# On Negative Transfer and Structure of Latent Functions in Multi-output Gaussian Processes

arXiv: https://arxiv.org/abs/2004.02382 · HTML: https://mlsanity.com/paper/2004.02382/

## Key facts

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

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

- [The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning](https://mlsanity.com/paper/2111.05326/) (2021)
- [Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes](https://mlsanity.com/paper/2407.16935/) (2024)
- [Local transfer learning Gaussian process modeling, with applications to surrogate modeling of expensive computer simulators](https://mlsanity.com/paper/2410.12690/) (2024)
- [Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learning](https://mlsanity.com/paper/2508.16434/) (2025)
- [Residual Correlation as a Diagnostic for Joint-Uncertainty Gains from GP Coregionalisation](https://mlsanity.com/paper/2609.30085/) (2026)
- [Collaborative Principle Evolution via Evidence Transfer for Scientific Discovery](https://mlsanity.com/paper/2609.35315/) (2026)

## Abstract (arXiv)

The multi-output Gaussian process (MGP) is based on the assumption that outputs share commonalities, however, if this assumption does not hold negative transfer will lead to decreased performance relative to learning outputs independently or in subsets. In this article, we first define negative transfer in the context of an MGP and then derive necessary conditions for an MGP model to avoid negative transfer. Specifically, under the convolution construction, we show that avoiding negative transfer is mainly dependent on having a sufficient number of latent functions Q regardless of the flexibility of the kernel or inference procedure used. However, a slight increase in Q leads to a large increase in the number of parameters to be estimated. To this end, we propose two latent structures that scale to arbitrarily large datasets, can avoid negative transfer and allow any kernel or sparse approximations to be used within. These structures also allow regularization which can provide consistent and automatic selection of related outputs.