# Gaussian Process Models with Low-Rank Correlation Matrices for Both Continuous and Categorical Inputs

arXiv: https://arxiv.org/abs/2010.02574 · HTML: https://mlsanity.com/paper/2010.02574/

## Key facts

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

## Built on by (most cited first, 3 of 3)

- [Distributional encoding for Gaussian process regression with qualitative inputs](https://mlsanity.com/paper/2506.04813/) (2025)
- [Bayesian Optimisation for Mixed-Variable Inputs using Value Proposals](https://mlsanity.com/paper/2202.04832/) (2022)
- [A reproducible comparative study of categorical kernels for Gaussian process regression, with new clustering-based nested kernels](https://mlsanity.com/paper/2510.01840/) (2025)

## Abstract (arXiv)

We introduce a method that uses low-rank approximations of cross-correlation matrices in mixed continuous and categorical Gaussian Process models. This new method -- called Low-Rank Correlation (LRC) -- offers the ability to flexibly adapt the number of parameters to the problem at hand by choosing an appropriate rank of the approximation. Furthermore, we present a systematic approach of defining test functions that can be used for assessing the accuracy of models or optimization methods that are concerned with both continuous and categorical inputs. We compare LRC to existing approaches of modeling the cross-correlation matrix. It turns out that the new approach performs well in terms of estimation of cross-correlations and response surface prediction. Therefore, LRC is a flexible and useful addition to existing methods, especially for increasing numbers of combinations of levels of the categorical inputs.