Title: Convolutional Graph Auto-encoder: A Deep Generative Neural Architecture for Probabilistic Spatio-temporal Solar Irradiance Forecasting,
Abstract: Machine Learning on graph-structured data is an important and omnipresent
task for a vast variety of applications including anomaly detection and dynamic
network analysis. In this paper, a deep generative model is introduced to
capture continuous probability densities corresponding to the nodes of an
arbitrary graph. In contrast to all learning formulations in the area of
discriminative pattern recognition, we propose a scalable generative
optimization/algorithm theoretically proved to capture distributions at the
nodes of a graph. Our model is able to generate samples from the probability
densities learned at each node. This probabilistic data generation model, i.e.
convolutional graph auto-encoder (CGAE), is devised based on the localized
first-order approximation of spectral graph convolutions, deep learning, and
the variational Bayesian inference. We apply our CGAE to a new problem, the
spatio-temporal probabilistic solar irradiance prediction. Multiple solar
radiation measurement sites in a wide area in northern states of the US are
modeled as an undirected graph. Using our proposed model, the distribution of
future irradiance given historical radiation observations is estimated for
every site/node. Numerical results on the National Solar Radiation Database
show state-of-the-art performance for probabilistic radiation prediction on
geographically distributed irradiance data in terms of reliability, sharpness,
and continuous ranked probability score.