Simultaneous Dimensionality Reduction for Extracting Useful Representations of Large Empirical Multimodal Datasets

TL;DR

This paper introduces a unified framework for simultaneous dimensionality reduction of multimodal datasets, demonstrating its effectiveness in capturing covariation, reducing data requirements, and discovering meaningful coordinates in complex systems.

Contribution

It proposes the Deep Variational Multivariate Information Bottleneck framework and novel techniques for nonlinear simultaneous reduction, advancing the analysis of high-dimensional, multimodal data.

Findings

Simultaneous reduction outperforms independent methods in capturing covariation.

The new methods require less data for effective dimensionality reduction.

Successfully discovers coordinates in high-dimensional dynamical systems.

Abstract

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data, facilitating comprehension and analysis. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within neural systems or high-dimensional dynamical systems. Leveraging insights from both theoretical physics and machine learning, this work unifies diverse reduction methods under a comprehensive framework, the Deep Variational Multivariate Information Bottleneck. This framework enables the design of tailored reduction algorithms based on specific research questions. We explore and assert the efficacy of simultaneous reduction approaches over their independent reduction counterparts, demonstrating their superiority in capturing covariation between multiple modalities, while requiring less data. We also introduced novel techniques, such as the Deep Variational Symmetric Information Bottleneck, for general nonlinear simultaneous reduction. We show that the same principle of simultaneous reduction is the key to efficient estimation of mutual information. We show that our new method is able to discover the coordinates of high-dimensional observations of dynamical systems. Through analytical investigations and empirical validations, we shed light on the intricacies of dimensionality reduction methods, paving the way for enhanced data analysis across various domains. We underscore the potential of these methodologies to extract meaningful insights from complex datasets, driving advancements in fundamental research and applied sciences. As these methods evolve, they promise to deepen our understanding of complex systems and inform more effective data analysis strategies.