# Variable selection for Gaussian processes via sensitivity analysis of the posterior predictive distribution

arXiv: https://arxiv.org/abs/1712.08048 · HTML: https://mlsanity.com/paper/1712.08048/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2017.

## Built on by (most cited first, 15 of 15)

- [Benchmarking the Performance of Bayesian Optimization across Multiple Experimental Materials Science Domains](https://mlsanity.com/paper/2106.01309/) (2021)
- [Select Wisely and Explain: Active Learning and Probabilistic Local Post-hoc Explainability](https://mlsanity.com/paper/2108.06907/) (2021)
- [Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection](https://mlsanity.com/paper/2109.09264/) (2021)
- [Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling](https://mlsanity.com/paper/2205.14283/) (2022)
- [Fast and Scalable Spike and Slab Variable Selection in High-Dimensional Gaussian Processes](https://mlsanity.com/paper/2111.04558/) (2021)
- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning models](https://mlsanity.com/paper/2209.11539/) (2022)
- [Model Predictive Robustness of Signal Temporal Logic Predicates](https://mlsanity.com/paper/2209.07881/) (2022)
- [Polynomial Chaos Expanded Gaussian Process](https://mlsanity.com/paper/2405.01052/) (2024)
- [Nowcasting with Mixed Frequency Data Using Gaussian Processes](https://mlsanity.com/paper/2402.10574/) (2024)
- [Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression](https://mlsanity.com/paper/2403.13300/) (2024)
- [Bayesian Optimization for Automatic Tuning of Torque-Level Nonlinear Model Predictive Control](https://mlsanity.com/paper/2512.03772/) (2025)
- [Gaussian Process-based learning with new MCMC-based implementation of Wishart prior on correlation matrix](https://mlsanity.com/paper/2605.27093/) (2026)
- [Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection](https://mlsanity.com/paper/2609.33549/) (2026)
- [Sparsity by Default: The Theory and Practice of ARD in Gaussian Process Regression for Variable Selection](https://mlsanity.com/paper/2609.33550/) (2026)

## Abstract (arXiv)

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined relevance has several drawbacks that prevent the selection of optimal input variables in terms of predictive performance. To improve on this, we propose two novel variable selection methods for Gaussian process models that utilize the predictions of a full model in the vicinity of the training points and thereby rank the variables based on their predictive relevance. Our empirical results on synthetic and real world data sets demonstrate improved variable selection compared to automatic relevance determination in terms of variability and predictive performance.