发表机构
University of Massachusetts Amherst; University of North Carolina at Chapel Hill（马萨诸塞大学阿默斯特分校; 北卡罗来纳大学教堂山分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出CVaR-GPA算法，通过CVaR惩罚的Wasserstein梯度流微调生成模型，无需先验尾部知识，在多类重尾分布及真实数据集上显著提升了生成模型的全局与尾部精度。
AI 中文摘要
我们提出了CVaR惩罚的生成粒子算法（CVaR-GPA），这是一种用于微调生成模型以学习重尾分布并捕获极端事件的鲁棒、与尾部无关的算法，无需事先了解或估计目标的尾部特征。该方法是 Lipschitz 正则化的 Kullback-Leibler（KL）散度的 Wasserstein 梯度流，由条件风险价值（CVaR）差异项进行惩罚：Lipschitz 正则化的 KL 散度在对目标分布假设极少的情况下实现鲁棒学习，而 CVaR 惩罚则恢复了在欠采样尾部会过早消失的速度。该惩罚流具有有界但非 Lipschitz 的速度场，这与标准生成器的 Lipschitz 传输图不同，标准生成器的 Lipschitz 传输图保留了轻尾源的尾部行为，而 CVaR-GPA 能够向更重尾的目标进行传输。为了在经验测度上定义该流，我们从 Rockafellar-Uryasev 表示中推导了 CVaR 的一阶变分次梯度，其在经典基于密度的公式失效的地方有效。粒子算法 CVaR-GPA 可对任何预训练模型的输出样本进行微调，无需访问其架构，且运行时采用由动能停止准则设定的自适应时间范围，而非预设深度。在合成的各向同性和各向异性 Student-t 目标分布、Neal 漏斗分布以及真实世界的高维 Fama-French 25 投资组合数据集上，CVaR-GPA 相较于预训练基线，显著提高了重尾目标的全局和尾部精度。
英文摘要
In many high-stakes domains, extreme events carry substantial consequences, yet learning the heavy-tailed distributions that govern them from finite samples remains challenging: the quantities of interest are driven by a few extreme observations, so the tail is under-sampled relative to its importance. Even generative models tailored for heavy tails capture the tail region inadequately in practice. We propose the Conditional Value-at-Risk (CVaR)-penalized Generative Particle Algorithm (CVaR-GPA), a tail-agnostic algorithm for fine-tuning generative models toward heavy-tailed targets, built as a time discretization of the Wasserstein gradient flow of the Lipschitz-regularized KL divergence penalized by a CVaR discrepancy term. Such a flow can be initialized from the output samples of the pre-trained model, which are then transported along the gradient descent of the loss functional, without requiring access to the pre-trained model's internal architecture. The Lipschitz-regularized KL divergence requires minimal assumptions on the target, while the CVaR penalty focuses the flow on the tail. The CVaR penalty depends on the target only through a scalar tail statistic, inducing a velocity field that remains active in the under-sampled tail region at a dimension-free estimation cost. The resulting velocity field, and hence the depth of the transport map, implicitly adapts to the target, without target-specific modifications. Across four targets, including two real-world, high-dimensional datasets (daily streamflow in the Ohio River basin ($d=64$) and the Fama-French portfolios ($d=25$) with tail indices ranging from $1.05$ to $3.34$), fine-tuning with CVaR-GPA reduces global and tail errors by geometric-mean factors of $14.0 \times$ and $9.8 \times$, respectively, across seven pre-trained models spanning GANs, diffusion models, and other generative flows, with a single set of hyperparameters.
