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.

翻译：在样本量有限的领域中，高效学习算法至关重要。基于特权信息的学习（LuPI）通过允许预测模型在训练阶段访问辅助信息（这些信息在模型使用时不可获取）来提升样本效率。近期研究表明，在线性-高斯动态系统的预测中，能够访问中间时间序列数据的LuPI学习器在期望性能上始终不劣于且通常优于任何无偏经典学习器。本文为该分析提供了新见解，并将其推广至隐式动态系统中的非线性预测任务，将理论保证扩展至潜变量与观测值之间的映射已知（至多相差线性变换）的情形。此外，针对映射未知的情况，我们提出了基于随机特征和表征学习的算法。一系列实证结果验证了理论发现，并展示了利用时间序列特权信息进行非线性预测的潜力。