Related papers: Optional P\'{o}lya tree and Bayesian inference
A general theory of stochastic decision forests is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
Several structure-learning algorithms for staged trees, asymmetric extensions of Bayesian networks, have been proposed. However, these either do not scale efficiently as the number of variables considered increases, a priori restrict the…
We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…
In this paper adapting to $p$-adic case some methods of real valued Gibbs measures on Cayley trees we construct several $p$-adic distributions on the set $\mathbb{Z}_p$ of $p$-adic integers. Moreover, we give conditions under which these…
Anomaly detection at scale is an extremely challenging problem of great practicality. When data is large and high-dimensional, it can be difficult to detect which observations do not fit the expected behaviour. Recent work has coalesced on…
This paper proposes a new nonparametric Bayesian bootstrap for a mixture model, by developing the traditional Bayesian bootstrap. We first reinterpret the Bayesian bootstrap, which uses the P\'olya-urn scheme, as a gradient ascent algorithm…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
The theme in this paper is a composition of random graphs and P\'olya urns. The random graphs are generated through a small structure called the seed. Via P\'olya urns, we study the asymptotic degree structure in a random $m$-ary hooking…
We investigate the profile of random P\'olya trees of size $n$ when only nodes of degree $d$ are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process…
We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…
Big Data often presents as massive non-probability samples. Not only is the selection mechanism often unknown, but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches…
Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique…
This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we…
In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a non-negative random variable $X$ with moment sequence $(\mu_s)_{s\in\mathbb{N}}$ we determine a discrete random…
Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a P\'olya-Gamma sampler algorithm that allows us to sample from the exact…
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of…
Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…