mlsanityData to 7 Oct 2026

Exact Post-Selection Inference for Sequential Regression Procedures

arXiv 1401.3889 ↗First posted 16 Jan 2014stat.MEcited by 47

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Abstract (arXiv)

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso regularization path, because, as it turns out, selection events for these procedures can be expressed as polyhedral constraints on y. The p-values associated with these tests are exactly uniform under the null distribution, in finite samples, yielding exact type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. The R package "selectiveInference", freely available on the CRAN repository, implements the new inference tools described in this paper.

Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Jan 2014.

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Citing papers per year: 2021: 10; 2022: 8; 2023: 7; 2024: 8; 2025: 9; 2026: 5.

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  1. 2021More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programmingcited by 24
  2. 2022Selective inference for k-means clusteringcited by 21
  3. 2023Valid P-Value for Deep Learning-Driven Salient Regioncited by 17
  4. 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
  5. 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
  6. 2021Tree-Values: selective inference for regression treescited by 15
  7. 2024Confidence on the Focal: Conformal Prediction with Selection-Conditional Coveragecited by 14
  8. 2021Data fission: splitting a single data pointcited by 13
  9. 2023DRCFS: Doubly Robust Causal Feature Selectioncited by 12
  10. 2021The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Controlcited by 10
  11. 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
  12. 2022Valid Inference After Causal Discoverycited by 10
35 more
  1. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
  2. 2025PCS-UQ: Uncertainty Quantification via the Predictability-Computability-Stability Frameworkcited by 9
  3. 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7
  4. 2024Statistical Test for Attention Map in Vision Transformercited by 6
  5. 2024Statistical Test for Anomaly Detections by Variational Auto-Encoderscited by 6
  6. 2025A Statistical Case Against Empirical Human-AI Alignmentcited by 6
  7. 2023Selective Inference for Changepoint detection by Recurrent Neural Networkcited by 4
  8. 2021The Adaptive Multi-Factor Model and the Financial Marketcited by 3
  9. 2024Statistical Test for Feature Selection Pipelines by Selective Inferencecited by 3
  10. 2024Statistical Test for Auto Feature Engineering by Selective Inferencecited by 3
  11. 2025Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inferencecited by 3
  12. 2024Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptationcited by 2
  13. 2024Controllable RANSAC-based Anomaly Detection via Hypothesis Testingcited by 2
  14. 2025Change Point Detection in the Frequency Domain with Statistical Reliabilitycited by 2
  15. 2025Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptationcited by 2
  16. 2026Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offscited by 2
  17. 2021Spatially relaxed inference on high-dimensional linear modelscited by 1
  18. 2022Multi-Study Boosting: Theoretical Considerations for Merging vs. Ensemblingcited by 1
  19. 2023Bounded P-values in Parametric Programming-based Selective Inferencecited by 1
  20. 2024Statistical Test for Diffusion-Based Anomaly Localization via Selective Inferencecited by 1
  21. 2025Statistical Test for Saliency Maps of Graph Neural Networks via Selective Inferencecited by 1
  22. 2026Bayesian Sparse Low-Rank Adaptation for Large Language Model Uncertainty Estimationcited by 1
  23. 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detectioncited by 0
  24. 2022Adaptive Noisy Data Augmentation for Regularized Estimation and Inference in Generalized Linear Modelscited by 0
  25. 2022An Analysis of Selection Bias Issue for Online Advertisingcited by 0
  26. 2022Inferring independent sets of Gaussian variables after thresholding correlationscited by 0
  27. 2022Confidence Intervals for Unobserved Eventscited by 0
  28. 2023A parametric distribution for exact post-selection inference with data carvingcited by 0
  29. 2023Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Modelscited by 0
  30. 2025Post-Transfer Learning Statistical Inference in High-Dimensional Regressioncited by 0
  31. 2025Statistical Inference for Clustering-based Anomaly Detectioncited by 0
  32. 2025Spacing Test for Fused Lassocited by 0
  33. 2026Automatic Statistical Test for Rationally Expressible Algorithms by Selective Inference, with Applications to Feature Selectioncited by 0
  34. 2026Statistical Testing for Multiple Instance Learning via Selective Inference with Applications to Computational Pathologycited by 0
  35. 2026Post-Anomaly Detection Inference for Deep SVDDcited by 0