  Time series forecasting is an extensively studied subject in statistics,
economics, and computer science. Exploration of the correlation and causation
among the variables in a multivariate time series shows promise in enhancing
the performance of a time series model. When using deep neural networks as
forecasting models, we hypothesize that exploiting the pairwise information
among multiple (multivariate) time series also improves their forecast. If an
explicit graph structure is known, graph neural networks (GNNs) have been
demonstrated as powerful tools to exploit the structure. In this work, we
propose learning the structure simultaneously with the GNN if the graph is
unknown. We cast the problem as learning a probabilistic graph model through
optimizing the mean performance over the graph distribution. The distribution
is parameterized by a neural network so that discrete graphs can be sampled
differentiably through reparameterization. Empirical evaluations show that our
method is simpler, more efficient, and better performing than a recently
proposed bilevel learning approach for graph structure learning, as well as a
broad array of forecasting models, either deep or non-deep learning based, and
graph or non-graph based.
