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<p>We present a supervised learning approach that employs density estimates from a smoothed mixture of multivariate Polya tree models. Further, we propose a FAST Markov chain Monte Carlo (MCMC) sampling technique that overcomes difficulties in traditional procedures for sampling and completes in a fraction of the time, permitting Bayesian nonparametric solutions to contexts requiring many or repeated density estimates. We demonstrate the smoothing of the proposed FAST sampler in bivariate density estimation and the efficacy of its use in simulated bivariate regression scenarios. We evaluate the robustness of the model using several regression benchmark datasets. Finally, we illustrate the effectiveness of this approach in two applied contexts. First, we conduct smoothed nonparametric density estimation for prediction using data from a randomized, double-blind, placebo-controlled study of subjects with extensive-stage small-cell lung cancer where we predict hemoglobin levels with and without darbepoetin alfa treatment. Second, we demonstrate an implementation of a nonparametric classification scheme that improves (Cipolli and Hanson, 2019) via smoothing using data from a study evaluating human microfibrillar-associated protein 4 (MFAP4) as a biomarker for Hepatitis C.</p>

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Fast MMPTs: a fast approximate sampler toward a mixture of multivariate Polya trees

  • 期刊论文

  • 发表日期：

    2025年12月24日

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  • William Cipolli III

摘要

We present a supervised learning approach that employs density estimates from a smoothed mixture of multivariate Polya tree models. Further, we propose a FAST Markov chain Monte Carlo (MCMC) sampling technique that overcomes difficulties in traditional procedures for sampling and completes in a fraction of the time, permitting Bayesian nonparametric solutions to contexts requiring many or repeated density estimates. We demonstrate the smoothing of the proposed FAST sampler in bivariate density estimation and the efficacy of its use in simulated bivariate regression scenarios. We evaluate the robustness of the model using several regression benchmark datasets. Finally, we illustrate the effectiveness of this approach in two applied contexts. First, we conduct smoothed nonparametric density estimation for prediction using data from a randomized, double-blind, placebo-controlled study of subjects with extensive-stage small-cell lung cancer where we predict hemoglobin levels with and without darbepoetin alfa treatment. Second, we demonstrate an implementation of a nonparametric classification scheme that improves (Cipolli and Hanson, 2019) via smoothing using data from a study evaluating human microfibrillar-associated protein 4 (MFAP4) as a biomarker for Hepatitis C.