# Multi-Output Convolution Spectral Mixture for Gaussian Processes

arXiv: https://arxiv.org/abs/1808.02266 · HTML: https://mlsanity.com/paper/1808.02266/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2018.

## Built on by (most cited first, 4 of 4)

- [Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains](https://mlsanity.com/paper/2202.12636/) (2022)
- [Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey](https://mlsanity.com/paper/2103.10134/) (2021)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [Offline Multi-Task Multi-Objective Data-Driven Evolutionary Algorithm with Language Surrogate Model and Implicit Q-Learning](https://mlsanity.com/paper/2512.15149/) (2025)

## Abstract (arXiv)

Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of time and phase delayed components in the spectral domain. The resulting kernel is called Multi-Output Convolution Spectral Mixture (MOCSM) kernel. Results of extensive experiments on synthetic and real-life datasets demonstrate the advantages of the proposed kernel and its state of the art performance. MOCSM enjoys the desirable property to reduce to the well known Spectral Mixture (SM) kernel when a single-channel is considered. A comparison with the recently introduced Multi-Output Spectral Mixture kernel reveals that this is not the case for the latter kernel, which contains quadratic terms that generate undesirable scale effects when the spectral densities of different channels are either very close or very far from each other in the frequency domain.