Beyond Empirical Support: Structured Outlier Generation via Sinkhorn Optimal Transport
Abstract
Outliers are essential for evaluating and improving the robustness of machine learning systems, especially when future distributions may differ significantly from historical training data. In high-stakes applications, robustness often depends on rare cases that finite datasets fail to capture, making simple resampling or perturbation insufficient for stress scenario generation. Existing outlier synthesis methods typically rely on sparse neighborhoods, low support latent regions, or classifier boundary crossings, which can be heuristic, unstable, and tied to specific modalities or architectures. We therefore propose Sinkhorn Boundary Outlier Generation (SBOG), a structured framework for latent-space outlier generation that couples Sinkhorn optimal transport geometry with distributionally robust boundary modeling. The resulting Sinkhorn-induced support cost guides the sampler toward weakly supported boundary regions, while semantic constraints prevent uncontrolled drift from the intended context, yielding controlled deviations from the in-distribution reference measure rather than arbitrary sparse-region samples. Experiments on time series anomaly generation and image outlier synthesis show that our framework produces informative, semantically controlled outliers and improves downstream robustness evaluation across modalities, providing a foundation for stress scenario generation beyond empirical support.
Related
- Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parameter
- Accelerating Sinkhorn for Entropy-Regularized Optimal Transport
- Exponential convergence of Sinkhorn algorithm for entropy martingale optimal transport
- Forward Tangent-Centered Sinkhorn DRO: Exact Nominal Recovery from Optimal Transport to KL
- Annealed Sinkhorn with Momentum: Certified Unregularized Optimal Transport in Linear Memory
BibTeX
@misc{sun2026beyond,
title = {{Beyond Empirical Support: Structured Outlier Generation via Sinkhorn Optimal Transport}},
author = {Haixiang Sun and Andrew L. Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31470},
eprint = {2609.31470},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31470},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond Empirical Support: Structured Outlier Generation via Sinkhorn Optimal Transport
AU - Haixiang Sun
AU - Andrew L. Liu
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31470
UR - https://arxiv.org/abs/2609.31470
AB - Outliers are essential for evaluating and improving the robustness of machine learning systems, especially when future distributions may differ significantly from historical training data. In high-stakes applications, robustness often depends on rare cases that finite datasets fail to capture, making simple resampling or perturbation insufficient for stress scenario generation. Existing outlier synthesis methods typically rely on sparse neighborhoods, low support latent regions, or classifier boundary crossings, which can be heuristic, unstable, and tied to specific modalities or architectures. We therefore propose Sinkhorn Boundary Outlier Generation (SBOG), a structured framework for latent-space outlier generation that couples Sinkhorn optimal transport geometry with distributionally robust boundary modeling. The resulting Sinkhorn-induced support cost guides the sampler toward weakly supported boundary regions, while semantic constraints prevent uncontrolled drift from the intended context, yielding controlled deviations from the in-distribution reference measure rather than arbitrary sparse-region samples. Experiments on time series anomaly generation and image outlier synthesis show that our framework produces informative, semantically controlled outliers and improves downstream robustness evaluation across modalities, providing a foundation for stress scenario generation beyond empirical support.
ER -