BKP: An R Package for Beta Kernel Process Modeling

2025-08-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Software Development & Engineering · Depth: Expert, quick

Summary

The BKP R package introduces Beta Kernel Process (BKP) and Dirichlet Kernel Process (DKP) models for estimating input-dependent probability surfaces from discrete response data, including binary, binomial, categorical, or multinomial types. These models offer an alternative to latent Gaussian process classifiers by leveraging kernel-weighted pseudo-count aggregation and beta-binomial conjugacy. This approach yields closed-form conjugate posterior summaries and posterior predictive distributions for binomial probabilities, simplifying inference. For larger datasets, the package incorporates scalable twinning-based global-local approximations, TwinBKP and TwinDKP. The BKP workflow supports diverse features such as multiple kernel families, fixed and data-adaptive priors, effective-sample-size calibration, and loss-based hyperparameter tuning. It also provides standard S3 methods for fitting, prediction, simulation, visualization, and posterior summary extraction. Real-data applications include Loa loa infection prevalence mapping and Mourning Warbler distribution modeling.

Key takeaway

For Data Scientists or Research Scientists modeling discrete response data, the BKP R package offers a robust alternative to traditional Gaussian process classifiers. You can achieve direct, closed-form posterior inference for binomial and multi-class probabilities, avoiding complex approximations. Consider integrating BKP or DKP models when your projects require efficient, transparent probability surface estimation, especially for applications like disease mapping or species distribution modeling, utilizing its scalable approximations for larger datasets.

Key insights

Beta and Dirichlet Kernel Processes enable closed-form posterior inference for discrete response probability surfaces.

Principles

• Kernel-weighted pseudo-count aggregation simplifies posterior inference.
• Beta-binomial conjugacy provides closed-form solutions for binomial probabilities.
• Twinning-based approximations scale kernel processes to larger datasets.

Method

The BKP package implements BKP and DKP models using kernel-weighted pseudo-count aggregation and conjugacy for direct posterior summaries and predictions. It includes scalable twinning approximations.

In practice

• Estimate probability surfaces for binary or multi-class classification.
• Model disease prevalence (e.g., Loa loa infection).
• Predict species distribution (e.g., Mourning Warbler).

Topics

• Beta Kernel Process
• Dirichlet Kernel Process
• R Package
• Probability Surface Estimation
• Nonparametric Models
• Bayesian Inference
• Machine Learning

Best for: AI Scientist, Research Scientist, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.