# A Power and Prediction Analysis for Knockoffs with Lasso Statistics

arXiv: https://arxiv.org/abs/1712.06465 · HTML: https://mlsanity.com/paper/1712.06465/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2017.

## Built on by (most cited first, 5 of 5)

- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [Near-optimal multiple testing in Bayesian linear models with finite-sample FDR control](https://mlsanity.com/paper/2211.02778/) (2022)
- [Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection](https://mlsanity.com/paper/2405.03063/) (2024)
- [The Conditional Prediction Function: A Novel Technique to Control False Discovery Rate for Complex Models](https://mlsanity.com/paper/2310.04919/) (2023)

## Abstract (arXiv)

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.