More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming

Duy, Vo Nguyen Le; Takeuchi, Ichiro

doi:10.48550/arxiv.2105.04920

Cited by 4 publications

(3 citation statements)

References 30 publications

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“…Valid confidence intervals are provided from conditional hypothesis tests for each model of the collection in addition to a PR control. Their work has been generalized by [27,28,29] and a review can be found in [30].…”

Section: Related Workmentioning

confidence: 99%

Trade-off between prediction and FDR for high-dimensional Gaussian model selection

Lacroix¹,

Martin²

2023

Preprint

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In the context of the high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where we propose to control predictive risk and False Discovery Rate simultaneously. For this purpose, we obtain a convenient trade-off thanks to a proper calibration of the hyperparameter K appearing in the penalty function. We obtain non-asymptotic theoretical bounds on the False Discovery Rate with respect to K. We then provide an algorithm for the calibration of K. It is based on completely observable quantities in view of applications. Our algorithm is validated by an extensive simulation study.

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Section: Related Workmentioning

confidence: 99%

Trade-off between prediction and FDR for high-dimensional Gaussian model selection

Lacroix¹,

Martin²

2023

Preprint

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“…Methods for calculating selective p-values have been developed for the change in mean problem with Gaussian noise and for a range of detection algorithms. Hyun et al (2021) develop an approach for binary segmentation and its variants, and for the fused lasso; while Jewell et al (2021) and Duy and Takeuchi (2021) propose methods that work if changes are detected using an L 0 penalised likelihood. Furthermore Jewell et al (2021) show how to improve on the method of Hyun et al (2021) by conditioning on less information when defining the selective p-value, and show that conditioning on less information can lead to a substantial increase in power.…”

Section: Introductionmentioning

confidence: 99%

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints

Carrington¹,

Fearnhead²

2023

Preprint

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Post-selection inference has recently been proposed as a way of quantifying uncertainty about detected changepoints. The idea is to run a changepoint detection algorithm, and then re-use the same data to perform a test for a change near each of the detected changes. By defining the p-value for the test appropriately, so that it is conditional on the information used to choose the test, this approach will produce valid p-values. We show how to improve the power of these procedures by conditioning on less information. This gives rise to an ideal selective p-value that is intractable but can be approximated by Monte Carlo. We show that for any Monte Carlo sample size, this procedure produces valid p-values, and empirically that noticeable increase in power is possible with only very modest Monte Carlo sample sizes.Our procedure is easy to implement given existing post-selection inference methods, as we just need to generate perturbations of the data set and re-apply the post-selection method to each of these. On genomic data consisting of human GC content, our procedure increases the number of significant changepoints that are detected from e.g. 17 to 27, when compared to the method of Jewell et al. (2021).

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“…A well-known homotopy algorithm in statistical machine learning is the LARS-LASSO algorithm to construct the exact regularization paths of LASSO solutions (Efron et al 2004). Recently there have been other studies which also exploited the homotopy method in the context of conditional SI to improve the statistical efficiency (Duy and Takeuchi 2021b;Sugiyama, Le Duy, and Takeuchi 2021;Duy and Takeuchi 2021a) .…”

Section: Introductionmentioning

confidence: 99%

Fast and More Powerful Selective Inference for Sparse High-Order Interaction Model

Das

Duy²,

Hanada³

et al. 2022

AAAI

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Automated high-stake decision-making, such as medical diagnosis, requires models with high interpretability and reliability. We consider the sparse high-order interaction model as an interpretable and reliable model with a good prediction ability. However, finding statistically significant high-order interactions is challenging because of the intrinsically high dimensionality of the combinatorial effects. Another problem in data-driven modeling is the effect of ``cherry-picking" (i.e., selection bias). Our main contribution is extending the recently developed parametric programming approach for selective inference to high-order interaction models. An exhaustive search over the cherry tree (all possible interactions) can be daunting and impractical, even for small-sized problems. We introduced an efficient pruning strategy and demonstrated the computational efficiency and statistical power of the proposed method using both synthetic and real data.

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More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming

Cited by 4 publications

References 30 publications

Trade-off between prediction and FDR for high-dimensional Gaussian model selection

Trade-off between prediction and FDR for high-dimensional Gaussian model selection

Improving Power by Conditioning on Less in Post-selection Inference for Changepoints

Fast and More Powerful Selective Inference for Sparse High-Order Interaction Model

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