Deep Dynamic Probabilistic Canonical Correlation Analysis

2025-02-07

AI Summary

This work addresses two key challenges in modeling nonlinear dynamical systems: (1) difficulty in uncovering latent dynamics, and (2) weak characterization of multivariate temporal couplings across heterogeneous sources. To this end, we propose a novel latent-variable model that synergistically integrates deep learning with probabilistic inference. Methodologically, we introduce the first framework that embeds dynamic factor analysis, KL annealing optimization, and normalizing flows for flexible posterior approximation into a probabilistic canonical correlation analysis (P-CCA) architecture—supporting both multivariate extension and domain-specific prior encoding. Experiments on real-world financial time series demonstrate that our model significantly improves latent dynamic recovery, achieves robust and interpretable representation of complex nonlinear coupling structures, and establishes a new paradigm for joint dynamical modeling of high-dimensional, heterogeneous time series.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Analyzing nonlinear dynamical systems
• Capturing latent dynamics in datasets
• Enhancing convergence and flexibility in modeling

Innovation

• Integrates deep learning, probabilistic modeling
• Captures nonlinear latent dynamics effectively
• Supports KL annealing, normalizing flows