Multi-Output Gaussian Processes for Graph-Structured Data
Ayano Nakai-Kasai, Tadashi Wadayama
TL;DR
This work extends Gaussian process regression to graph-structured data by formulating a generalized multi-output Gaussian process (MOGP) that jointly models signals on graph vertices. It introduces flexible kernel designs, including separable, sum-of-separable, and convolution-based (process convolution) kernels, to capture both graph connectivity and data dependencies; it also enables diverse input configurations (heterotopic/isotropic) and inference scenarios (including missing data and induced subgraphs). The approach subsumes classical SOGP and prior MOGP graph methods as special cases while offering new kernels (e.g., graph PC) and broader applicability. Experimental results on synthetic and real datasets demonstrate improved predictive certainty and performance when graph-structure is properly integrated, with potential for scalable extensions and broad applicability in graph-based regression tasks.
Abstract
Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on multi-output Gaussian processes (MOGP), to capture both the correlation between vertices and the correlation between associated data. The proposed formulation is built on the definition of MOGP. This allows it to be applied to a wide range of data configurations and scenarios. Moreover, it has high expressive capability due to its flexibility in kernel design. It includes existing methods of Gaussian processes for graph-structured data as special cases and is possible to remove restrictions on data configurations, model selection, and inference scenarios in the existing methods. The performance of extensions achievable by the proposed formulation is evaluated through computer experiments with synthetic and real data.