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In this paper, we consider the problem of quickly detecting an abrupt change in linear regression models. Specifically, an observer sequentially obtains a sequence of observations, whose underlying linear model changes at an unknown time. Moreover, the pre-change linear model is perfectly known by the observer but the post-change linear model is unknown. The observer aims to design an efficient online algorithm to detect the presence of the change via his sequential observations. Based on different assumptions on the change-point, both non-Bayesian and Bayesian problem formulations are considered. In the non-Bayesian setting, the change-point is modeled as a fixed but unknown constant. Two performance metrics, namely the worst case detection delay and the average run length to false alarm, are adopted to evaluate the performance of detection algorithms. In the Bayesian setting, the change-point is modeled as a geometrically distributed random variable. For this case, the average detection delay and the probability of false alarm are used as performance metrics. We propose a novel algorithm, namely the parallel-sum algorithm, for the purpose of change detection. For both setups, we show that the proposed algorithm has a low computational complexity while still offering a good performance in terms of the performance metrics of the respective setting. [ABSTRACT FROM AUTHOR]

Spectrum sensing is a key technology enabling the cognitive radio system. In this paper, the problem of how to quickly and accurately find an unoccupied channel from a large amount of potential channels is considered. The cognitive radio system under consideration is equipped with a narrow band sensor, hence it can only sense those potential channels in a sequential manner. In this scenario, we propose a novel two-stage mixed-observation sensing strategy. In the first stage, which is named as scanning stage, the sensor observes a linear combination of the signals from a pair of channels. The purpose of the scanning stage is to quickly identify a pair of channels such that at least one of them is highly likely to be unoccupied. In the second stage, which is called refinement stage, the sensor only observers the signal from one of those two channels identified from the first stage, and selects one of them as the unoccupied channel. The problem under this setup is an ordered two concatenated Markov stopping time problem. The optimal solution is solved using the tools from the multiple stopping time theory. It turns out that the optimal solution has a rather complex structure, hence a low complexity algorithm is proposed to facilitate the implementation. In the proposed low complexity algorithm, the cumulative sum test is adopted in the scanning stage and the sequential probability ratio test is adopted in the refinement stage. The performance of this low complexity algorithm is analyzed when the presence of unoccupied channels is rare. Numerical simulation results show that the proposed sensing strategy can significantly reduce the sensing time when the majority of potential channels are occupied. [ABSTRACT FROM PUBLISHER]

We consider linear regression problems for which the underlying model undergoes multiple changes. Our goal is to estimate the number and locations of change-points that segment available data into different regions, and further produce sparse and interpretable models for each region. To address challenges of the existing approaches and to produce interpretable models, we propose a sparse group Lasso based approach for linear regression problems with change-points. Under certain mild assumptions and a properly chosen regularization term, we prove that the solution of the proposed approach is asymptotically consistent. In particular, we show that the estimation error of linear coefficients diminishes, and the locations of the estimated change-points are close to those of true change-points. We further propose a method to choose the regularization term so that the results mentioned above hold. In addition, we show that the complexity of the proposed algorithm is much smaller than those of existing approaches. Numerical examples are provided to validate the analytical results. [ABSTRACT FROM PUBLISHER]