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As communication and control systems become more complex, connected and process data at higher velocities, detecting changes in patterns becomes increasingly difficult yet still crucial to guarantee a level of QoS, security, reliability etc.For large systems, usually there are many modes of failure and they are also prone to attacks from different surfaces. Still, there are numerous zero-day vulnerabilities that are unidentified until they cause a fault or are exploited. Change detection with unknown distributions provides a way of detecting the occurrence of faults or the gain of access by malicious parties by comparing the time series system features to their norm.In a wide variety of the applications, on the other hand, it is feasible to assume a certain level of knowledge of the system before the effect takes place and utilizing the knowledge of initial conditions increases the detection performance.With an ever increasing data rate and connectivity, any change in the observed process has to be detected on the fly before it is outdated, without the necessity to store and with a small blast radius for malicious activities. A delay in real time change detection may result in QoS disruption, cyber-physical threats and inability to contain the spread of a disease. So, minimal computational complexity is a key ingredient for modern change detection algorithms.In this dissertation, we assume non-Bayesian change detection problems under a finite alphabet with varying change point and cost models and with unknown post-change distributions. We focus on robust detection algorithms that utilize the knowledge of pre-change system dynamics and are of low complexity.Given that the effect of the change on the system is unknown, the distribution of observations may divert in many ways without much structure, whereas, before the change point, a false alarm is structured by Sanov's theorem, following a particular sample path. The proposed methods characterize the most likely alarms when there is no change present and test the observations, relative to the identified distributions.Throughout, we change the problem setting from a single node to networks where both the subset of sensors undergoing a change and the local post-change distributions are unknown and from detecting stationary permanent changes to detecting dynamic changes.For each problem studied, we prove asymptotic performance guarantees and compare our algorithms theoretically with the bounds in the literature. Then, we empirically contrast our methods on synthetic problems with alternative methods like finite moving average method, generalized likelihood ratio test, M-statistic kernel algorithm and identifying least favorable distributions.We also apply our new tools to real world problems. Towards this aim, exogenous factors like crises in the stock market and the oil industry and anthropogenic affects on the slowly changing climate provide satisfying examples of changes that can only be detected by assuming an unknown system model after the change.Finally, we emphasize future directions of work where we believe new ideas would make the greatest impact. |
