Relaxing the Assumptions of Knockoffs by Conditioning
| Autor: | Dongming Huang, Lucas Janson |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Gaussian topological measure 01 natural sciences High-dimensional inference Methodology (stat.ME) 010104 statistics & probability symbols.namesake Covariate false discovery rate (FDR) Applied mathematics 62G10 62B05 62J02 62J02 Graphical model 0101 mathematics 62B05 Statistics - Methodology Mathematics Lebesgue measure knockoffs graphical model Conditional probability distribution Sample size determination Parametric model symbols model-X Statistics Probability and Uncertainty sufficient statistic Sufficient statistic 62G10 |
| Zdroj: | Ann. Statist. 48, no. 5 (2020), 3021-3042 |
| Popis: | The recent paper Candès et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 (2018) 551–577) introduced model-X knockoffs, a method for variable selection that provably and nonasymptotically controls the false discovery rate with no restrictions or assumptions on the dimensionality of the data or the conditional distribution of the response given the covariates. The one requirement for the procedure is that the covariate samples are drawn independently and identically from a precisely-known (but arbitrary) distribution. The present paper shows that the exact same guarantees can be made without knowing the covariate distribution fully, but instead knowing it only up to a parametric model with as many as $\Omega (n^{*}p)$ parameters, where $p$ is the dimension and $n^{*}$ is the number of covariate samples (which may exceed the usual sample size $n$ of labeled samples when unlabeled samples are also available). The key is to treat the covariates as if they are drawn conditionally on their observed value for a sufficient statistic of the model. Although this idea is simple, even in Gaussian models conditioning on a sufficient statistic leads to a distribution supported on a set of zero Lebesgue measure, requiring techniques from topological measure theory to establish valid algorithms. We demonstrate how to do this for three models of interest, with simulations showing the new approach remains powerful under the weaker assumptions. |
| Databáze: | OpenAIRE |
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