mlsanityData to 7 Oct 2026

A significance test for forward stepwise model selection

arXiv 1405.3920 ↗First posted 15 May 2014stat.MEcited by 17

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Abstract (arXiv)

We apply the methods developed by Lockhart et al. (2013) and Taylor et al. (2013) on significance tests for penalized regression to forward stepwise model selection. A general framework for selection procedures described by quadratic inequalities includes a variant of forward stepwise with grouped variables, allowing us to handle categorical variables and factor models. We provide an algorithm to compute a new statistic with an exact null distribution conditional on the outcome of the model selection procedure. This new statistic, which we denote Tchi, has a truncated chi distribution under the global null. We apply this test in forward stepwise iteratively on the residual after each step. The resulting method has the computational strengths of stepwise selection and addresses the problem of invalid test statistics due to model selection. We illustrate the flexibility of this method by applying it to several specialized applications of forward stepwise including a hierarchical interactions model and a recently described additive model that adaptively chooses between linear and nonlinear effects for each variable.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 May 2014.

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Citing papers per year: 2021: 5; 2022: 2; 2023: 3; 2024: 3; 2025: 4.

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  2. 2022Selective inference for k-means clusteringcited by 21
  3. 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
  4. 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
  5. 2023DRCFS: Doubly Robust Causal Feature Selectioncited by 12
  6. 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
  7. 2023CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inferencecited by 10
  8. 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7
  9. 2024Statistical Test for Attention Map in Vision Transformercited by 6
  10. 2024Statistical Test for Anomaly Detections by Variational Auto-Encoderscited by 6
  11. 2024Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptationcited by 2
  12. 2025Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptationcited by 2
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  1. 2023Bounded P-values in Parametric Programming-based Selective Inferencecited by 1
  2. 2025Statistical Test for Saliency Maps of Graph Neural Networks via Selective Inferencecited by 1
  3. 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detectioncited by 0
  4. 2025Post-Transfer Learning Statistical Inference in High-Dimensional Regressioncited by 0
  5. 2025Statistical Inference for Clustering-based Anomaly Detectioncited by 0