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Partial Information Decomposition: Redundancy as Information Bottleneck.

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|July 26, 2024
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Summary
This summary is machine-generated.

Partial Information Decomposition (PID) is reframed as a Redundancy Bottleneck (RB) problem. This approach quantifies redundant information from sources predicting a target, balancing prediction and compression effectively.

Keywords:
information bottleneckpartial information decompositionrate distortionredundancy

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Area of Science:

  • Information Theory
  • Machine Learning
  • Computational Neuroscience

Background:

  • Partial Information Decomposition (PID) quantifies shared information from multiple sources about a target.
  • Existing PID measures face challenges in scalability and interpretation.
  • The concept of Blackwell redundancy offers a principled approach to measuring PID redundancy.

Purpose of the Study:

  • To reformulate Partial Information Decomposition (PID) as an Information Bottleneck (IB) problem, termed the Redundancy Bottleneck (RB).
  • To develop a method for quantifying the prediction-compression tradeoff in redundant information.
  • To identify subsets of redundant sources efficiently.

Main Methods:

  • Formulation of the Redundancy Bottleneck (RB) as an information-theoretic optimization problem.
  • Development of the 'RB curve' to visualize the prediction-compression tradeoff.
  • An efficient iterative algorithm for computing the RB curve.

Main Results:

  • The RB problem formalizes the tradeoff between predicting a target and compressing information from sources.
  • The RB curve generalizes Blackwell redundancy and quantifies this tradeoff at multiple scales.
  • Individual source RB curves enable identification of redundant source subsets without combinatorial search.

Conclusions:

  • The Redundancy Bottleneck (RB) provides a unified and efficient framework for Partial Information Decomposition (PID).
  • This approach offers a principled way to understand and quantify information redundancy.
  • The developed algorithm facilitates practical application in analyzing complex information systems.