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The Double-Sided Information Bottleneck Function.

Michael Dikshtein1, Or Ordentlich2, Shlomo Shamai Shitz1

  • 1Department of Electrical and Computer Engineering, Technion, Haifa 3200003, Israel.

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Summary
This summary is machine-generated.

This study explores a double-sided information bottleneck method, optimizing independent channels for data transmission. It finds Gaussian and binary symmetric channels are optimal only under specific conditions, not universally.

Keywords:
biclusteringinformation bottlenecklossy compressionremote source coding

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Area of Science:

  • Information Theory
  • Machine Learning
  • Signal Processing

Background:

  • The information bottleneck method is a powerful tool for dimensionality reduction.
  • Understanding optimal channel selection is crucial for efficient data compression and transmission.
  • The double-sided variant introduces complexities in optimizing independent channels.

Purpose of the Study:

  • To investigate a double-sided information bottleneck method for optimizing independent channels.
  • To determine the optimality of specific channel types (Gaussian, binary symmetric) under varying signal-to-noise ratios (SNR) and correlations.
  • To develop and evaluate an algorithm for solving this optimization problem.

Main Methods:

  • Formulation of a double-sided information bottleneck problem with constraints on mutual information.
  • Analysis of jointly Gaussian and doubly symmetric binary sources.
  • Application of a Blahut-Arimoto type alternating maximization algorithm.
  • Numerical evaluation for specific settings and correlations.

Main Results:

  • Gaussian channels are optimal for jointly Gaussian sources only in the low-SNR regime.
  • Binary symmetric channels are optimal for doubly symmetric binary sources at low correlations but suboptimal at high correlations.
  • Conjecture that Z and S channels are optimal for a correlation of 1 (X=Y), supported by numerical evidence.
  • Demonstration of the algorithm's performance.

Conclusions:

  • The optimality of specific channel types is highly dependent on source characteristics (SNR, correlation).
  • The proposed algorithm provides a practical approach to solving the double-sided information bottleneck problem.
  • Findings have implications for data compression, communication systems, and biclustering techniques.