Efficient posterior sampling for high-dimensional imbalanced logistic regression.

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• High-dimensional data classification is crucial but challenging, especially with imbalanced datasets.
• Current Bayesian classification methods using Markov chain Monte Carlo (MCMC) are computationally inefficient for large datasets due to slow mixing rates and high computational cost per step.
• Standard subsampling techniques for efficiency fail with imbalanced data.

Purpose of the Study:

• To develop efficient Bayesian classification algorithms for high-dimensional and imbalanced data.
• To overcome the computational limitations of traditional MCMC methods in large-scale Bayesian classification.
• To address the breakdown of standard subsampling in imbalanced data scenarios.

Main Methods:

• Generalization of piecewise-deterministic Markov chain Monte Carlo (PD-MCMC) algorithms.
• Incorporation of importance-weighted and mini-batch subsampling strategies.
• Theoretical analysis and validation through simulated data and a real-world cancer dataset.

Main Results:

• The proposed generalized PD-MCMC algorithms maintain correct stationary distributions even with small subsamples.
• These novel methods demonstrate substantial performance gains over existing competitors.
• The approach shows effectiveness in both simulated scenarios and practical application to cancer data.

Conclusions:

• The developed importance-weighted and mini-batch subsampling for PD-MCMC offers a robust solution for Bayesian classification with high-dimensional, imbalanced data.
• This approach significantly improves computational efficiency and classification accuracy.
• The methods provide a valuable tool for analyzing complex biological datasets, such as cancer data.