  Conditional probabilistic graphical models provide a powerful framework for
structured regression in spatio-temporal datasets with complex correlation
patterns. However, in real-life applications a large fraction of observations
is often missing, which can severely limit the representational power of these
models. In this paper we propose a Marginalized Gaussian Conditional Random
Fields (m-GCRF) structured regression model for dealing with missing labels in
partially observed temporal attributed graphs. This method is aimed at learning
with both labeled and unlabeled parts and effectively predicting future values
in a graph. The method is even capable of learning from nodes for which the
response variable is never observed in history, which poses problems for many
state-of-the-art models that can handle missing data. The proposed model is
characterized for various missingness mechanisms on 500 synthetic graphs. The
benefits of the new method are also demonstrated on a challenging application
for predicting precipitation based on partial observations of climate variables
in a temporal graph that spans the entire continental US. We also show that the
method can be useful for optimizing the costs of data collection in climate
applications via active reduction of the number of weather stations to
consider. In experiments on these real-world and synthetic datasets we show
that the proposed model is consistently more accurate than alternative
semi-supervised structured models, as well as models that either use imputation
to deal with missing values or simply ignore them altogether.
