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This summary is machine-generated.

This study unifies Information Bottleneck (IB) and Privacy Funnel (PF) theory, introducing new cardinality bounds for IB computation. It also generalizes these to "bottleneck problems" with interpretable privacy-accuracy guarantees.

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Area of Science:

  • Information Theory
  • Optimization
  • Machine Learning

Background:

  • Information Bottleneck (IB) and Privacy Funnel (PF) are crucial optimization problems with broad applications.
  • Existing frameworks lack unified theoretical investigation and direct connections to coding problems.

Purpose of the Study:

  • To unify the theoretical framework of IB and PF.
  • To establish connections between IB/PF and information-theoretic coding problems.
  • To introduce and analyze a generalized family of
  • bottleneck problems
  • with enhanced interpretability for privacy-preserving inference.

Main Methods:

  • Unified theoretical analysis of IB and PF properties.
  • Establishing connections to hypothesis testing, noisy source coding, and dependence dilution.
  • Developing a closed-form evaluation technique for bottleneck problems using convex/concave envelopes.

Main Results:

  • A novel cardinality bound for the auxiliary variable in IB, improving computational tractability for discrete variables.
  • Demonstration that generalized bottleneck problems offer clearer privacy-accuracy trade-offs.
  • Derivation of closed-form solutions for bottleneck problems in the binary case.

Conclusions:

  • The unified framework enhances understanding of IB and PF.
  • The new cardinality bound offers practical computational benefits.
  • Generalized bottleneck problems provide a promising direction for interpretable privacy-preserving machine learning.