On the Information Bottleneck Problems: Models, Connections, Applications and Information Theoretic Views.

Area of Science:

• Information Theory
• Machine Learning
• Signal Processing

Background:

• The information bottleneck problem seeks to find a compressed representation of a random variable that is maximally informative about another related variable.
• This problem has deep connections to various fields including coding theory, statistical inference, and deep learning architectures like autoencoders.

Purpose of the Study:

• To provide a tutorial on variants of the information bottleneck problem from an information-theoretic perspective.
• To discuss practical methods for solving the bottleneck problem and its extensions.
• To highlight the connections between the information bottleneck and diverse areas such as coding, learning, and communication networks.

Main Methods:

• Information-theoretic analysis of bottleneck problem variants.
• Exploration of connections to remote source-coding, information combining, and common reconstruction.
• Extension to the distributed information bottleneck problem, particularly for Gaussian models.
• Analysis of trade-offs between relevance (information) and complexity (rates) in discrete and vector Gaussian frameworks.

Main Results:

• Established intimate connections to remote source-coding, Wyner-Ahlswede-Korner problem, and learning aspects like generalization and representation learning.
• Discussed the distributed information bottleneck problem with emphasis on the Gaussian model.
• Determined optimal trade-offs between relevance and complexity for the Gaussian information bottleneck in Cloud Radio Access Networks (CRAN).

Conclusions:

• The information bottleneck framework offers a unified perspective on diverse problems in information theory, coding, and machine learning.
• Further research is needed to characterize optimal input distributions for the Gaussian information bottleneck under power and complexity constraints.
• The study provides a foundation for understanding and optimizing information processing in complex systems.