  Post-selection inference is a statistical technique for determining salient
variables after model or variable selection. Recently, selective inference, a
kind of post-selection inference framework, has garnered the attention in the
statistics and machine learning communities. By conditioning on a specific
variable selection procedure, selective inference can properly control for
so-called selective type I error, which is a type I error conditional on a
variable selection procedure, without imposing excessive additional
computational costs. While selective inference can provide a valid hypothesis
testing procedure, the main focus has hitherto been on Gaussian linear
regression models. In this paper, we develop a selective inference framework
for binary classification problem. We consider a logistic regression model
after variable selection based on marginal screening, and derive the high
dimensional statistical behavior of the post-selection estimator. This enables
us to asymptotically control for selective type I error for the purposes of
hypothesis testing after variable selection. We conduct several simulation
studies to confirm the statistical power of the test, and compare our proposed
method with data splitting and other methods.
