The theory of trackability and robustness for process detection

Many applications of current interests involve detecting instances of processes from databases or streams of sensor reports. Detecting processes relies on identifying evidences for the existence of such processes from usually noisy and incomplete observable events through statistical inferences. The performance of inferences can vary dramatically, depending on the complexity of processes' behavioral patterns, sensor resolution and sampling rate, SNR, location and coverage, and so on. Stochastic models are mathematical representations of all these factors. In this dissertation, we intend to answer the following questions: (1) Performance—How accurate are the inference results given the model? (2) Trackability—What are the boundaries of the performance of inferences? (3) Robustness—How sensitive is the performance of inferences to perturbations on input data or model parameters? (4) Methodology—How can we improve the trackability and robustness of process detection? From the information theoretic point of view, we address the reason of errors in detection to the losses of source information during the sensing stage, measured as entropy in the Shannon sense. We propose a series of entropic measures of the trackability and robustness for a popular modeling technique—hidden Markov models (HMM). Our major contributions include: the theory of trackability; structural analysis of trackability for HMMs through its non-parametric counterpart—DFA/NFAs; an effective visualization method for analyzing the trackability for HMMs—the Tracking Characteristic Curves (TCC); a series of polynomial time algorithms to compute the proposed measures; a clustering approach for efficient hypothesis management ; and many other results. Our results are evaluated by mathematical analysis and/or numerical simulations.