Date of Award
Doctor of Philosophy (PhD)
Electrical Engineering and Computer Science
Date driven, Detection, Nonparametric
The major goal of signal detection is to distinguish between hypotheses about the state of events based on observations. Typically, signal detection can be categorized into centralized detection, where all observed data are available for making decision, and decentralized detection, where only quantized data from distributed sensors are forwarded to a fusion center for decision making. While these problems have been intensively studied under parametric and semi-parametric models with underlying distributions being fully or partially known, nonparametric scenarios are not well understood yet. This thesis mainly explores nonparametric models with unknown underlying distributions as well as semi-parametric models as an intermediate step to solve nonparametric problems.
One major topic of this thesis is on nonparametric decentralized detection, in which the joint distribution of the state of an event and sensor observations are not known, but only some training data are available. The kernel-based nonparametric approach has been proposed by Nguyen, Wainwright and Jordan where sensors' quality is treated equally. We study heterogeneous sensor networks, and propose a weighted kernel so that weight parameters are utilized to selectively incorporate sensors' information into the fusion center's decision rule based on quality of sensors' observations. Furthermore, weight parameters also serve as sensor selection parameters with nonzero parameters corresponding to sensors being selected. Sensor selection is jointly performed with decision rules of sensors and the fusion center with the resulting optimal decision rule having only a sparse number of nonzero weight parameters. A gradient projection algorithm and a Gauss-Seidel algorithm are developed to solve the risk minimization problem, which is non-convex, and both algorithms are shown to converge to critical points.
The other major topic of this thesis is composite outlier detection in centralized scenarios. The goal is to detect the existence of data streams drawn from outlying distributions among data streams drawn from a typical distribution. We study both the semi-parametric model with known typical distribution and unknown outlying distributions, and the nonparametric model with unknown typical and outlying distributions. For both models, we construct generalized likelihood ratio tests (GLRT), and show that with the knowledge of the KL divergence between the outlier and typical distributions, GLRT is exponentially consistent (i.e, the error risk function decays exponentially fast). We also show that with the knowledge of the Chernoff distance between the outlying and typical distributions, GLRT for semi-parametric model achieves the same risk decay exponent as the parametric model, and GLRT for nonparametric model achieves the same performance when the number of data streams gets asymptotically large. We further show that for both models without any knowledge about the distance between distributions, there does not exist an exponentially consistent test. However, GLRT with a diminishing threshold can still be consistent.
Wang, Weiguang, "Data Driven Nonparametric Detection" (2016). Dissertations - ALL. 531.