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In this paper, we study statistical inference of change-points (CPs) inmulti-dimensional sequence. In CP detection from a multi-dimensional sequence,it is often desirable not only to detect the location, but also to identify thesubset of the components in which the change occurs. Several algorithms havebeen proposed for such problems, but no valid exact inference method has beenestablished to evaluate the statistical reliability of the detected locationsand components. In this study, we propose a method that can guarantee thestatistical reliability of both the location and the components of the detectedchanges. We demonstrate the effectiveness of the proposed method by applying itto the problems of genomic abnormality identification and human behavioranalysis.

Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference