Multi-Output Gaussian Processes for Graph-Structured Data
This work addresses regression problems for data with graph structures, offering a flexible framework that is incremental in extending Gaussian process methods.
The paper tackles regression on graph-structured data by proposing a multi-output Gaussian process method that captures correlations between vertices and associated data, showing it generalizes existing methods and removes restrictions in data configurations and inference scenarios.
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.