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Selective Inference (SI) has been actively studied in the past few years forconducting inference on the features of linear models that are adaptivelyselected by feature selection methods such as Lasso. The basic idea of SI is tomake inference conditional on the selection event. Unfortunately, the mainlimitation of the original SI approach for Lasso is that the inference isconducted not only conditional on the selected features but also on their signs-- this leads to loss of power because of over-conditioning. Although thislimitation can be circumvented by considering the union of such selectionevents for all possible combinations of signs, this is only feasible when thenumber of selected features is sufficiently small. To address thiscomputational bottleneck, we propose a parametric programming-based method thatcan conduct SI without conditioning on signs even when we have thousands ofactive features. The main idea is to compute the continuum path of Lassosolutions in the direction of a test statistic, and identify the subset of thedata space corresponding to the feature selection event by following thesolution path. The proposed parametric programming-based method not only avoidsthe aforementioned computational bottleneck but also improves the performanceand practicality of SI for Lasso in various respects. We conduct severalexperiments to demonstrate the effectiveness and efficiency of our proposedmethod.

Parametric Programming Approach for More Powerful and General Lasso Selective Inference