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

TL;DR

This paper develops a more powerful method for post-selection inference, especially after using the Lasso, by minimizing conditioning and strategically generating hypotheses to produce more informative confidence intervals.

Contribution

It introduces a computationally feasible minimal conditioning approach for post-selection inference and strategies to reduce the cost of data exploration, improving inference after Lasso.

Findings

Minimal conditioning yields narrower confidence intervals.

Strategic hypothesis generation reduces the exploration cost.

Method extends to general high-dimensional settings.

Abstract

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