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arXiv 2602.05033cs.LGmath.AG
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因果表示与通用几何下的随机建模

Causal Representation Meets Stochastic Modeling under Generic Geometry

Courant Institute of Mathematics(库朗数学科学研究所);University of Michigan(密歇根大学)

Jiaxu Ren, Yixin Wang, Biwei Huang

AI总结:

MUTATE通过时间自适应转换模块,实现了对连续时间随机点过程的可识别因果表示学习,应用于基因组突变和神经元尖峰触发机制的研究。

摘要:

从观测中学习有意义的因果表示已成为促进机器学习应用和推动气候科学、生物学和物理学等领域的科学发现的关键任务。这一过程涉及从低层次观测中解构高层次潜在变量及其因果关系。以往在该领域的研究通常集中在观测为独立同分布或遵循潜在离散时间过程的情况。然而,许多现实世界场景需要识别连续时间随机过程(例如多元点过程)的潜在变量。为此,我们开发了适用于连续时间潜在随机点过程的可识别因果表示学习方法。我们通过分析参数空间的几何结构来研究其可识别性。此外,我们开发了MUTATE,一种具有时间自适应转换模块的可识别变分自编码器框架,以推断随机动态。在模拟和实证研究中,我们发现MUTATE能够有效回答科学问题,例如基因组中突变的积累以及神经元尖峰触发机制在时间变化动态下的驱动因素。

英文摘要:

Learning meaningful causal representations from observations has emerged as a crucial task for facilitating machine learning applications and driving scientific discoveries in fields such as climate science, biology, and physics. This process involves disentangling high-level latent variables and their causal relationships from low-level observations. Previous work in this area that achieves identifiability typically focuses on cases where the observations are either i.i.d. or follow a latent discrete-time process. Nevertheless, many real-world settings require identifying latent variables that are continuous-time stochastic processes (e.g., multivariate point processes). To this end, we develop identifiable causal representation learning for continuous-time latent stochastic point processes. We study its identifiability by analyzing the geometry of the parameter space. Furthermore, we develop MUTATE, an identifiable variational autoencoder framework with a time-adaptive transition module to infer stochastic dynamics. Across simulated and empirical studies, we find that MUTATE can effectively answer scientific questions, such as the accumulation of mutations in genomics and the mechanisms driving neuron spike triggers in response to time-varying dynamics.

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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