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Investigators often use the data to generate interesting hypotheses and thenperform inference for the generated hypotheses. P-values and confidenceintervals must account for this explorative data analysis. A fruitful methodfor doing so is to condition any inferences on the components of the data usedto generate the hypotheses, thus preventing information in those componentsfrom being used again. Some currently popular methods "over-condition", leadingto wide intervals. We show how to perform the minimal conditioning in acomputationally tractable way. In high dimensions, even this minimalconditioning can lead to intervals that are too wide to be useful, suggestingthat up to now the cost of hypothesis generation has been underestimated. Weshow how to generate hypotheses in a strategic manner that sharply reduces thecost of data exploration and results in useful confidence intervals. Ourdiscussion focuses on the problem of post-selection inference after fitting alasso regression model, but we also outline its extension to a much moregeneral setting.

More powerful post-selection inference, with application to the Lasso