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The Convex Information Bottleneck Lagrangian.

Borja Rodríguez Gálvez1, Ragnar Thobaben1, Mikael Skoglund1

  • 1Department of Intelligent Systems, Division of Information Science and Engineering (ISE), KTH Royal Institute of Technology, 11428 Stockholm, Sweden.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

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This study introduces new Lagrangians for the information bottleneck (IB) problem, enabling exploration of compression-prediction trade-offs. It simplifies finding optimal compressed representations for predictive tasks.

Area of Science:

  • Information Theory
  • Machine Learning
  • Optimization

Background:

  • The Information Bottleneck (IB) problem seeks optimal compressed representations for prediction.
  • Traditional methods maximize an IB Lagrangian, often requiring multiple solutions.
  • Deterministic relationships between variables pose challenges for standard IB approaches.

Purpose of the Study:

  • To develop a general family of Lagrangians for exploring the IB curve in all scenarios.
  • To establish a direct mapping between Lagrange multipliers and compression rates.
  • To enable approximate attainment of specific compression levels with a single optimization.

Main Methods:

  • Introducing a general family of Lagrangians for the IB problem.
  • Deriving an exact one-to-one mapping between Lagrange multipliers and compression rates.
Keywords:
information bottleneckmutual informationoptimizationrepresentation learning

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  • Utilizing the convex IB Lagrangian for approximate compression level attainment.

    • Main Results:

    • A general family of Lagrangians is presented, allowing IB curve exploration across all scenarios.
    • An exact mapping is provided between Lagrange multipliers and compression rates for known IB curve shapes.
    • Approximate attainment of specific compression levels is demonstrated using the convex IB Lagrangian.

    Conclusions:

    • The proposed methods facilitate the exploration of the IB curve irrespective of variable relationships.
    • A single optimization can now solve the constrained IB problem, reducing computational burden.
    • This work offers a more efficient approach to finding optimal compressed representations for predictive tasks.