Quickest statistical inference over networked data

Abstract

There exists a line of study in which the decision-making and data acquisition processes are decoupled and the focus is placed on forming the most reliable decisions based on a given set of data samples. These approaches lack efficiency when facing large networks and high dimensional data, in which data acquisition incurs substantial communication, sensing, and decision delay costs. Driven by controlling such costs, it is imperative to determine the fundamentally minimum number of measurements for forming decisions with desired reliability and characterize the attendant sampling strategies. Such sampling strategies over networks are specified by the number of samples to be collected, as well as the order in which they should be collected.

In this dissertation, we consider two paradigms; static networks, in which the states of the agents remain the same throughout the data collection and inference processes, and dynamic networks, where at some unknown time instant during the monitoring process the state of the network changes and we want to detect such changes with minimum delay. For static networks, we start by considering a setting in which each agent is either normal or an outlier according to a dependency kernel and aim to detect an outlier agent with the minimum number of samples by performing a linear search. Then we extend the results to the setting in which the dependency kernel parameters are unknown, and the goal is to estimate these parameters besides detecting the outliers. Also, we consider detection of local and global correlation structures hidden in a network via data-adaptive data collection techniques. For dynamic networks, we first consider a fully sequential change-point detection under the sampling budget constraint. Specifically, we assume that only a subset of the agents can be observed at each time instant and we want to characterize the optimal sampling strategy as well as the change-point detection rules. Next, we consider a setting in which the network undergoes multiple changes and aim to detect one of those changes in a short window after the change. This is in contrast to the previous setting in which we want to minimize the delay in detecting the change, but the delay can go to infinity. For each problem, fully dynamic data collection strategies are designed through sequential analysis and the number of samples, the order of sampling and the final decision rules (detection or estimation action) are characterized.

Sequential methods have been studied extensively for analyzing one information source that generates a time series of data. When facing networks of information sources, the existing literature usually treats each constituent module as an independent source of data. The goal of this dissertation is to extend the state of the art to the networked-data and develop new tools for analyzing such interacting modules by accounting for their underlying dependency structures.

In this dissertation, we develop data-adaptive decision-making strategies for performing statistical learning and inference tasks over networked-data. Driven by advances in information sensing and data acquisition, many application domains have evolved towards networks of interconnected information sources, which are constantly processed for various decision-making purposes. Induced by their physical couplings, such sources generate data streams that often follow a dependency kernel. The couplings and the associated dependency kernels can represent, for instance, the adjacency of modules in physical networks, the interaction of subscribers in social networks, or the electrical connectivity of buses in power grids. Determining and leveraging the co-dependence of data in such networks significantly influences the design of inference rules, which makes it imperative to incorporate the dependency kernels into the decision rules. Also, inference over a network becomes more efficient by accounting for such correlation structures.