Scalable Bayesian nonparametric regression via a Plackett-Luce model for conditional ranks.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Regression models are fundamental for understanding relationships between variables.
• Bayesian nonparametric methods offer flexibility but can be computationally intensive.
• Scalability to large datasets with numerous covariates remains a challenge.

Purpose of the Study:

• To introduce a novel Bayesian nonparametric regression model.
• To enable efficient posterior inference for complex regression problems.
• To demonstrate scalability for large-scale data analysis.

Main Methods:

• Parametrization using marginal distributions and a regression function.
• Approximate composite likelihood approach for decoupled posterior inference.
• Leveraging existing software for Bayesian nonparametric density and ranking estimation.

Main Results:

• The proposed model allows for decoupled posterior inference.
• The method demonstrates scalability to very large datasets.
• Successful application to a US Census dataset with over 1.3 million data points and 100+ covariates.

Conclusions:

• The novel Bayesian nonparametric regression model offers a scalable solution.
• The decoupled inference approach simplifies complex analyses.
• The method is applicable to real-world, large-scale datasets.