A Bayesian Framework for Built-in Input Dimension Reduction for Gaussian Process Modeling

arXiv:2607.19498 · stat.ML, cs.LG, math.PR, stat.AP, stat.CO, stat.ME · Submitted 2026-07-21 · Read on arXiv

Eric Herrison Gyamfi, Emily L. Kang, Bledar A. Konomi, Guang Lin

stat.ML, cs.LG, math.PR, stat.AP, stat.CO, stat.ME

Submitted: 2026-07-21

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Uncertainty Quantification — 27× in this paper · explained in 9 episodes
• Accuracy — 17× in this paper · explained in 1 episode
• Stiefel Manifold — 17× in this paper · explained in 3 episodes
• Matrix Langevin — 16× in this paper
• Deep Gaussian Processes — 15× in this paper
• Calibration — 11× in this paper · explained in 9 episodes
• Hyperparameters — 10× in this paper · explained in 2 episodes
• Fidelity — 9× in this paper · explained in 2 episodes
• Surrogate Model — 9× in this paper · explained in 3 episodes
• Bayesian Framework — 7× in this paper · explained in 3 episodes
• Bayesian Inference — 7× in this paper · explained in 6 episodes
• Benchmark — 7× in this paper · explained in 2 episodes
• Surrogate Modeling — 7× in this paper · explained in 2 episodes
• Hamiltonian Monte Carlo — 6× in this paper
• Surrogate Models — 6× in this paper · explained in 3 episodes
• Dimensionality Reduction — 5× in this paper · explained in 2 episodes
• Latent Variables — 5× in this paper · explained in 2 episodes
• Curse of Dimensionality — 4× in this paper · explained in 6 episodes
• Elliptical Slice Sampling — 4× in this paper
• Active Learning — 3× in this paper · explained in 6 episodes
• Gaussian Process (GP) — 3× in this paper · explained in 2 episodes
• Bayesian Information Criterion — 2× in this paper
• Benchmarking — 2× in this paper · explained in 4 episodes
• Continuous Ranked Probability Score — 2× in this paper
• Continuous Ranked Probability Score (CRPS) — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Empirical Coverage — 2× in this paper · explained in 2 episodes
• Latin Hypercube Sampling — 2× in this paper
• Mean Log Pointwise Predictive Density — 2× in this paper
• Parameterization — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 3 episodes
• Agent-Based Simulation — 1× in this paper · explained in 2 episodes
• Bayesian Optimization — 1× in this paper · explained in 3 episodes
• Computational Biology — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Free-Form Deformation — 1× in this paper
• Generalization — 1× in this paper · explained in 14 episodes
• Hierarchical Structure — 1× in this paper · explained in 3 episodes
• Intrinsic Dimension — 1× in this paper · explained in 3 episodes
• Overfitting — 1× in this paper · explained in 2 episodes
• Performance Gap — 1× in this paper · explained in 2 episodes
• Quantifying Uncertainty — 1× in this paper · explained in 5 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 6 episodes
• Root Mean Square Prediction Error — 1× in this paper
• Uncertainty Propagation — 1× in this paper · explained in 4 episodes
• Uncertainty Quantification (UQ) — 1× in this paper · explained in 3 episodes
• Unified Framework — 1× in this paper · explained in 6 episodes
• Variational Bayesian — 1× in this paper
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Gradient-based kernel dimension reduction for supervised learning
• A Fully Bayesian Gradient-Free Supervised Dimension Reduction Method using Gaussian Processes
• Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions

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