Related papers: Dirichlet Fragmentation Processes
Dirichlet Process(DP) is a Bayesian non-parametric prior for infinite mixture modeling, where the number of mixture components grows with the number of data items. The Hierarchical Dirichlet Process (HDP), is an extension of DP for grouped…
We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in…
This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in…
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…
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according…
While reinforcement learning (RL) algorithms are achieving state-of-the-art performance in various challenging tasks, they can easily encounter catastrophic forgetting or interference when faced with lifelong streaming information. In the…
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of…
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according…
The Chinese restaurant process (CRP) and the stick-breaking process are the two most commonly used representations of the Dirichlet process. However, the usual proof of the connection between them is indirect, relying on abstract properties…
The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It is motivated with the study of groups of clustered data. Each group is modelled through a level two Dirichlet…
Random partition distribution is a crucial tool for model-based clustering. This study advances the field of random partition in the context of functional spatial data, focusing on the challenges posed by hourly population data across…
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the…
Learning from a continuous stream of non-stationary data in an unsupervised manner is arguably one of the most common and most challenging settings facing intelligent agents. Here, we attack learning under all three conditions…
We develop the distance dependent Chinese restaurant process (CRP), a flexible class of distributions over partitions that allows for non-exchangeability. This class can be used to model many kinds of dependencies between data in infinite…
The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we…