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We study prediction of future outcomes with supervised models that useprivileged information during learning. The privileged information comprisessamples of time series observed between the baseline time of prediction and thefuture outcome; this information is only available at training time whichdiffers from the traditional supervised learning. Our question is when usingthis privileged data leads to more sample-efficient learning of models that useonly baseline data for predictions at test time. We give an algorithm for thissetting and prove that when the time series are drawn from a non-stationaryGaussian-linear dynamical system of fixed horizon, learning with privilegedinformation is more efficient than learning without it. On synthetic data, wetest the limits of our algorithm and theory, both when our assumptions hold andwhen they are violated. On three diverse real-world datasets, we show that ourapproach is generally preferable to classical learning, particularly when datais scarce. Finally, we relate our estimator to a distillation approach boththeoretically and empirically.

Using Time-Series Privileged Information for Provably Efficient Learning of Prediction Models