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[2601.06830] Constrained Density Estimation via Optimal Transport
Summary
This paper presents a novel framework for constrained density estimation using optimal transport, focusing on minimizing Wasserstein distance while adhering to expectation constraints.
Why It Matters
The proposed framework addresses significant challenges in density estimation, particularly in fields like finance where constraints on expected values are crucial. By utilizing optimal transport, this method enhances the accuracy and reliability of density estimates, making it relevant for practitioners and researchers in statistics and machine learning.
Key Takeaways
- Introduces a framework for density estimation under expectation constraints.
- Minimizes Wasserstein distance between estimated and prior densities.
- Includes regularization techniques to reduce artifacts in target measures.
- Develops an annealing-like algorithm for non-smooth constraints.
- Demonstrates effectiveness through synthetic and real-world finance examples.
Statistics > Machine Learning arXiv:2601.06830 (stat) [Submitted on 11 Jan 2026 (v1), last revised 21 Feb 2026 (this version, v2)] Title:Constrained Density Estimation via Optimal Transport Authors:Yinan Hu, Esteban G.Tabak View a PDF of the paper titled Constrained Density Estimation via Optimal Transport, by Yinan Hu and 1 other authors View PDF HTML (experimental) Abstract:A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of functions adopts or exceeds given values. The framework is generalized to include regularization inequalities to mitigate the artifacts in the target measure. An annealing-like algorithm is developed to address non-smooth constraints, with its effectiveness demonstrated through both synthetic and proof-of-concept real world examples in finance. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Numerical Analysis (math.NA); Optimization and Control (math.OC); Probability (math.PR) Cite as: arXiv:2601.06830 [stat.ML] (or arXiv:2601.06830v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2601.06830 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yinan Hu [view email] [v1] Sun, 11 Jan 2026 09:44:04 UTC (3,740 KB) [v2] Sat, 21 Feb 2026 14:50:49 UTC (3,884 KB) Full-text links: Access Paper: View a PDF of the paper tit...
