Fusion of Gaussian Processes Predictions with Monte Carlo Sampling
Marzieh Ajirak Daniel Waxman Fernando Llorente Petar M. Djuric
In science and engineering, we often work with models designed for accurate
prediction of variables of interest. Recognizing that these models are
approximations of reality, it becomes desirable to apply multiple models to the
same data and integrate their outcomes. In this paper, we operate within the
Bayesian paradigm, relying on Gaussian processes as our models. These models
generate predictive probability density functions (pdfs), and the objective is
to integrate them systematically, employing both linear and log-linear pooling.
We introduce novel approaches for log-linear pooling, determining
input-dependent weights for the predictive pdfs of the Gaussian processes. The
aggregation of the pdfs is realized through Monte Carlo sampling, drawing
samples of weights from their posterior. The performance of these methods, as
well as those based on linear pooling, is demonstrated using a synthetic
dataset.