  We study the problem of detecting change points (CPs) that are characterized
by a subset of dimensions in a multi-dimensional sequence. A method for
detecting those CPs can be formulated as a two-stage method: one for selecting
relevant dimensions, and another for selecting CPs. It has been difficult to
properly control the false detection probability of these CP detection methods
because selection bias in each stage must be properly corrected. Our main
contribution in this paper is to formulate a CP detection problem as a
selective inference problem, and show that exact (non-asymptotic) inference is
possible for a class of CP detection methods. We demonstrate the performances
of the proposed selective inference framework through numerical simulations and
its application to our motivating medical data analysis problem.
