Deep Dynamic Probabilistic Canonical Correlation Analysis

This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of Canonical Correlation Analysis (CCA), D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>PCCA captures nonlinear latent dynamics and supports enhancements such as KL annealing for improved convergence and normalizing flows for a more flexible posterior approximation. D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>PCCA 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 D<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>PCCA and its extensions in capturing latent dynamics.