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Abstract:
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We consider the problem of change point detection for Self-Exciting Point Processes (SEPP). SEPPs are commonly used to model data from biological neural networks, crime event data across multiple regions, and a variety of other scientific studies. In these scenarios, we observe a collection of discrete events at each time t, and we assume that the distribution of future events only depends on past events. When the data-generating mechanism of the SEPP is stable over time, the estimation of the self-excitation parameters is well-studied. In this talk, we consider the setting in which the self-excitation parameters are unstable and change over time in a piecewise constant manner. Within a general high-dimensional change point framework, we will develop algorithms that accurately can estimate the locations of the change points. Our approach is based on a novel variant of the fused LASSO combined with multivariate binary segmentation of the regression coefficients. We provide sharp theoretical bounds as well as real data examples to justify our findings.
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