More Powerful and General Selective Inference for Stepwise Feature Selection using the Homotopy Continuation Approach
This work provides a more powerful and general statistical inference method for researchers and practitioners using stepwise feature selection, especially for complex algorithms where existing methods suffer from power loss.
This paper addresses the power loss in conditional selective inference (SI) for stepwise feature selection (SFS) caused by over-conditioning. The authors propose a homotopy-based SI method that overcomes this limitation, demonstrating its effectiveness and efficiency, particularly for complex algorithms like forward-backward SFS with AIC-based stopping criteria.
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.