Deep Dynamic Probabilistic Canonical Correlation Analysis

TL;DR

D2PCCA is a novel deep probabilistic model that captures nonlinear latent dynamics in sequential data, extending CCA with deep learning techniques and probabilistic enhancements for improved flexibility and interpretability.

Contribution

It introduces D2PCCA, integrating deep learning with probabilistic CCA extensions to model nonlinear dynamical systems with multiple observed variables.

Findings

Effective in modeling financial sequential data

Improves convergence with KL annealing

Enhances posterior flexibility with normalizing flows

Abstract

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.