Large-Scale Inference with Knockoffs

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models.

In this paper, we provide theoretical foundations on the power and robustness for the model- free knockoffs procedure introduced recently in Cand`es, Fan, Janson and Lv (2018) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model.

We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity.

When moving away from the ideal case, we suggest the modified model-free knockoffs method called graphical nonlinear knockoffs to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution.

To the best of our knowledge, this is the first formal theoretical result on the power for the knock- offs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.

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About Yingying Fan

Yingying Fan is Dean's Associate Professor in Business Administration in Data Sciences and Operations Department of the Marshall School of Business at the University of Southern California, Associate Professor in Departments of Economics and Computer Science at USC, and an Associate Fellow of USC Dornsife Institute for New Economic Thinking (INET).

She received her Ph.D. in Operations Research and Financial Engineering from Princeton University in 2007. She was Lecturer in the Department of Statistics at Harvard University from 2007-2008. Her research interests include statistics, data science, machine learning, economics, and big data and business applications.

Her papers have been published in journals in statistics, economics, computer science, and information theory. She is the recipient of Fellow of American Statistical Association (2019), NIH R01 Grant (2018), the Royal Statistical Society Guy Medal in Bronze (2017), USC Marshall Dean's Award for Research Excellence (2017), the USC Marshall Inaugural Dr. Douglas Basil Award for Junior Business Faculty (2014), the American Statistical Association Noether Young Scholar Award (2013), NSF Faculty Early Career Development (CAREER) Award (2012), Zumberge Individual Award from USC's James H. Zumberge Faculty Research and Innovation Fund (2010), and USC Marshall Dean's Award for Research Excellence (2010), as well as a Plenary Speaker at the 2011 Institute of Mathematical Statistics Workshop on Finance, Probability, and Statistics held at Columbia University.

She has served as an associate editor of Journal of the American Statistical Association (2014-present), Journal of Econometrics (2015-2018), Journal of Business & Economic Statistics (2018-present), The Econometrics Journal (2012-present), and Journal of Multivariate Analysis (2013-2016).