# Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem

arXiv: https://arxiv.org/abs/2004.00166 · HTML: https://mlsanity.com/paper/2004.00166/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Kernel Conditional Moment Constraints for Confounding Robust Inference](https://mlsanity.com/paper/2302.13348/) (2023)
- [A Convex Framework for Confounding Robust Inference](https://mlsanity.com/paper/2309.12450/) (2023)

## Abstract (arXiv)

In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the generalized moment problem whose ambiguity set (i.e., the moment constraint) is described by constraints in the associated reproducing kernel Hilbert space in a nonparametric manner. We then present the tractable approximation and its theoretical justification. As a concrete application, we numerically test the proposed method in characterizing the worst-case constraint violation probability in the context of a constrained stochastic control system.