Stability Selection

Abstract

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with (high-dimensional) selection algorithms. As such, the method is extremely general and has a very wide range of applicability. Stability selection provides finite sample control for some error rates of false discoveries and hence a transparent principle to choose a proper amount of regularisation for structure estimation. Variable selection and structure estimation improve markedly for a range of selection methods if stability selection is applied. We prove for randomised Lasso that stability selection will be variable selection consistent even if the necessary conditions needed for consistency of the original Lasso method are violated. We demonstrate stability selection for variable selection and Gaussian graphical modelling, using real and simulated data.

30 pages, 7 figures

References in corpus (12)

• Rejoinder to "Least angle regression" by Efron et al
• Least Angle Regression
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Simultaneous analysis of Lasso and Dantzig selector
• Pathwise coordinate optimization

Cited by in corpus (10)

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• Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models
• Variable selection in high-dimensional linear models: partially faithful distributions and the PC-simple algorithm
• Stable Feature Selection for Biomarker Discovery
• P-values for high-dimensional regression
• Household poverty classification in data-scarce environments: a machine learning approach
• Model-Consistent Sparse Estimation through the Bootstrap
• Monte Carlo Simulation for Lasso-Type Problems by Estimator Augmentation
• Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models