Abstract
In the past few years, Selective Inference (SI) has been actively studied for
inference on the features of linear models that are adaptively selected by
feature selection methods. A seminal work is proposed by Lee et al. (2016) in
the case of the Lasso. The basic idea of SI is to make inference conditional on
the selection event. In Lee et al. (2016), the authors proposed a tractable way
to conduct inference conditional on the selected features and their signs.
Unfortunately, additionally conditioning on the signs leads to low statistical
power because of over-conditioning. To improve the power, a current available
possible solution is to remove the conditioning on signs by considering the
union of an exponentially large number of all possible sign vectors, which
leads to an unrealistically large amount of computational cost unless the
number of selected features is sufficiently small. To address this problem, we
propose an efficient method to characterize the selection event without
conditioning on signs by using parametric programming. The main idea is to
compute the continuum path of Lasso solutions in the direction of a test
statistic, and identify the subset of data space corresponding to the feature
selection event by following the solution path. We conduct several experiments
to demonstrate the effectiveness and efficiency of our proposed method.
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