  In domains where sample sizes are limited, efficient learning algorithms are
critical. Learning using privileged information (LuPI) offers increased sample
efficiency by allowing prediction models access to auxiliary information at
training time which is unavailable when the models are used. In recent work, it
was shown that for prediction in linear-Gaussian dynamical systems, a LuPI
learner with access to intermediate time series data is never worse and often
better in expectation than any unbiased classical learner. We provide new
insights into this analysis and generalize it to nonlinear prediction tasks in
latent dynamical systems, extending theoretical guarantees to the case where
the map connecting latent variables and observations is known up to a linear
transform. In addition, we propose algorithms based on random features and
representation learning for the case when this map is unknown. A suite of
empirical results confirm theoretical findings and show the potential of using
privileged time-series information in nonlinear prediction.
