Scalable high-dimensional nonparametric density estimation, with Bayesian applications

Few methods have been proposed for flexible, nonparametric density estimation, and they do not scale well to high-dimensional problems. We describe a new approach based on smoothed trees called the kudzu density (Grant 2022). This fits the little-known density estimation tree (Ram & Gray 2011) to a dataset and convolves the edges with inverse logistic functions, which are in the class of computationally minimal smooth ramps. New Stata commands provide tree fitting, kudzu tuning, estimates of joint, marginal and cumulative densities, and pseudo-random numbers. Results will be shown for fidelity and computational cost. Preliminary results will also be shown for ensembles of kudzu under bagging and boosting. Kudzu densities are useful for Bayesian model updating where models have many unknowns, require rapid update, datasets are large, and posteriors have no guarantee of convexity and unimodality. The input “dataset” is the posterior sample from a previous analysis. This is demonstrated with a real-life large dataset. A new command outputs code to use the kudzu prior in bayesmh evaluators, BUGS/JAGS, and Stan.