Selective inference (SI) has been actively studied as a promising framework
for statistical hypothesis testing for data-driven hypotheses. The basic idea
of SI is to make inferences conditional on an event that a hypothesis is
selected. In order to perform SI, this event must be characterized in a
traceable form. When selection event is too difficult to characterize,
additional conditions are introduced for tractability. This additional
conditions often causes the loss of power, and this issue is referred to as
over-conditioning. Parametric programming-based SI (PP-based SI) has been
proposed as one way to address the over-conditioning issue. The main problem of
PP-based SI is its high computational cost due to the need to exhaustively
explore the data space. In this study, we introduce a procedure to reduce the
computational cost while guaranteeing the desired precision, by proposing a
method to compute the upper and lower bounds of p-values. We also proposed
three types of search strategies that efficiently improve these bounds. We
demonstrate the effectiveness of the proposed method in hypothesis testing
problems for feature selection in linear models and attention region
identification in deep neural networks.

我们提出了一种方法来减少计算成本，同时保证所需的精度，通过计算 p 值的上下界，并提出了三种有效提升这些界限的搜索策略。我们在线性模型的特征选择和深度神经网络中的注意区域识别的假设检验问题中展示了该方法的有效性。