用于Sinkhorn分布鲁棒假设检验的生成式神经网络
Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing
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中文总结 AI 辅助
本文针对现有Sinkhorn分布鲁棒假设检验方法可扩展性不足的问题，提出基于超输入凸神经网络的生成式框架，实现了更优的检测精度与鲁棒性，且具备良好的可扩展性。
中文摘要 AI 辅助
本文研究Sinkhorn分布鲁棒假设检验（SDRHT）问题，旨在构建一种鲁棒检测器，以应对基于Sinkhorn散度、以经验分布为中心的歧义集中最不利分布。现有方法通过求解大规模锥规划来解决该问题，存在可扩展性不足的缺陷。为克服这一问题，本文提出一种生成式框架，可学习最不利分布，支持高效训练与端到端采样。针对基于Sinkhorn散度的歧义集，本文首先推导了关于核平滑参考分布的等价条件KL散度表示，该性质使我们能针对约束与无约束极小极大SDRHT公式证明强对偶性。基于闭式最优检测器与Brenier定理，本文将极大极小对偶公式重新表述为凸势函数上的最大化问题，其梯度刻画了核平滑分布与其最不利对应分布之间的可逆传输映射。本文使用配备随机梯度估计器的超输入凸神经网络（HyCNNs）高效近似这些势函数，并证明了HyCNNs的表示能力及其诱导传输映射的分布普适性。数值结果表明，所提方法在不同样本量与维度下均实现了更优的精度与鲁棒性，同时避免了经典SDRHT方法的可扩展性限制。
英文摘要
This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distributions in Sinkhorn discrepancy-based ambiguity sets centered at the empirical distributions. Existing approaches solve this problem by solving large-scale conic programs, which are not scalable. To overcome this, we propose a generative framework that learns least-favorable distributions and supports efficient training and end-to-end sampling. For the Sinkhorn discrepancy-based ambiguity sets, we first derive an equivalent conditional-KL-divergence representation with respect to kernel-smoothed reference distributions. This property allows us to prove strong duality for both constrained and unconstrained minimax SDRHT formulations. Based on the closed-form optimal detector and Brenier's theorem, we reformulate the max-min dual formulation as a maximization problem over convex potentials whose gradients characterize invertible transport maps between kernel-smoothed distributions and their least-favorable counterparts. We efficiently approximate these potentials using Hyper Input Convex Neural Networks (HyCNNs) equipped with stochastic gradient estimators and prove the representation power of HyCNNs and the distributional universality of their induced transport maps. Numerical results show that the proposed method achieves superior accuracy and robustness across different sample sizes and dimensions, while avoiding the scalability limitations of classical SDRHT methods.
发表机构
- School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）人工智能学院）
- College of Business, City University of Hong Kong（香港城市大学商学院）
- School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。
