  Multi-task learning (MTL) improves prediction performance in different
contexts by learning models jointly on multiple different, but related tasks.
Network data, which are a priori data with a rich relational structure, provide
an important context for applying MTL. In particular, the explicit relational
structure implies that network data is not i.i.d. data. Network data also often
comes with significant metadata (i.e., attributes) associated with each entity
(node). Moreover, due to the diversity and variation in network data (e.g.,
multi-relational links or multi-category entities), various tasks can be
performed and often a rich correlation exists between them. Learning algorithms
should exploit all of these additional sources of information for better
performance. In this work we take a metric-learning point of view for the MTL
problem in the network context. Our approach builds on structure preserving
metric learning (SPML). In particular SPML learns a Mahalanobis distance metric
for node attributes using network structure as supervision, so that the learned
distance function encodes the structure and can be used to predict link
patterns from attributes. SPML is described for single-task learning on single
network. Herein, we propose a multi-task version of SPML, abbreviated as
MT-SPML, which is able to learn across multiple related tasks on multiple
networks via shared intermediate parametrization. MT-SPML learns a specific
metric for each task and a common metric for all tasks. The task correlation is
carried through the common metric and the individual metrics encode task
specific information. When combined together, they are structure-preserving
with respect to individual tasks. MT-SPML works on general networks, thus is
suitable for a wide variety of problems. In experiments, we challenge MT-SPML
on two real-word problems, where MT-SPML achieves significant improvement.
