It is common to show the confidence intervals or p-values of selected
features, or predictor variables in regression, but they often involve
selection bias. The selective inference approach solves this bias by
conditioning on the selection event. Most existing studies of selective
inference consider a specific algorithm, such as Lasso, for feature selection,
and thus they have difficulties in handling more complicated algorithms.
Moreover, existing studies often consider unnecessarily restrictive events,
leading to over-conditioning and lower statistical power. Our novel and
widely-applicable resampling method addresses these issues to compute an
approximately unbiased selective p-value for the selected features. We prove
that the p-value computed by our resampling method is more accurate and more
powerful than existing methods, while the computational cost is the same order
as the classical bootstrap method. Numerical experiments demonstrate that our
algorithm works well even for more complicated feature selection methods such
as non-convex regularization.Comment: The title has changed (The previous title is "Selective inference
after variable selection via multiscale bootstrap"). 23 pages, 11 figure