[Ml-stat-talks] Special seminar: Jianqing Fan, Wed. March 11, 12:30 PM

Amir Ali Ahmadi a_a_a at princeton.edu
Fri Mar 6 19:31:40 EST 2015

Where: Wednesday, March 11, 12:30 PM
Where: Sherrerd 125

Spurious discoveries, random geometry, and endogeneity for Big Data
Jianqing Fan
Princeton University

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool.  Can the discoveries by such data mining approaches be spurious?  Can our fundamental assumptions on exogeneity of covariates needed for such variable selection be validated with the data?  To answer these questions, we need to derive the distributions of the maximum spurious correlations given certain number of predictors. When the covariance matrix of covariates possesses the restricted eigenvalue property, we derive such distributions, using Gaussian approximation and empirical process techniques.  However, such a distribution depends on the unknown covariance matrix of the covariate. Hence, we propose a multiplier bootstrap method to approximate the unknown distributions and establish the consistency of such a simple bootstrap approach. The results are further extended to the situation where residuals are from regularized fits.  Our approach is then applied to construct the upper confidence limit for the maximum spurious correlation and testing exogeneity of covariates.   The former provides a baseline for guiding false discoveries due to data mining and the latter tests whether our fundamental assumptions for high-dimensional model selection are statistically valid.  Our techniques and results are illustrated by both numerical examples.
(Based on a joint paper with Qiman Shao and Wenxin Zhou)
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