Multicarving for high-dimensional post-selection inference

Schultheiss, Christoph; Renaux, Claude; Bühlmann, Peter

doi:10.1214/21-ejs1825

Cited by 11 publications

(10 citation statements)

References 32 publications

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“…Third, p-values computed under our asymptotic selective likelihood can be easily adapted to address the p-value lottery problem. In this sense, our procedure is related to the multi-carving approach for improved replication [35], but yields us a much faster, sampling-free solution to the same problem.…”

Section: Contributions and Other Related Workmentioning

confidence: 99%

“…Finally, our procedure can be easily adapted to address the "p-value lottery" problem, which arises frequently with model selection on random splits of data. The proposal serves as an efficient alternative to multi-splitting in [11], and multi-carving in [35]. Multi-carving is a more powerful version of multi-splitting, and is based on techniques that are known as carving [13,26].…”

Section: Introductionmentioning

confidence: 99%

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Selective Inference with Distributed Data

Liu¹,

Panigrahi²

2023

Preprint

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Nowadays, big datasets are spread over many machines which compute in parallel, and communicate with a central machine through short messages. We consider a sparse regression setting in our paper, and develop a new procedure for selective inference with distributed data. While there are many distributed procedures for point estimation in the sparse setting, not many options exist for estimating uncertainties or conducting hypothesis tests in models based on the estimated sparsity. We solve a generalized linear regression on each machine which communicates a selected set of predictors to the central machine. The central machine forms a generalized linear model with the selected predictors. How do we conduct selective inference for the selected regression coefficients? Is it possible to re-use distributed data, in an aggregated form, for selective inference?Our proposed procedure bases approximately-valid selective inference on an asymptotic likelihood. The proposal seeks only aggregated information, in relatively few dimensions, from each machine which is merged at the central machine to construct selective inference. Our procedure is also broadly applicable as a solution to the p-value lottery problem that arises with model selection on random splits of data.

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Section: Contributions and Other Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Selective Inference with Distributed Data

Liu¹,

Panigrahi²

2023

Preprint

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“…To develop the test, we leverage the selective inference framework, which has been applied extensively in high-dimensional linear modeling (Lee et al, 2016;Tibshirani et al, 2016;Fithian et al, 2014;Rügamer et al, 2022;Schultheiss et al, 2021;Taylor & Tibshirani, 2018;Charkhi & Claeskens, 2018;Yang et al, 2016;Loftus & Taylor, 2014), changepoint detection (Jewell et al, 2022;Hyun et al, 2021Hyun et al, , 2018Chen et al, 2021b;Le Duy & Takeuchi, 2021;Duy et al, 2020;Benjamini et al, 2019), and clustering (Zhang et al, 2019;Gao et al, 2020;Watanabe & Suzuki, 2021). The key insight behind selective inference is as follows: to obtain a valid test of H 0 , we need to condition on the aspect of the data that led us to test it.…”

Section: Introductionmentioning

confidence: 99%

Selective inference for k-means clustering

Chen¹,

Witten²

2022

Preprint

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We consider the problem of testing for a difference in means between clusters of observations identified via k-means clustering. In this setting, classical hypothesis tests lead to an inflated Type I error rate. To overcome this problem, we take a selective inference approach. We propose a finite-sample p-value that controls the selective Type I error for a test of the difference in means between a pair of clusters obtained using k-means clustering, and show that it can be efficiently computed. We apply our proposal in simulation, and on hand-written digits data and single-cell RNA-sequencing data.

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“…The idea of conditioning upon the observed selection, previously explored in [7,17,11], among others, discards bias from model selection through p-values, confidence intervals, credible intervals based on conditional probabilities. The estimator we propose here implements the principles of data carving [4,12,10,14] within the conditional framework. Data carving resembles data-splitting in the selection stage, because model selection operates on only a subset of the full data.…”

Section: Introductionmentioning

confidence: 99%

Treatment Effect Estimation with Efficient Data Aggregation

Panigrahi¹,

Wang²,

He³

2022

Preprint

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Data aggregation, also known as meta analysis, is widely used to synthesize knowledge on parameters shared in common (e.g., average treatment effect) between multiple studies. We introduce in this paper an attractive data aggregation protocol based on summary statistics from existing studies, to inform the design of a (new) validation study and estimate shared parameters by combining all the studies. In particular, we focus on the scenario where each existing study relies on an 1 -regularized regression analysis to select a parsimonious model from a set of high dimensional covariates. We derive an estimator for the shared parameter by aggregating summary statistics from each study through a novel technique called data carving. Our estimator (a) aims to make the fullest possible use of data from the existing studies without the bias from data re-use in model selection and parameter estimation, and (b) provides the added benefit of individual data privacy, because full data from these studies need not be shared for efficient estimation.

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Multicarving for high-dimensional post-selection inference

Cited by 11 publications

References 32 publications

Selective Inference with Distributed Data

Selective Inference with Distributed Data

Selective inference for k-means clustering

Treatment Effect Estimation with Efficient Data Aggregation

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