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We present a principled study on defining Gaussian processes (GPs) with inputs on the product of directional manifolds. A circular kernel is first presented according to the von Mises distribution. Based thereon, the hypertoroidal von Mises…

Machine Learning · Computer Science 2024-06-19 Ziyu Cao , Kailai Li

Multi-output Gaussian processes (MOGP) are probability distributions over vector-valued functions, and have been previously used for multi-output regression and for multi-class classification. A less explored facet of the multi-output…

Machine Learning · Statistics 2015-02-10 Sebastián Gómez-González , Mauricio A. Álvarez , Hernán Felipe García

Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for…

Machine Learning · Statistics 2024-09-06 Wang Xinming , Li Yongxiang , Yue Xiaowei , Wu Jianguo

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability,…

Machine Learning · Computer Science 2026-05-29 Xiaoyu Jiang , Xinxing Shi , Sokratia Georgaka , Magnus Rattray , Mauricio A Álvarez

Spectral mixture (SM) kernels comprise a powerful class of generalized kernels for Gaussian processes (GPs) to describe complex patterns. This paper introduces model compression and time- and phase (TP) modulated dependency structures to…

Machine Learning · Computer Science 2023-07-27 Kai Chen , Yijue Dai , Feng Yin , Elena Marchiori , Sergios Theodoridis

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

Machine Learning · Statistics 2018-07-19 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…

Machine Learning · Statistics 2024-03-20 Dionissios T. Hristopulos

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging…

Machine Learning · Statistics 2025-10-20 Tengjie Zheng , Jilan Mei , Di Wu , Lin Cheng , Shengping Gong

This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem…

Machine Learning · Statistics 2015-11-25 Yehong Zhang , Trong Nghia Hoang , Kian Hsiang Low , Mohan Kankanhalli

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

Machine Learning · Statistics 2026-02-27 Arsalan Jawaid , Abdullah Karatas , Jörg Seewig

Hidden Markov Model (HMM) combined with Gaussian Process (GP) emission can be effectively used to estimate the hidden state with a sequence of complex input-output relational observations. Especially when the spectral mixture (SM) kernel is…

Machine Learning · Computer Science 2020-01-08 Yohan Jung , Jinkyoo Park

In learning from demonstrations, it is often desirable to adapt the behavior of the robot as a function of the variability retrieved from human demonstrations and the (un)certainty encoded in different parts of the task. In this paper, we…

Robotics · Computer Science 2019-10-14 Noémie Jaquier , David Ginsbourger , Sylvain Calinon

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…

Machine Learning · Statistics 2023-05-09 Michael Minyi Zhang , Bianca Dumitrascu , Sinead A. Williamson , Barbara E. Engelhardt

Aggregate data often appear in various fields such as socio-economics and public security. The aggregate data are associated not with points but with supports (e.g., spatial regions in a city). Since the supports may have various…

Gaussian processes (GP) are a versatile tool in machine learning and computational science. We here consider the case of multi-output Gaussian processes (MOGP) and present low-rank approaches for efficiently computing the posterior mean of…

Numerical Analysis · Mathematics 2025-05-01 Sebastian Esche , Martin Stoll

We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present…

Machine Learning · Statistics 2019-10-15 Zheyang Shen , Markus Heinonen , Samuel Kaski

Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function…

Machine Learning · Statistics 2009-12-18 Mauricio A. Álvarez , David Luengo , Michalis K. Titsias , Neil D. Lawrence

This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels…

Machine Learning · Statistics 2021-06-11 Magnus Ross , Michael T. Smith , Mauricio A. Álvarez

Multi-output Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatio-temporal modelling. The key problem with MOGPs is their…

Machine Learning · Statistics 2020-07-20 Wessel P. Bruinsma , Eric Perim , Will Tebbutt , J. Scott Hosking , Arno Solin , Richard E. Turner

This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization…

Machine Learning · Statistics 2022-12-12 Jieren Xu , Yitong Li , Haizhao Yang , David Dunson , Ingrid Daubechies