# Meta-Learning Mean Functions for Gaussian Processes

arXiv: https://arxiv.org/abs/1901.08098 · HTML: https://mlsanity.com/paper/1901.08098/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2019.

## Built on by (most cited first, 17 of 17)

- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Environmental Sensor Placement with Convolutional Gaussian Neural Processes](https://mlsanity.com/paper/2211.10381/) (2022)
- [Non-Gaussian Gaussian Processes for Few-Shot Regression](https://mlsanity.com/paper/2110.13561/) (2021)
- [MARS: Meta-Learning as Score Matching in the Function Space](https://mlsanity.com/paper/2210.13319/) (2022)
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- [End-to-End Learning of Deep Kernel Acquisition Functions for Bayesian Optimization](https://mlsanity.com/paper/2111.00639/) (2021)
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- [Meta-learning for Out-of-Distribution Detection via Density Estimation in Latent Space](https://mlsanity.com/paper/2206.09543/) (2022)
- [Sparse Gaussian Neural Processes](https://mlsanity.com/paper/2504.01650/) (2025)
- [Principal component analysis for Gaussian process posteriors](https://mlsanity.com/paper/2107.07115/) (2021)
- [Transfer Bayesian Meta-learning via Weighted Free Energy Minimization](https://mlsanity.com/paper/2106.10711/) (2021)
- [Multi-Task Neural Processes](https://mlsanity.com/paper/2110.14953/) (2021)
- [Meta-learning to Calibrate Gaussian Processes with Deep Kernels for Regression Uncertainty Estimation](https://mlsanity.com/paper/2312.07952/) (2023)
- [Few-shot Scooping Under Domain Shift via Simulated Maximal Deployment Gaps](https://mlsanity.com/paper/2408.02949/) (2024)
- [Prevention of Overfitting on Mesh-Structured Data Regressions with a Modified Laplace Operator](https://mlsanity.com/paper/2507.06631/) (2025)
- [Amortising Inference and Meta-Learning Priors in Neural Networks](https://mlsanity.com/paper/2602.08782/) (2026)
- [Transformed Latent Variable Multi-Output Gaussian Processes](https://mlsanity.com/paper/2605.05133/) (2026)

## Abstract (arXiv)

When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge from data acquired in related tasks. When it comes to meta-learning in Gaussian process models, approaches in this setting have mostly focused on learning the kernel function of the prior, but not on learning its mean function. In this work, we explore meta-learning the mean function of a Gaussian process prior. We present analytical and empirical evidence that mean function learning can be useful in the meta-learning setting, discuss the risk of overfitting, and draw connections to other meta-learning approaches, such as model agnostic meta-learning and functional PCA.