Hidden Markov Pólya trees for high-dimensional distributions

@article{Awaya2022HiddenMP,
  title={Hidden Markov P{\'o}lya trees for high-dimensional distributions},
  author={Naoki Awaya and Li Ma},
  journal={Journal of the American Statistical Association},
  year={2022}
}
  • Naoki Awaya, Li Ma
  • Published 5 November 2020
  • Computer Science
  • Journal of the American Statistical Association
The P\'olya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. The PT has a simple analytic form and the resulting posterior computation boils down to straight-forward beta-binomial conjugate updates along a partition tree over the sample space. Recent development in PT models shows that performance of these models can be substantially improved by (i) incorporating latent state variables that characterize local… 

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References

SHOWING 1-10 OF 50 REFERENCES

Recursive partitioning and multi-scale modeling on conditional densities

  • Li Ma
  • Mathematics, Computer Science
  • 2016
TLDR
A nonparametric prior on the conditional distribution of a (univariate or multivariate) response given a set of predictors is introduced, allowing exact Bayesian inference to be completed analytically through a forward-backward recursive algorithm without the need of MCMC, and enjoying high computational efficiency.

Rubbery Polya Tree

TLDR
This work proposes a generalization of the PT prior that mitigates this undesirable dependence on the partition structure, by allowing the branching probabilities to be dependent within the same level.

A Bayesian hierarchical model for related densities by using Pólya trees

  • J. ChristensenLi Ma
  • Computer Science
    Journal of the Royal Statistical Society: Series B (Statistical Methodology)
  • 2019
TLDR
A new hierarchical model based on the Pólya tree is proposed, which enables direct modelling of densities and enjoys some computational advantages over the Dirichlet process and can be extended to cluster samples in situations where the observed samples are believed to have been drawn from several latent populations.

Polya tree distributions for statistical modeling of censored data

TLDR
This paper will present a straightforward method for determining the mixing distribution of Polya tree distributions in the Dirichlet process as a prior for Bayesian nonparametric problems.

Coupling Optional Pólya Trees and the Two Sample Problem

TLDR
This work proposes a theoretical framework for inference that addresses challenges in the form of a prior for Bayesian nonparametric analysis based on a random-partition-and-assignment procedure similar to the one that defines the standard optional Pólya tree distribution, but has the ability to generate multiple random distributions jointly.

Modeling Regression Error With a Mixture of Polya Trees

We model the error distribution in the standard linear model as a mixture of absolutely continuous Polya trees constrained to have median 0. By considering a mixture, we smooth out the partitioning

More Aspects of Polya Tree Distributions for Statistical Modelling

The definition and elementary properties of Polya tree distributions are reviewed. Two theorems are presented showing that Polya trees can be constructed to concentrate arbitrarily closely about any

Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives

Testing the fit of data to a parametric model can be done by embedding the parametric model in a nonparametric alternative and computing the Bayes factor of the parametric model to the nonparametric

Inference for Mixtures of Finite Polya Tree Models

Mixtures of Polya tree models provide a flexible alternative when a parametric model may only hold approximately. I provide computational strategies for obtaining full semiparametric inference for

Multivariate Density Estimation by Bayesian Sequential Partitioning

TLDR
The Bayesian sequential partitioning (BSP) method proposed here is capable of providing much more accurate estimates when the sample space is of moderate to high dimension and can be used to design new classification methods competitive with the state of the art.