Global and local Gaussian process for multioutput and treed data

Abstract

We propose a novel Multi-Level Multiple Output Gaussian Process framework for dealing with multivariate and treed data.We define a two-layer hierarchical tree with parent nodes on the upper layer and children nodes on the lower layer in order to represent the interaction between the multiple outputs.Then we compute the Multiple Output Gaussian Process (MGP) covariance matrix as a linear combination of a global multiple output covariance matrix (using the total number of outputs) and a set of local matrices (only using the outputs belonging to each parent node). With this construction of the covariance matrix and the tree we are capable to do interpolation using the MGP framework. To improve the results, we also test different ways of computing the Intrinsic Model of Coregionalization covariance matrix that uses the input space. Results over synthetic data, Motion Capture data and Wireless data shows that the proposed methodology makes a better representation of treed multiple output data.