# Constrained Density Estimation via Optimal Transport

arXiv: https://arxiv.org/abs/2601.06830 · HTML: https://mlsanity.com/paper/2601.06830/

## Key facts

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- First posted on arXiv 11 Jan 2026.

## Abstract (arXiv)

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.