Ichiro Takeuchi (Nagoya University)

Title: More powerful and general conditional selective inference by parametric programming and its application to change-point detection and image segmentation.

Abstract: Conditional selective inference (SI) framework was recently introduced as a new statistical inference method for Lasso. This framework allows us to derive the exact conditional sampling distribution of the selected test statistic when the selection event is characterized by a polyhedron. In fact, this framework is not only useful for Lasso but also generally applicable to a certain class of data-driven hypotheses. A common limitation of existing SI methods is that the hypothesis selection event must be characterized in a simple tractable form such as a set of linear or quadratic inequalities. To overcome this limitation, we propose a new computational method for conditional SI based on parametric programming (PP), which we call called PP-based SI. In this talk, after briefly reviewing the conditional SI framework, we show that the proposed PP-based SI is more powerful than (vanilla) SI and applicable to a wider class of problems. As examples of how PP-based SI can extend the applicability of conditional SI, we present our recent works on conditional SI for multi-dimensional change-point detection and image segmentation by a deep neural network (this is joint work with Vo Nguyen Le Duy at Nagoya Institute of Technology).