Statistics Department Seminar Series: Jonathan Taylor, Professor of Statistics, Stanford University

Abstract:
We begin with a description of recent work in the conditional approach to selective inference. These methods typically require describing potentially complex conditional distributions. In this work, we describe a model-agnostic simplification to such conditional distributions when the selection stage can be expressed as a sequence of (randomized) convex programs with convex loss and structure inducing constraints or penalties. Our main result is a change of measure formula that expresses the selective likelihood in terms of an integral over variables appearing in the optimization problem. The region of integration can often be interpreted geometrically in terms of the normal cycle of the balls in the corresponding penalty. Using this change of measure, we give a brief description of "inferactive data analysis", so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis.

This is joint work with Xiaoying Tian, Nan Bi, Snigdha Panigrahi and Jelena Markovic.