Learning Ensembles of Linear Gaussian Networks for Nonlinear and Spatial Data

The ability to accurately model nonlinear relationships is important in many real-world domains. Ensembled linear Gaussian networks (ELGNs), a class of ensembled Bayesian networks in which each conditional probability distribution (CPD) is a linear Gaussian distribution, have been shown to be capable of performing nonlinear regression. In this thesis, we introduce weighted bagging for ELGNs, which allows the components of the ensemble to train on individual clusters within the data and better model local relationships. When combined with Gaussian mixture regression (GMR), we have a powerful model for performing nonlinear regression. Using both synthetic and real datasets, we demonstrate ELGN's effectiveness and explore how various parameter settings affect performance.

In addition to possessing nonlinear relationships between variables, many domains include spatial and temporal aspects. Dynamic Bayesian networks (DBNs) are a common model for representing the evolution of a system over time. To model correlations between variables at different points in space, we introduce a method for performing spatial inference. Rather than making predictions for a set of query variables based only on evidence observed at the same point in space, we also take into account observed evidence at nearby points. Nearby evidence is weighted by a kernel function, which results in strong correlations between predictions at points close together in space. We apply spatial inference to predict reflectivity in a weather dataset.