在期望约束下优化密度估计，提升金融等场景建模精度
Constrained Density Estimation via Optimal Transport
- 用最优传输最小化估计密度与先验的Wasserstein距离
- 约束条件确保函数期望值满足给定阈值，避免偏差
- 引入退火算法处理非光滑约束，实测有效且抗伪影
提出一种在期望约束下进行密度估计的新框架。该框架通过最小化估计密度与先验密度之间的Wasserstein距离，同时要求一组函数的期望值达到或超过给定数值。为缓解目标测度中的伪影，进一步引入正则化不等式。开发了一种类似退火的算法以应对非光滑约束，在合成数据及金融领域的概念验证实验中均表现出有效性。
原文摘要 · Abstract (English)
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.
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