  Time series datasets are often composed of a variety of sequences from the
same domain, but from different entities, such as individuals, products, or
organizations. We are interested in how time series models can be specialized
to individual sequences (capturing the specific characteristics) while still
retaining statistical power by sharing commonalities across the sequences. This
paper describes the multi-task dynamical system (MTDS); a general methodology
for extending multi-task learning (MTL) to time series models. Our approach
endows dynamical systems with a set of hierarchical latent variables which can
modulate all model parameters. To our knowledge, this is a novel development of
MTL, and applies to time series both with and without control inputs. We apply
the MTDS to motion-capture data of people walking in various styles using a
multi-task recurrent neural network (RNN), and to patient drug-response data
using a multi-task pharmacodynamic model.
