# BKP: An R Package for Beta Kernel Process Modeling

arXiv: https://arxiv.org/abs/2508.10447 · HTML: https://mlsanity.com/paper/2508.10447/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Builds on (most cited first, 7 of 7)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Honest calibration assessment for binary outcome predictions](https://mlsanity.com/paper/2203.04065/) (2022)
- [Efficient learning of smooth probability functions from Bernoulli tests with guarantees](https://mlsanity.com/paper/1812.04428/) (2018)
- [Calibration for computer experiments with binary responses and application to cell adhesion study](https://mlsanity.com/paper/1806.01453/) (2018)
- [Modeling microbial abundances and dysbiosis with beta-binomial regression](https://mlsanity.com/paper/1902.02776/) (2019)

## Built on by (most cited first, 1 of 1)

- [Shared Keyboard: An improved Bayesian design for phase I clinical trials via Beta kernel process](https://mlsanity.com/paper/2605.25043/) (2026)

## Abstract (arXiv)

Estimating input-dependent probability surfaces from binary, binomial, categorical, or multinomial response data is a common task in statistics and machine learning. Latent Gaussian process classifiers provide flexible nonparametric models for such problems, but posterior inference with discrete responses typically requires approximation or simulation. We discuss an implementation of probability-scale beta and Dirichlet kernel models in the pkgBKP package for proglangR. The package implements the Beta Kernel Process (BKP), which uses kernel-weighted pseudo-count aggregation and beta-binomial conjugacy to obtain closed-form conjugate posterior summaries and posterior predictive distributions for binomial probabilities. It also implements the Dirichlet Kernel Process (DKP) for multi-class responses, together with TwinBKP and TwinDKP, scalable twinning-based global-local approximations for larger datasets. The resulting workflow supports transparent kernel-weighted evidence borrowing, several kernel families, fixed and data-adaptive priors, effective-sample-size calibration, loss-based hyperparameter tuning, and standard S3 methods for fitting, prediction, simulation, visualization, and extraction of posterior summaries. Reproducible examples demonstrate probability-surface estimation, binary and multi-class classification, computational comparison, and real-data applications to Loa loa infection prevalence mapping and Mourning Warbler distribution modeling.