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Constrained Reweighting of Distributions: An Optimal Transport Approach.

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  • 1Department of Statistics, Texas A&M University, College Station, TX 77843, USA.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study introduces a flexible data re-weighting method using maximum entropy and optimal transport. It ensures adjusted data distributions meet constraints while staying close to a target distribution, aiding various statistical tasks.

Keywords:
complex surveysdemographic parityentropyoptimal transportportfolio allocation

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Area of Science:

  • Statistics
  • Machine Learning
  • Optimization

Background:

  • Empirical distribution weighting is crucial for statistical analysis.
  • Existing methods have limitations in handling complex constraints.

Purpose of the Study:

  • To develop a flexible framework for weight-adjusted empirical distributions.
  • To incorporate nonparametric distributional constraints using optimal transport.

Main Methods:

  • Leveraging the maximum entropy principle.
  • Utilizing optimal transport metrics for distributional closeness.
  • Developing a general framework for constrained data re-weighting.

Main Results:

  • Introduced a novel method enhancing flexibility in weight-adjusted distributions.
  • Demonstrated applicability to portfolio allocation, complex surveys, and algorithmic fairness.
  • The method allows subtle departures from pre-specified distributions.

Conclusions:

  • The proposed framework offers greater flexibility than empirical likelihood.
  • It effectively handles parametric distribution-guided constraints.
  • The approach is versatile across diverse statistical and machine learning applications.