \textit{a posteriori} probability based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal, i.e., the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves, and provides significant reduction in observation cost as compared to the naive approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.Comment: Preliminary version of this paper has been presented at ITA Workshop UCSD 201

Dynamics of Social Networks: Multi-agent Information Fusion, Anticipatory Decision Making and Polling

This paper surveys mathematical models, structural results and algorithms in controlled sensing with social learning in social networks. Part 1, namely Bayesian Social Learning with Controlled Sensing addresses the following questions: How does risk averse behavior in social learning affect quickest change detection? How can information fusion be priced? How is the convergence rate of state estimation affected by social learning? The aim is to develop and extend structural results in stochastic control and Bayesian estimation to answer these questions. Such structural results yield fundamental bounds on the optimal performance, give insight into what parameters affect the optimal policies, and yield computationally efficient algorithms. Part 2, namely, Multi-agent Information Fusion with Behavioral Economics Constraints generalizes Part 1. The agents exhibit sophisticated decision making in a behavioral economics sense; namely the agents make anticipatory decisions (thus the decision strategies are time inconsistent and interpreted as subgame Bayesian Nash equilibria). Part 3, namely {\em Interactive Sensing in Large Networks}, addresses the following questions: How to track the degree distribution of an infinite random graph with dynamics (via a stochastic approximation on a Hilbert space)? How can the infected degree distribution of a Markov modulated power law network and its mean field dynamics be tracked via Bayesian filtering given incomplete information obtained by sampling the network? We also briefly discuss how the glass ceiling effect emerges in social networks. Part 4, namely \emph{Efficient Network Polling} deals with polling in large scale social networks. In such networks, only a fraction of nodes can be polled to determine their decisions. Which nodes should be polled to achieve a statistically accurate estimates

An Effective Approach to Nonparametric Quickest Detection and Its Decentralized Realization

This dissertation focuses on the study of nonparametric quickest detection and its decentralized implementation in a distributed environment. Quickest detection schemes are geared toward detecting a change in the state of a data stream or a real-time process. Classical quickest detection schemes invariably assume knowledge of the pre-change and post-change distributions that may not be available in many applications. A distribution free nonparametric quickest detection procedure is presented based on a novel distance measure, referred to as the Q-Q distance calculated from the Quantile-Quantile plot. Theoretical analysis of the distance measure and detection procedure is presented to justify the proposed algorithm and provide performance guarantees. The Q-Q distance based detection procedure presents comparable performance compared to classical parametric detection procedure and better performance than other nonparametric procedures. The proposed procedure is most effective when detecting small changes. As the technology advances, distributed sensing and detection become feasible. Existing decentralized detection approaches are largely parametric. The decentralized realization of Q-Q distance based nonparametric quickest detection scheme is further studied, where data streams are simultaneously collected from multiple channels located distributively to jointly reach a detection decision. Two implementation schemes, binary quickest detection and local decision fusion, are described. Experimental results show that the proposed method has a comparable performance to the benchmark parametric cumulative sum (CUSUM) test in binary detection. Finally the dissertation concludes with a summary of the contributions to the state of the art