We study prediction of future outcomes with supervised models that use privileged information during learning. The privileged information comprises samples of time series observed between the baseline time of prediction and the future outcome; this information is only available at training time which differs from the traditional supervised learning. Our question is when using this privileged data leads to more sample-efficient learning of models that use only baseline data for predictions at test time. We give an algorithm for this setting and prove that when the time series are drawn from a non-stationary Gaussian-linear dynamical system of fixed horizon, learning with privileged information is more efficient than learning without it. On synthetic data, we test the limits of our algorithm and theory, both when our assumptions hold and when they are violated. On three diverse real-world datasets, we show that our approach is generally preferable to classical learning, particularly when data is scarce. Finally, we relate our estimator to a distillation approach both theoretically and empirically.

翻译：我们用在学习期间使用特权信息的受监督模型来研究未来结果的预测。特权信息包括预测基线时间与未来结果之间观察到的时间序列样本;这种信息只能在培训时间提供,而培训时间不同于传统的受监督学习。我们的问题是,在使用这种特许数据时,如何使只使用基准数据进行试验时间预测的模型的抽样效率更高。我们为此设定了一个算法,并证明当时间序列从非静止的固定地平线动态系统中抽取时,学习特权信息比不学更有效率。在合成数据方面,我们测试我们的算法和理论的局限性,无论是在假设维持时还是在被违反时。在三种不同的现实世界数据集中,我们显示我们的方法一般比传统的学习更可取,特别是在数据稀少时。最后,我们把我们的估算方法与理论和经验的提法联系起来。