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Conditional selective inference (SI) has been studied intensively as a newstatistical inference framework for data-driven hypotheses. The basic conceptof conditional SI is to make the inference conditional on the selection event,which enables an exact and valid statistical inference to be conducted evenwhen the hypothesis is selected based on the data. Conditional SI has mainlybeen studied in the context of model selection, such as vanilla lasso orgeneralized lasso. The main limitation of existing approaches is the lowstatistical power owing to over-conditioning, which is required forcomputational tractability. In this study, we propose a more powerful andgeneral conditional SI method for a class of problems that can be convertedinto quadratic parametric programming, which includes generalized lasso. Thekey concept is to compute the continuum path of the optimal solution in thedirection of the selected test statistic and to identify the subset of the dataspace that corresponds to the model selection event by following the solutionpath. The proposed parametric programming-based method not only avoids theaforementioned major drawback of over-conditioning, but also improves theperformance and practicality of SI in various respects. We conducted severalexperiments to demonstrate the effectiveness and efficiency of our proposedmethod.

More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming