融合深度学习与概率建模，捕捉非线性动态系统的潜在演化规律。
Deep Dynamic Probabilistic Canonical Correlation Analysis
- 基于概率CCA构建深层动态模型，支持非线性潜变量建模
- 引入KL退火与归一化流提升收敛性与后验逼近灵活性
- 可扩展至多变量序列数据，适合金融等时序建模场景
本文提出深度动态概率典型相关分析（D2PCCA），将深度学习与概率建模结合，用于分析非线性动力系统。在概率典型相关分析基础上，D2PCCA 能捕捉非线性潜变量动态，并通过KL退火提升收敛性、利用归一化流实现更灵活的后验近似。该模型天然可扩展至多个观测变量，适用于编码序列数据先验知识，并提供系统动态的完整概率解释。在真实金融数据集上的实验验证了D2PCCA及其扩展的有效性。
原文摘要 · Abstract (English)
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.
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