Sparsity by Default: The Theory and Practice of ARD in Gaussian Process Regression for Variable Selection

arXiv:2609.33550 · stat.ML, cs.LG · Submitted 2026-09-27 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-27

Updated: 2026-09-27

Code: https://github.com/heffieldML/GPy

Terminology

• Sparsity — 42× in this paper · explained in 4 episodes
• Consistency — 19× in this paper · explained in 3 episodes
• Trace — 9× in this paper · explained in 2 episodes
• Bayesian Optimization — 8× in this paper · explained in 3 episodes
• Calibration — 7× in this paper · explained in 7 episodes
• Regularization — 7× in this paper · explained in 3 episodes
• Pruning — 5× in this paper · explained in 4 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Bayesian Inference — 3× in this paper · explained in 5 episodes
• Failure Modes — 3× in this paper · explained in 3 episodes
• Uncertainty Quantification — 3× in this paper · explained in 8 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Active Learning — 2× in this paper · explained in 6 episodes
• Bayesian Framework — 2× in this paper · explained in 3 episodes
• Conference on Uncertainty in Artificial Intelligence — 2× in this paper
• Feature Selection — 2× in this paper · explained in 4 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• International Conference on Machine Learning — 2× in this paper
• Additive Decomposition — 1× in this paper · explained in 1 episode
• Additivity — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Commentary — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Quantifying Uncertainty — 1× in this paper · explained in 5 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• Bayesian Smoothing and Feature Selection Using variational Automatic Relevance Determination
• Bayesian Bridge Gaussian Process Regression
• Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• Efficient quadratic entropy with distance sketches
• Embedding-Bias in Conditional Independence Testing
• From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier