Related papers: On collapsed representation of hierarchical Comple…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…
We demonstrate how to calculate posteriors for general CRM-based priors and likelihoods for Bayesian nonparametric models. We further show how to represent Bayesian nonparametric priors as a sequence of finite draws using a size-biasing…
Infinite-activity completely random measures (CRMs) have become important building blocks of complex Bayesian nonparametric models. They have been successfully used in various applications such as clustering, density estimation, latent…
This paper presents theory for Normalized Random Measures (NRMs), Normalized Generalized Gammas (NGGs), a particular kind of NRM, and Dependent Hierarchical NRMs which allow networks of dependent NRMs to be analysed. These have been used,…
This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The…
Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM…
A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact…
Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient…
Completely random measures (CRMs) provide a broad class of priors, arguably, the most popular, for Bayesian nonparametric (BNP) analysis of trait allocations. As a peculiar property, CRM priors lead to predictive distributions that share…
The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…
Hierarchical beta process has found interesting applications in recent years. In this paper we present a modified hierarchical beta process prior with applications to hierarchical modeling of multiple data sources. The novel use of the…
Nested Chinese Restaurant Process (nCRP) topic models are powerful nonparametric Bayesian methods to extract a topic hierarchy from a given text corpus, where the hierarchical structure is automatically determined by the data. Hierarchical…
There is a growing interest in the estimation of the number of unseen features, mostly driven by biological applications. A recent work brought out a peculiar property of the popular completely random measures (CRMs) as prior models in…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and…
We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…
In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
Topic modeling is traditionally applied to word counts without accounting for the context in which words appear. Recent advancements in large language models (LLMs) offer contextualized word embeddings, which capture deeper meaning and…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…