A Power and Prediction Analysis for Knockoffs with Lasso Statistics
arXiv:1712.06465
Abstract
Knockoffs is a new framework for controlling the false discovery rate (FDR) in multiple hypothesis testing problems involving complex statistical models. While there has been great emphasis on Type-I error control, Type-II errors have been far less studied. In this paper we analyze the false negative rate or, equivalently, the power of a knockoff procedure associated with the Lasso solution path under an i.i.d. Gaussian design, and find that knockoffs asymptotically achieve close to optimal power with respect to an omniscient oracle. Furthermore, we demonstrate that for sparse signals, performing model selection via knockoff filtering achieves nearly ideal prediction errors as compared to a Lasso oracle equipped with full knowledge of the distribution of the unknown regression coefficients. The i.i.d. Gaussian design is adopted to leverage results concerning the empirical distribution of the Lasso estimates, which makes power calculation possible for both knockoff and oracle procedures.
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Cited by in corpus (9)
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- A Power Analysis of the Conditional Randomization Test and Knockoffs
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- Power analysis of knockoff filters for correlated designs
- GGM knockoff filter: False Discovery Rate Control for Gaussian Graphical Models
- BONuS: Multiple multivariate testing with a data-adaptivetest statistic
- Whiteout: when do fixed-X knockoffs fail?
- Optimal False Discovery Control of Minimax Estimator
- Controlling the False Discovery Rate for Binary Feature Selection via Knockoff