Constrained Density Estimation via Optimal Transport
Machine Learning
2026-02-24 v2 Machine Learning
Numerical Analysis
Numerical Analysis
Optimization and Control
Probability
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.
Cite
@article{arxiv.2601.06830,
title = {Constrained Density Estimation via Optimal Transport},
author = {Yinan Hu and Esteban G. Tabak},
journal= {arXiv preprint arXiv:2601.06830},
year = {2026}
}