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Exact Post Model Selection Inference for Marginal Screening

Authors: Jason D. Lee, Jonathan E. Taylor - Conference on Neural Information Processing Systems, NeurIPS 2014 cited by 107

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response y, conditional on the model being selected (“condi-tion on selection ” framework). This allows us to construct valid con-fidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and re-quire no eigenvalue-like assumptions on the design matrix X. Further-more, the computational cost of marginal regression, constructing con-fidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to ap-ply the proposed framework to several other selection procedures in-cluding orthogonal matching pursuit, non-negative least squares, and marginal screening+Lasso. 1

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