Exact post-selection inference, with application to the lasso

By Jason D. Lee, Dennis L. Sun, Yuekai Sun, Jonathan E. Taylor. 2013

811 citations recorded by the source corpus.

We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.

Subfields: Statistics and Probability

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Citations in the corpus

Forward stability and model path selection (2021, neutral): “Finally, we are not seeking to select a particular model and adjust variance estimates to account for additional uncertainty as might be done via some form of post-selection inference (e.g. Berk et al. 2013; Lee et al. 2016; Tibshi-rani et al. 2016; Taylor and Tibshirani 2018).”
Optimal Inference After Model Selection (2014, methodology): “we choose which null hypotheses to test after inspecting the data. The same is true of the conditional condence intervals of Weinstein et al. (2013), the saturated-model selective z-test proposed by Lee et al. (2016) and discussed in 4.2, and the rank verication methods proposed in Hung and Fithian ”
Assumption Lean Regression (2018, background): “Research is underway to provide valid post-selection inference (e.g., Berk et al. 2013, Lee et al. 2016), which is an important special case.”
Panning for gold: ‘model‐X’ knockoffs for high dimensional controlled variable selection (2016, methodology): “Relationship with work on inference after selection There is a line of work on inference after selection, or post-selection inference, for high dimensional regression, the goal of which is first to perform selection to make the problem low dimensional, and then to produce p-values that are valid con”
Covariate powered cross‐weighted multiple testing (2017, background): “ghts with the first stage p-value as the covariate. Conditional inference is a classical topic in statistics, aiming at the relevance and tractability of conducted inference (Cox, 1958; Fisher, 1934; Lee et al., 2016). However, for single hypothesis testing, it has also been considered to be more co”
Controlling Bias in Adaptive Data Analysis Using Information Theory (2015, background): “ese papers correct for selection bias by explicitly conditioning on the event that a particular model was chosen. While some powerful results can be derived in the selective inference framework (e.g. [10, 11]), it requires that the conditional distribution P(˚ i = jT = i) is known and can be directl”
Models as Approximations I: Consequences Illustrated with Linear Regression (2014, background): “A drawback is that it can invalidate subsequent inferences in unpredictable ways, as does any data-driven variable selection, formal or informal (see, e.g., Berk et al. 2013; Lee et al. 2016).”
Assessing Treatment Effect Variation in Observational Studies: Results from a Data Challenge (2019, background): “They argue that using the same data for both discovery and estimation of effect modification will generally lead to bias (Fithian et al., 2014), which motivates their post-selection inference procedure (Lee et al., 2016).”
Identification of and Correction for Publication Bias (2017, neutral): “1 in Lee et al. (2016). In particular, note that for z1>z0 and ω1>ω0, fZ|Ω(z1|ω1) fZ|Ω(z0|ω1) > fZ|Ω(z1|ω0) fZ|Ω(z0|ω0) ,”
Uniform asymptotic inference and the bootstrap after model selection (2015, methodology): “…has been a recent surge of work on conducting formally valid inference in a regression setting after a model selection event has occurred, see Berk et al. (2013), Lockhart et al. (2014), Tibshirani et al. (2016), Lee et al. (2016), Fithian et al. (2014), Bachoc et al. (2014), just to name a few.”
Machine Learning Advances for Time Series Forecasting (2020, background): “Finally, it is important to stress that Lee et al. (2016) inference is carried on the coefficients of the selected model, while van de Geer et al. (2014 More specifically, Babii et al. (2020a) consider inference in time-series regression models underheteroskedastic and autocorrelated errors.”
Targeted Undersmoothing. (2017, methodology): “See, for instance, [38], which carries out selective inference in the high-dimensional linear model in the case that Ŝ is chosen using lasso.”
Distribution-Free Predictive Inference for Regression (2016, background): “In the second class, post-selection approaches, the focus is on covering coefficients in the best linear approximation to μ given a subset of selected covariates (see, e.g., Berk et al. 2013; Fithian, Sun, and Taylor 2014; Tian and Taylor 2017, 2018; Lee et al. 2016; Tibshirani et al. 2016).”
How Much Does Your Data Exploration Overfit? Controlling Bias via Information Usage (2015, background): “[10], [11]), it requires that the conditional distribution P(φi = ·|T = i) is known and can be directly analyzed.”