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

arXiv: https://arxiv.org/abs/2110.14993 · HTML: https://mlsanity.com/paper/2110.14993/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Model-Based Value Estimation for Efficient Model-Free Reinforcement Learning](https://mlsanity.com/paper/1803.00101/) (2018)
- [Neural Pharmacodynamic State Space Modeling](https://mlsanity.com/paper/2102.11218/) (2021)
- [Patterns for Learning with Side Information](https://mlsanity.com/paper/1511.06429/) (2015)
- [Policy Optimization with Second-Order Advantage Information](https://mlsanity.com/paper/1805.03586/) (2018)

## Built on by (most cited first, 6 of 6)

- [Efficient learning of nonlinear prediction models with time-series privileged information](https://mlsanity.com/paper/2209.07067/) (2022)
- [Unsupervised domain adaptation by learning using privileged information](https://mlsanity.com/paper/2303.09350/) (2023)
- [Improving Text-based Early Prediction by Distillation from Privileged Time-Series Text](https://mlsanity.com/paper/2301.10887/) (2023)
- [When are radiology reports useful for training medical image classifiers?](https://mlsanity.com/paper/2510.24385/) (2025)
- [Longitudinal Risk Prediction in Mammography with Privileged History Distillation](https://mlsanity.com/paper/2603.15814/) (2026)
- [Which Histories Matter for Time Series Forecasting? Learning Predictive Relevance with Future Supervision](https://mlsanity.com/paper/2608.23221/) (2026)

## Abstract (arXiv)

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.