Constrained Density Estimation via Optimal Transport

TL;DR

This paper introduces a new density estimation framework using optimal transport that incorporates expectation constraints and regularization, with an annealing algorithm to handle non-smooth constraints, demonstrated on synthetic and financial data.

Contribution

It presents a novel optimal transport-based density estimation method with expectation constraints and a new annealing algorithm for non-smooth constraints.

Findings

Effective in synthetic examples

Successful application to financial data

Reduces artifacts in estimated densities

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.