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

Abdellatif Zaidi1,2, Iñaki Estella-Aguerri2, Shlomo Shamai Shitz3

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Summary
This summary is machine-generated.

This tutorial explores the information bottleneck problem using an information-theoretic approach. It details practical solutions and connections to coding, learning, and distributed systems like Cloud Radio Access Networks (CRAN).

Keywords:
information bottlenecklogarithmic lossrate distortion theoryrepresentation learning

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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.