The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction

1974/02/01 by David M. Allen · 29 citations
Mathematics · Decision Sciences · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Statistical Methods and Inference

paper · doi:10.1080/00401706.1974.10489157

Abstract

We show that data augmentation provides a rather general formulation for the study of biased prediction techniques using multiple linear regression. Variable selection is a limiting case, and Ridge regression is a special case of data augmentation. We propose a way to obtain predictors given a credible criterion of good prediction.

Citations

• Ridge Regression: Applications to Nonorthogonal Problems

Cited by

• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Simultaneous Optimization of Multiple Responses Represented by Polynomial Regression Functions
• Machine Learning for Electrode Materials: Property Prediction via Composition
• Approximate cross-validation formula for Bayesian linear regression
• Optimizing Approximate Leave-one-out Cross-validation to Tune\n Hyperparameters
• On the Accuracy of Newton Step and Influence Function Data Attributions
• True Few-Shot Learning with Language Models
• Can we globally optimize cross-validation loss? Quasiconvexity in ridge\n regression
• Cross-Validation: What Does It Estimate and How Well Does It Do It?
• Estimating Subagging by cross-validation
• Contributors of carbon dioxide in the atmosphere in Europe
• Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation
• Veridical data science
• Concentration inequalities of the cross-validation estimate for stable predictors
• Transfer Learning for Benign Overfitting in High-Dimensional Linear Regression
• Model Selection by Loss Rank for Classification and Unsupervised Learning
• Consistent Risk Estimation in Moderately High-Dimensional Linear Regression
• V-fold cross-validation improved: V-fold penalization
• Pharmacokinetic Equations Applied to Obtain New Topological Models in the Search of Antibacterial Compounds
• Model selection for ecologists: the worldviews of AIC and BIC
• Prediction Measures in Nonlinear Beta Regression Models
• A novel hybrid trust region algorithm based on nonmonotone and LOOCV techniques
• Estimating the genetic architecture of quantitative traits
• Prediction Measures in Beta Regression Models
• Approximating Full Conformal Prediction for Neural Network Regression with Gauss-Newton Influence
• Irredundant k-Fold Cross-Validation
• Comparing Classes of Estimators: When does Gradient Descent Beat Ridge\n Regression in Linear Models?
• A random model for multidimensional fitting method
• A scalable estimate of the extra-sample prediction error via approximate leave-one-out

Related

• A note on selection stability: combining stability and prediction
• Variable Selection in Seemingly Unrelated Regressions with Random Predictors
• Estimating the theoretical error rate for prediction
• Variable Selection in High Dimensional Linear Regressions with Parameter Instability
• Ridge Regression: Biased Estimation for Nonorthogonal Problems