Multioutput Convolution Spectral Mixture for Gaussian Processes.

Area of Science:

• Machine Learning
• Statistical Modeling

Background:

• Multi-output Gaussian processes (MOGPs) extend Gaussian processes (GPs) for simultaneous prediction of multiple output variables.
• Modeling cross-channel dependencies is crucial for improving MOGP performance.

Purpose of the Study:

• To introduce a novel kernel for MOGPs that effectively models cross-channel dependencies.
• To evaluate the performance of the proposed kernel against existing methods.

Main Methods:

• Utilized the convolution theorem to design a new kernel for MOGPs.
• Modeled cross-channel dependencies via cross-convolution in the spectral domain.
• Developed the Multi-Output Convolution Spectral Mixture (MOCSM) kernel.

Main Results:

• The MOCSM kernel demonstrated state-of-the-art performance on synthetic and real-life datasets.
• MOCSM reduces to the standard Spectral Mixture (SM) kernel for single-channel cases.
• Outperformed a recently introduced multi-output SM kernel by avoiding undesirable scale effects.

Conclusions:

• The proposed MOCSM kernel is a significant advancement for multi-output Gaussian processes.
• MOCSM offers a robust and effective approach for modeling complex multi-channel data.
• The kernel's design addresses limitations of previous multi-output kernels.