A Gibbs Posterior Framework for Fair Clustering.

Area of Science:

• Machine Learning
• Algorithmic Fairness
• Clustering

Background:

• Algorithmic fairness is crucial in machine learning, with 'balance' used as a fairness criterion in clustering.
• Existing fair clustering methods (e.g., k-means) lack uncertainty quantification and struggle with model misspecification.
• Mixture model-based approaches offer uncertainty quantification but are computationally intensive and brittle.

Purpose of the Study:

• To propose a novel probabilistic formulation for fair clustering that enables uncertainty quantification.
• To develop a generalized Bayesian fair clustering framework with decision-theoretic interpretation.
• To devise efficient computational algorithms for fair clustering.

Main Methods:

• A generalized Bayesian framework for fair clustering was developed.
• Efficient algorithms leveraging optimal transport and loss-based clustering techniques were devised.
• The approach facilitates uncertainty quantification even under mild model misspecifications.

Main Results:

• The proposed Bayesian framework provides valid uncertainty quantification for fair clustering.
• The developed algorithms are computationally efficient, overcoming limitations of existing methods.
• Numerical experiments and real-world data demonstrated the effectiveness of the proposed approach.

Conclusions:

• The novel Bayesian fair clustering framework offers a robust solution for uncertainty quantification.
• The efficient algorithms make fair clustering more accessible and reliable.
• This work advances the field of algorithmic fairness in machine learning applications.