# High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

arXiv: https://arxiv.org/abs/2102.01142 · HTML: https://mlsanity.com/paper/2102.01142/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2021.

## Built on by (most cited first, 5 of 5)

- [Conformal Predictive Programming for Chance Constrained Optimization](https://mlsanity.com/paper/2402.07407/) (2024)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [Risk-Averse Certification of Bayesian Neural Networks](https://mlsanity.com/paper/2411.19729/) (2024)
- [Efficient Distribution Learning with Error Bounds in Wasserstein Distance](https://mlsanity.com/paper/2602.08063/) (2026)
- [Distributionally Robust Federated Learning with Multi-Source Data](https://mlsanity.com/paper/2609.20501/) (2026)

## Abstract (arXiv)

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out-of-sample guarantees. We assume the random variable evolves in discrete time under uncertain initial conditions and dynamics, and that noisy partial measurements are available. All random elements have unknown probability distributions and we make inferences about the distribution of the state vector using several output samples from multiple realizations of the process. To this end, we leverage an observer to estimate the state of each independent realization and exploit the outcome to construct the ambiguity sets. We illustrate our results in an economic dispatch problem involving distributed energy resources over which the scheduler has no direct control.