# Gaussian Process Regression with Local Explanation

arXiv: https://arxiv.org/abs/2007.01669 · HTML: https://mlsanity.com/paper/2007.01669/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 6 of 6)

- [Glass-box model representation of seismic failure mode prediction for conventional RC shear walls](https://mlsanity.com/paper/2111.13580/) (2021)
- [Training Deep Models to be Explained with Fewer Examples](https://mlsanity.com/paper/2112.03508/) (2021)
- [Explainable Learning with Gaussian Processes](https://mlsanity.com/paper/2403.07072/) (2024)
- [Integrated Gradient attribution for Gaussian Processes with non-Gaussian likelihoods](https://mlsanity.com/paper/2205.12797/) (2022)
- [Physics Inspired Approaches To Understanding Gaussian Processes](https://mlsanity.com/paper/2305.10748/) (2023)
- [Explanation-based Training with Differentiable Insertion/Deletion Metric-aware Regularizers](https://mlsanity.com/paper/2310.12553/) (2023)

## Abstract (arXiv)

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various applications. However, in GPR, how the features of an input contribute to its prediction cannot be interpreted. Herein, we propose GPR with local explanation, which reveals the feature contributions to the prediction of each sample, while maintaining the predictive performance of GPR. In the proposed model, both the prediction and explanation for each sample are performed using an easy-to-interpret locally linear model. The weight vector of the locally linear model is assumed to be generated from multivariate Gaussian process priors. The hyperparameters of the proposed models are estimated by maximizing the marginal likelihood. For a new test sample, the proposed model can predict the values of its target variable and weight vector, as well as their uncertainties, in a closed form. Experimental results on various benchmark datasets verify that the proposed model can achieve predictive performance comparable to those of GPR and superior to that of existing interpretable models, and can achieve higher interpretability than them, both quantitatively and qualitatively.