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Optimal Inference After Model Selection

arXiv 1410.2597 ↗First posted 9 Oct 2014math.ST stat.ME stat.THcited by 63

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Abstract (arXiv)

To perform inference after model selection, we propose controlling the selective type I error; i.e., the error rate of a test given that it was performed. By doing so, we recover long-run frequency properties among selected hypotheses analogous to those that apply in the classical (non-adaptive) context. Our proposal is closely related to data splitting and has a similar intuitive justification, but is more powerful. Exploiting the classical theory of Lehmann and Scheff'e (1955), we derive most powerful unbiased selective tests and confidence intervals for inference in exponential family models after arbitrary selection procedures. For linear regression, we derive new selective z-tests that generalize recent proposals for inference after model selection and improve on their power, and new selective t-tests that do not require knowledge of the error variance.

Key facts. Cited by 63 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Oct 2014.

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Citing papers per year: 2021: 9; 2022: 12; 2023: 8; 2024: 8; 2025: 15; 2026: 11.

63 papers.

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  1. 2021MMD Aggregated Two-Sample Testcited by 74
  2. 2022Efficient Aggregated Kernel Tests using Incomplete U-statisticscited by 27
  3. 2021More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programmingcited by 24
  4. 2022Selective inference for k-means clusteringcited by 21
  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. 2021Data fission: splitting a single data pointcited by 13
  8. 2023Data thinning for convolution-closed distributionscited by 12
  9. 2021The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Controlcited by 10
  10. 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
  11. 2022Valid Inference After Causal Discoverycited by 10
  12. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
38 more
  1. 2025PCS-UQ: Uncertainty Quantification via the Predictability-Computability-Stability Frameworkcited by 9
  2. 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7
  3. 2022Certified Policy Smoothing for Cooperative Multi-Agent Reinforcement Learningcited by 7
  4. 2023Generalized Data Thinning Using Sufficient Statisticscited by 7
  5. 2022Exact Selective Inference with Randomizationcited by 6
  6. 2024Statistical Test for Attention Map in Vision Transformercited by 6
  7. 2024A Flexible Defense Against the Winner's Cursecited by 6
  8. 2025A Statistical Case Against Empirical Human-AI Alignmentcited by 6
  9. 2026Towards Reliable LLM Evaluation: Correcting the Winner's Curse in Adaptive Benchmarkingcited by 5
  10. 2025Calibrating Decision Robustness via Inverse Conformal Risk Controlcited by 4
  11. 2023Selective inference using randomized group lasso estimators for general modelscited by 3
  12. 2025Quantifying Statistical Significance of Deep Nearest Neighbor Anomaly Detection via Selective Inferencecited by 3
  13. 2022Tree-based Subgroup Discovery In Electronic Health Records: Heterogeneity of Treatment Effects for DTG-containing Therapiescited by 2
  14. 2023On the Validity of Conformal Prediction for Network Data Under Non-Uniform Samplingcited by 2
  15. 2024Decomposing Gaussians with Unknown Covariancecited by 2
  16. 2024Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptationcited by 2
  17. 2024Controllable RANSAC-based Anomaly Detection via Hypothesis Testingcited by 2
  18. 2025Online Selective Conformal Prediction: Errors and Solutionscited by 2
  19. 2025Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptationcited by 2
  20. 2025Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Datacited by 2
  21. 2021Fast and Interpretable Consensus Clustering via Minipatch Learningcited by 1
  22. 2022Black-box Selective Inference via Bootstrappingcited by 1
  23. 2022Selective Inference for Sparse Multitask Regression with Applications in Neuroimagingcited by 1
  24. 2022A Confidence Machine for Sparse High-Order Interaction Modelcited by 1
  25. 2023Bounded P-values in Parametric Programming-based Selective Inferencecited by 1
  26. 2024Statistical Test for Diffusion-Based Anomaly Localization via Selective Inferencecited by 1
  27. 2024Adaptive Data Analysis for Growing Datacited by 1
  28. 2025Statistical Test for Saliency Maps of Graph Neural Networks via Selective Inferencecited by 1
  29. 2025Reliable Inference in Edge-Cloud Model Cascades via Conformal Alignmentcited by 1
  30. 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detectioncited by 0
  31. 2022Robust Output Analysis with Monte-Carlo Methodologycited by 0
  32. 2022Inferring independent sets of Gaussian variables after thresholding correlationscited by 0
  33. 2023A parametric distribution for exact post-selection inference with data carvingcited by 0
  34. 2023Optimal Conditional Inference in Adaptive Experimentscited by 0
  35. 2024Predictive Modeling, Pattern Recognition, and Spatiotemporal Representations of Plant Growth in Simulated and Controlled Environments: A Comprehensive Reviewcited by 0
  36. 2025Post-Transfer Learning Statistical Inference in High-Dimensional Regressioncited by 0
  37. 2025Statistical Inference for Clustering-based Anomaly Detectioncited by 0
  38. 2025Flexible Selective Inference with Flow-based Transport Mapscited by 0

50 most cited of 63 All 63 (JSON)