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The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

We develop a new class of dynamic multivariate Poisson count models that allow for fast online updating and we refer to these models as multivariate Poisson-scaled beta (MPSB). The MPSB model allows for serial dependence in the counts as…

Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…

In this paper, we face the problem of simulating discrete random variables with general and varying distributions in a scalable framework, where fully parallelizable operations should be preferred. The new paradigm is inspired by the…

While several Gaussian mixture models-based biclustering approaches currently exist in the literature for continuous data, approaches to handle discrete data have not been well researched. A multivariate Poisson-lognormal (MPLN) model-based…

In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…

An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models…

It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…

Inferring causal directions on discrete and categorical data is an important yet challenging problem. Even though the additive noise models (ANMs) approach can be adapted to the discrete data, the functional structure assumptions make it…

This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…

In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to…

We provide a differentially private algorithm for producing synthetic data simultaneously useful for multiple tasks: marginal queries and multitask machine learning (ML). A key innovation in our algorithm is the ability to directly handle…

Generating multivariate time series is a promising approach for sharing sensitive data in many medical, financial, and IoT applications. A common type of multivariate time series originates from a single source such as the biometric…

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…

We propose a way to remove the bias of a Poisson regression when the subjects are partially observed. In this paper we address this issue under certain assumptions about the missing-data generating process. We fix the total number of…

Individual-level data (microdata) that characterizes a population, is essential for studying many real-world problems. However, acquiring such data is not straightforward due to cost and privacy constraints, and access is often limited to…

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…

The problem of overdispersion in multivariate count data is a challenging issue. Nowadays, it covers a central role mainly due to the relevance of modern technologies data, such as Next Generation Sequencing and textual data from the web or…

Causal inference is made challenging by confounding, selection bias, and other complications. A common approach to addressing these difficulties is the inclusion of auxiliary data on the superpopulation of interest. Such data may measure a…

Generative models are used in a wide range of applications building on large amounts of contextually rich information. Due to possible privacy violations of the individuals whose data is used to train these models, however, publishing or…