相关论文: Normalized random measures driven by increasing ad…

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…

Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian…

We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…

We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

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…

Dirichlet distributions are probability measures on the unit simplex. They are often used as prior distributions in modeling categorical data, such as in topic analysis of text data. Motivated by this application, we consider Monte Carlo…

We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…

One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of…

This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…

In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric…

Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical…

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…

Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular,…