# Fast Empirical Scenarios

arXiv: https://arxiv.org/abs/2307.03927 · HTML: https://mlsanity.com/paper/2307.03927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 57 references that are in the map.
- First posted on arXiv 8 Jul 2023.

## Builds on (most cited first, 8 of 8)

- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Kernel quadrature with DPPs](https://mlsanity.com/paper/1906.07832/) (2019)
- [Positively Weighted Kernel Quadrature via Subsampling](https://mlsanity.com/paper/2107.09597/) (2021)
- [Exact Worst-case Performance of First-order Methods for Composite Convex Optimization](https://mlsanity.com/paper/1512.07516/) (2015)
- [Adaptive Restart of the Optimized Gradient Method for Convex Optimization](https://mlsanity.com/paper/1703.04641/) (2017)
- [A Randomized Algorithm to Reduce the Support of Discrete Measures](https://mlsanity.com/paper/2006.01757/) (2020)

## Abstract (arXiv)

We seek to extract a small number of representative scenarios from large panel data that are consistent with sample moments. Among two novel algorithms, the first identifies scenarios that have not been observed before, and comes with a scenario-based representation of covariance matrices. The second proposal selects important data points from states of the world that have already realized, and are consistent with higher-order sample moment information. Both algorithms are efficient to compute and lend themselves to consistent scenario-based modeling and multi-dimensional numerical integration that can be used for interpretable decision-making under uncertainty. Extensive numerical benchmarking studies and an application in portfolio optimization favor the proposed algorithms.