  Conditional selective inference (SI) has been actively studied as a new
statistical inference framework for data-driven hypotheses. The basic idea of
conditional SI is to make inferences conditional on the selection event
characterized by a set of linear and/or quadratic inequalities. Conditional SI
has been mainly studied in the context of feature selection such as stepwise
feature selection (SFS). The main limitation of the existing conditional SI
methods is the loss of power due to over-conditioning, which is required for
computational tractability. In this study, we develop a more powerful and
general conditional SI method for SFS using the homotopy method which enables
us to overcome this limitation. The homotopy-based SI is especially effective
for more complicated feature selection algorithms. As an example, we develop a
conditional SI method for forward-backward SFS with AIC-based stopping criteria
and show that it is not adversely affected by the increased complexity of the
algorithm. We conduct several experiments to demonstrate the effectiveness and
efficiency of the proposed method.
