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We develop tools to do valid post-selective inference for a family of model selection procedures, including choosing a model via cross-validated Lasso.
Bootstrapping regression models
David A Freedman et al · 1981
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Controlling the false discovery rate: a practical and powerful approach to multiple testing
Yoav Benjamini and Yosef Hochberg · 1995
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The elements of statistical learning , volume 1
Jerome Friedman, Trevor Hastie, and Robert Tibshirani · 2001
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Asymptotics of cross-validated risk estimation in estimator selection and performance assessment
Sandrine Dudoit and Mark J van der Laan · 2005
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Testing statistical hypotheses
Erich L Lehmann and Joseph P Romano · 2006
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Valid post-selection inference
Richard Berk, Lawrence Brown, Andreas Buja, Kai Zhang, Linda Zhao, et al · 2013
Earlier work this paper cites.
The lasso, persistence, and cross-validation
Darren Homrighausen and Daniel J McDonald · 2013
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Exact post model selection inference for marginal screening
Jason D Lee and Jonathan E Taylor · 2014
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A conspiracy of random predictors and model violations against classical inference in regression
A Buja, R Berk, L Brown, E George, E Pitkin, M Traskin, K Zhang, L Zhao, and Dedicated To Halbert White · 2014
Cited alongside, same era.
Optimal inference after model selection
William Fithian, Dennis Sun, and Jonathan Taylor · 2014
Cited alongside, same era.
Statistical learning and selective inference
Jonathan Taylor and Robert J Tibshirani · 2015
Cited alongside, same era.
Selective inference after cross-validation
Joshua R Loftus · 2015
Cited alongside, same era.
Sampling from a log-concave distribution with Projected Langevin Monte Carlo
Sébastien Bubeck, Ronen Eldan, and Joseph Lehec · 2015
Cited alongside, same era.
glmnet: Lasso and elastic-net regularized generalized linear models, 2015
J Friedman, T Hastie, and Tibshirani R · 2015
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Bootstrapping and sample splitting for high-dimensional, assumption-free inference
Alessandro Rinaldo, Larry Wasserman, Max G’Sell, Jing Lei, and Ryan Tibshirani · 2016
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Exact post-selection inference, with application to the lasso
Jason D Lee, Dennis L Sun, Yuekai Sun, and Jonathan E Taylor · 2016
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Exact post-selection inference for sequential regression procedures
Ryan J. Tibshirani, Jonathan Taylor, Richard Lockhart, and Robert Tibshirani · 2016
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Bootstrap inference after using multiple queries for model selection
Jelena Markovic and Jonathan Taylor · 2016
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Selective inference with a randomized response
Xiaoying Tian and Jonathan E Taylor · 2015
Cited alongside, same era.
Controlling the false discovery rate via knockoffs
Rina Foygel Barber and Emmanuel J Candès · 2015
Cited alongside, same era.
Magic: a general, powerful and tractable method for selective inference
Xiaoying Tian, Nan Bi, and Jonathan Taylor
Cited in the paper.
Selective sampling after solving a convex problem
Xiaoying Tian, Panigrahi Snigdha, Jelena Markovic, Nan Bi, and Jonathan Taylor
Cited in the paper.
Can one estimate the conditional distribution of post-model-selection estimators?
Hannes Leeb and Benedikt M Pötscher
Cited in the paper.
Performance limits for estimators of the risk or distribution of shrinkage-type estimators, and some general lower risk-bound results
Hannes Leeb and Benedikt M Pötscher
Cited in the paper.
Panning for gold: Model-free knockoffs for high-dimensional controlled variable selection
Emmanuel Candes, Yingying Fan, Lucas Janson, and Jinchi Lv · 2016
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A knockoff filter for high-dimensional selective inference
Rina Foygel Barber and Emmanuel J Candes · 2016
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