arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2510.02499stat.MLcs.LG

超越线性扩散:面向稀有条件生成建模的改进表示

Beyond Linear Diffusions: Improved Representations for Rare Conditional Generative Modeling

University of Chicago(芝加哥大学);J.P. Morgan AI Research(摩根大通AI研究);J.P. Morgan Quantitative Research(摩根大通量化研究)

Kulunu Dharmakeerthi, Yousef El-Laham, Henry H. Wong, Vamsi K. Potluru, Changhong He, Taosong He

AI总结:

针对线性扩散模型在条件分布低概率区域样本稀缺、建模困难的问题,结合条件极值理论提出带数据驱动非线性漂移项的尾部自适应扩散方法,在合成与真实金融数据集上表现优于标准模型。

摘要:

扩散模型已成为强大的生成框架,在机器学习与人工智能系统中应用广泛。当前研究主要聚焦于线性扩散,但这类方法在建模条件分布$P(Y|X=x)$且$P(X=x)$较小时会面临显著挑战。在这些区域中,可用于训练的样本极少(甚至没有),因此对相应的条件密度建模十分困难。基于此,我们证明可以通过调整数据表示与前向方案,降低在条件空间低概率区域学习基于得分的生成模型所需的样本复杂度。我们受条件极值理论启发,在条件变量$X$的尾部区域这一特殊情形下精确刻画了该方法。我们展示了采用数据驱动的非线性漂移项的扩散模型,在合适的数据表示下最适合建模尾部事件。通过在两个合成数据集与一个真实金融数据集上的实验验证,我们证明所提出的尾部自适应方法在准确捕捉极端尾部条件下的响应分布方面,显著优于标准扩散模型。

英文摘要:

Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these approaches can face significant challenges when modeling a conditional distribution, $P(Y|X=x)$, when $P(X=x)$ is small. In these regions, few samples, if any, are available for training, thus modeling the corresponding conditional density may be difficult. Recognizing this, we show it is possible to adapt the data representation and forward scheme so that the sample complexity of learning a score-based generative model is small in low probability regions of the conditioning space. Drawing inspiration from conditional extreme value theory we characterize this method precisely in the special case in the tail regions of the conditioning variable, $X$. We show how diffusion with a data-driven choice of nonlinear drift term is best suited to model tail events under an appropriate representation of the data. Through empirical validation on two synthetic datasets and a real-world financial dataset, we demonstrate that our tail-adaptive approach significantly outperforms standard diffusion models in accurately capturing response distributions at the extreme tail conditions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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