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Confidence Intervals and Hypothesis Testing for High-Dimensional Statistical Models
Adel Javanmard · Andrea Montanari

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the parameter estimates. This in turn implies that it is extremely challenging to quantify the uncertainty' associated with a certain parameter estimate. Concretely, no commonly accepted procedure exists for computing classical measures of uncertainty and statistical significance as confidence intervals or p-values. We consider here a broad class of regression problems, and propose an efficient algorithm for constructing confidence intervals and p-values. The resulting confidence intervals have nearly optimal size. When testing for the null hypothesis that a certain parameter is vanishing, our method has nearly optimal power. Our approach is based on constructing ade-biased' version of regularized M-estimators. The new construction improves over recent work in the field in that it does not assume a special structure on the design matrix. Furthermore, proofs are remarkably simple. We test our method on a diabetes prediction problem.

Author Information

Adel Javanmard (Stanford University)
Andrea Montanari (Stanford)

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