Title:  

Selective sampling after solving a convex problem

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. 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.

Time permitting, we discuss some asymptotic properties of such procedures,
providing a positive result on the asymptotic distribution of associated
pivotal quantities which can be used to test hypotheses and construct honest
confidence intervals, etc.

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