Related papers: A probability for classification based on the mixt…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…
Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…
We develop a Bayesian framework for tackling the supervised clustering problem, the generic problem encountered in tasks such as reference matching, coreference resolution, identity uncertainty and record linkage. Our clustering model is…
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…
The two parameter Poisson-Dirichlet Process (PDP), a generalisation of the Dirichlet Process, is increasingly being used for probabilistic modelling in discrete areas such as language technology, bioinformatics, and image analysis. There is…
One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive…
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…
We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…
Probabilistic mixture models are recognized as effective tools for unsupervised outlier detection owing to their interpretability and global characteristics. Among these, Dirichlet process mixture models stand out as a strong alternative to…
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…
Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of…
Prior distributions play a crucial role in Bayesian approaches to clustering. Two commonly-used prior distributions are the Dirichlet and Pitman-Yor processes. In this paper, we investigate the predictive probabilities that underlie these…
In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is…
We propose the use of probability models for ranked data as a useful alternative to a quantitative data analysis to investigate the outcome of bioassay experiments, when the preliminary choice of an appropriate normalization method for the…
The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…