Selective Inference for Multi-Dimensional Multiple Change Point Detection
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We consider the problem of multiple change point (CP) detection from a multi-dimensional sequence. We are mainly interested in the situation where changes are observed only in a subset of multiple dimensions at each CP. In such a situation, we need to select not only the time points but also the dimensions where changes actually occur. In this paper we study a class of multi-dimensional multiple CP detection algorithms for this task. Our main contribution is to introduce a statistical framework for controlling the false detection probability of these class of CP detection algorithms. The key idea is to regard a CP detection problem as a selective inference problem, and derive the sampling distribution of the test statistic under the condition that those CPs are detected by applying the algorithm to the data. By using an analytical tool recently developed in the selective inference literature, we show that, for a wide class of multi-dimensional multiple CP detection algorithms, it is possible to exactly (non-asymptotically) control the false detection probability at the desired significance level.
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