  Multi-task learning requires accurate identification of the correlations
between tasks. In real-world time-series, tasks are rarely perfectly temporally
aligned; traditional multi-task models do not account for this and subsequent
errors in correlation estimation will result in poor predictive performance and
uncertainty quantification. We introduce a method that automatically accounts
for temporal misalignment in a unified generative model that improves
predictive performance. Our method uses Gaussian processes (GPs) to model the
correlations both within and between the tasks. Building on the previous work
by Kazlauskaiteet al. [2019], we include a separate monotonic warp of the input
data to model temporal misalignment. In contrast to previous work, we formulate
a lower bound that accounts for uncertainty in both the estimates of the
warping process and the underlying functions. Also, our new take on a monotonic
stochastic process, with efficient path-wise sampling for the warp functions,
allows us to perform full Bayesian inference in the model rather than MAP
estimates. Missing data experiments, on synthetic and real time-series,
demonstrate the advantages of accounting for misalignments (vs standard
unaligned method) as well as modelling the uncertainty in the warping
process(vs baseline MAP alignment approach).
