The BKP package provides tools for nonparametric modeling of binary, binomial, or multinomial response data using the Beta Kernel Process (BKP) and its extension, the Dirichlet Kernel Process (DKP). These methods estimate latent probability surfaces through localized kernel smoothing under a Bayesian framework.
The package includes functionality for model fitting, probabilistic prediction with uncertainty quantification, posterior simulation, and visualization in both one- and two-dimensional input spaces. It also supports hyperparameter tuning and flexible prior specification.
Main Functions
Core functionality is organized into the following groups:
fit.BKP,fit.DKPFit a BKP or DKP model to (multi)binomial response data.
predict.BKP,predict.DKPPerform posterior predictive inference at new input locations, including predictive means, variances, and credible intervals. Classification labels are returned automatically when observations represent single trials (i.e., binary outcomes).
simulate.BKP,simulate.DKPDraw simulated responses from the posterior predictive distribution of a fitted model.
plot.BKP,plot.DKPVisualize model predictions and uncertainty bands in 1D and 2D input spaces.
summary.BKP,summary.DKP,print.BKP,print.DKPSummarize or print details of a fitted BKP or DKP model.
References
Goetschalckx R, Poupart P, Hoey J (2011). Continuous Correlated Beta Processes. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence - Volume Volume Two, IJCAI’11, p. 1269-1274. AAAI Press.
MacKenzie CA, Trafalis TB, Barker K (2014). A Bayesian Beta Kernel Model for Binary Classification and Online Learning Problems. Statistical Analysis and Data Mining: The ASA Data Science Journal, 7(6), 434-449.
Rolland P, Kavis A, Singla A, Cevher V (2019). Efficient learning of smooth probability functions from Bernoulli tests with guarantees. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, 9-15 June 2019, Long Beach, California, USA, volume 97 of Proceedings of Machine Learning Research, pp. 5459-5467. PMLR.