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On the Difference between the Information Bottleneck and the Deep Information Bottleneck.

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Summary

Deep variational information bottleneck (DVIB) models can be made more flexible by relaxing restrictive Markov chain assumptions. This study optimizes a lower bound for mutual information, enabling broader applications in deep learning and generative modeling.

Keywords:
Markov assumptionMarkov chainconditional independencedeep variational information bottleneckinformation bottleneckmutual information

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Information Theory

Background:

  • Deep learning models often utilize the information bottleneck principle.
  • Deep variational information bottleneck (DVIB) models rely on specific Markov chain assumptions (T-X-Y and X-T-Y) for data representation.
  • These assumptions can limit the applicability of DVIB to certain joint distributions.

Purpose of the Study:

  • To revisit the assumptions of deep variational information bottleneck (DVIB).
  • To propose a method to circumvent the limitations imposed by strict Markov chain assumptions.
  • To provide a more flexible framework for information bottleneck models.

Main Methods:

  • Optimizing a lower bound for the mutual information I(T;Y) instead of directly optimizing I(T;Y).
  • Relaxing the T-X-Y Markov chain assumption while maintaining the X-T-Y assumption.
  • Interpreting information bottleneck models as directed graphical models.

Main Results:

  • The proposed method allows optimization under relaxed constraints, expanding the range of applicable joint distributions.
  • The mutual information I(T;Y) is decomposed into an optimized lower bound and terms measuring the violation of the T-X-Y assumption.
  • Information bottleneck models are unified under a directed graphical model framework.

Conclusions:

  • The deep variational information bottleneck can be generalized by relaxing restrictive assumptions.
  • This generalization enhances the flexibility and applicability of information bottleneck methods in deep learning.
  • Information bottleneck models are presented as special cases within a broader directed graphical model framework.