Related papers: Optional P\'{o}lya tree and Bayesian inference
Optional P\'{o}lya Tree (OPT) is a flexible non-parametric Bayesian model for density estimation. Despite its merits, the computation for OPT inference is challenging. In this paper we present time complexity analysis for OPT inference and…
Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well as the dimensionality increases and…
We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional P\'olya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions…
P\'{o}lya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a…
Bayesian hierarchical models are used to share information between related samples and obtain more accurate estimates of sample-level parameters, common structure, and variation between samples. When the parameter of interest is the…
In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…
One way of defining probability distributions for circular variables (directions in two dimensions) is to radially project probability distributions, originally defined on $\mathbb{R}^2$, to the unit circle. Projected distributions have…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
P\'olya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate P\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with…
This paper proposes a novel approach for statistical modelling of a continuous random variable $X$ on $[0, 1)$, based on its digit representation $X=.X_1X_2\ldots$. In general, $X$ can be coupled with a latent random variable $N$ so that…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
The P\'olya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial…
This work studies the variation in Kullback-Leibler divergence between random draws from some popular nonparametric processes and their baseline measure. In particular we focus on the Dirichlet process, the P\'olya tree and the frequentist…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
Projected distributions have proved to be useful in the study of circular and directional data. Although any multivariate distribution can be used to produce a projected model, these distributions are typically parametric. In this article…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We introduce a hierarchical nonparametric model for probability measures based on a multi-resolution transformation of probability distributions. The model allows a varying amount of shrinkage to be applied to data features of different…
We introduce a comprehensive Bayesian multivariate predictive inference framework. The basis for our framework is a hierarchical Bayesian model, that is a mixture of finite Polya trees corresponding to multiple dyadic partitions of the unit…