Selective Inference for Change Point Detection in Multi-dimensional Sequences
This addresses the challenge of reliable change point detection in fields like medical data analysis, though it appears incremental as it builds on existing two-stage methods by adding a selective inference framework.
The paper tackles the problem of detecting change points in multi-dimensional sequences while controlling false detection probability, by formulating it as a selective inference problem and showing that exact inference is possible for a class of methods, with performance validated through simulations and medical data analysis.
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.