This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of Canonical Correlation Analysis (CCA), D2PCCA captures nonlinear latent dynamics and supports enhancements such as KL annealing for improved convergence and normalizing flows for a more flexible posterior approximation. D2PCCA naturally extends to multiple observed variables, making it a versatile tool for encoding prior knowledge about sequential datasets and providing a probabilistic understanding of the system's dynamics. Experimental validation on real financial datasets demonstrates the effectiveness of D2PCCA and its extensions in capturing latent dynamics.

翻译：本文提出深度动态概率典型相关分析（D2PCCA），该模型将深度学习与概率建模相结合，用于分析非线性动态系统。在概率化典型相关分析（CCA）扩展的基础上，D2PCCA能够捕捉非线性潜在动态，并支持诸如KL退火以改善收敛性以及标准化流以实现更灵活的后验近似等增强功能。D2PCCA自然地扩展到多个观测变量，使其成为编码序列数据先验知识并提供系统动态概率性理解的通用工具。在真实金融数据集上的实验验证证明了D2PCCA及其扩展在捕捉潜在动态方面的有效性。