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COVARIANCE LOSS, SZEMEREDI REGULARITY, AND DIFFERENTIAL PRIVACY.

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Area of Science:

  • Mathematics
  • Computer Science
  • Statistics

Background:

  • Covariance loss quantifies information reduction in conditional expectation.
  • Randomized rounding is a technique used in approximation algorithms.
  • Szemeredi regularity lemmas are fundamental in graph theory and combinatorics.

Purpose of the Study:

  • To establish a nearly tight bound on covariance loss using randomized rounding.
  • To introduce a novel weak Szemeredi regularity lemma for positive semidefinite matrices and kernels.
  • To explore the application of this method in constructing differentially private synthetic data.

Main Methods:

  • Application of randomized rounding based on Grothendieck's identity.
  • Development of a new weak Szemeredi regularity lemma.
  • Utilizing the lemma for synthetic data generation.

Main Results:

  • A nearly tight bound on covariance loss was proven.
  • A new type of weak Szemeredi regularity lemma for positive semidefinite matrices and kernels was established.
  • The method was shown to be applicable for creating differentially private synthetic data.

Conclusions:

  • Randomized rounding provides a powerful tool for analyzing covariance loss.
  • The developed regularity lemma offers new theoretical insights.
  • The approach facilitates the creation of privacy-preserving synthetic datasets.