Related papers: The Dependent Dirichlet Process and Related Models

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…

When machine learning models are deployed on a test distribution different from the training distribution, they can perform poorly, but overestimate their performance. In this work, we aim to better estimate a model's performance under…

In this paper we propose a new methodology for solving a discrete time stochastic Markovian control problem under model uncertainty. By utilizing the Dirichlet process, we model the unknown distribution of the underlying stochastic process…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…

The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…

In public health management there is a need to produce subnational estimates of health outcomes. Often, however, funds are not available to collect samples large enough to produce traditional survey sample estimates for each subnational…

This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures offer a more flexible…

Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…

Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples…

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…

Diffusion models generate samples by incrementally reversing a process that turns data into noise. We show that when the step size goes to zero, the reversed process is invariant to the distribution of these increments. This reveals a…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a…

Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed…

Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal…