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Area of Science:

  • Information Theory
  • Machine Learning
  • Data Compression

Background:

  • The Information Bottleneck (IB) is a dimensionality reduction technique.
  • The Symmetric Information Bottleneck (SIB) extends IB for simultaneous compression of two variables.
  • SIB preserves information between compressed versions of random variables.

Purpose of the Study:

  • Introduce the Generalized Symmetric Information Bottleneck (GSIB).
  • Investigate data set size requirements for GSIB compression.
  • Compare data efficiency of simultaneous vs. independent compression.

Main Methods:

  • Derive bounds on statistical fluctuations of loss functions.
  • Develop root-mean-squared estimates for these fluctuations.
  • Analyze functional forms of simultaneous reduction costs in GSIB.

Main Results:

  • GSIB demonstrates qualitatively lower data requirements for compression.
  • Simultaneous GSIB compression achieves similar error rates with less data.
  • Statistical fluctuation bounds quantify compression accuracy.

Conclusions:

  • Simultaneous compression is more data-efficient than independent compression.
  • GSIB provides a framework for optimizing data efficiency in compression.
  • Findings suggest a general principle of enhanced data efficiency through simultaneous methods.