# Sliced-Wasserstein Distance-based Data Selection

arXiv: https://arxiv.org/abs/2504.12918 · HTML: https://mlsanity.com/paper/2504.12918/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 13 of 13)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networks](https://mlsanity.com/paper/2002.10553/) (2020)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Fast Convex Optimization for Two-Layer ReLU Networks: Equivalent Model Classes and Cone Decompositions](https://mlsanity.com/paper/2202.01331/) (2022)
- [Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications](https://mlsanity.com/paper/1910.01624/) (2019)
- [WOOD: Wasserstein-based Out-of-Distribution Detection](https://mlsanity.com/paper/2112.06384/) (2021)
- [Wasserstein Distributionally Robust Shallow Convex Neural Networks](https://mlsanity.com/paper/2407.16800/) (2024)
- [Sliced-Wasserstein-based Anomaly Detection and Open Dataset for Localized Critical Peak Rebates](https://mlsanity.com/paper/2410.21712/) (2024)

## Abstract (arXiv)

We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying machine learning models in critical sectors, e.g., power systems, as it offers a conservative data selection and an optimal transport interpretation. To ensure the scalability of our method, we provide two efficient approximations. The first approximation processes reduced-cardinality representations of the datasets concurrently. The second makes use of a computationally light Euclidian distance approximation. Additionally, we open the first dataset showcasing localized critical peak rebate demand response in a northern climate. We present the filtering patterns of our method on synthetic datasets and numerically benchmark our method for training data selection. Finally, we employ our method as part of a first forecasting benchmark for our open-source dataset.