Related papers: Modeling data with zero inflation and overdispersi…

Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…

The success of diffusion probabilistic models in generative tasks, such as text-to-image generation, has motivated the exploration of their application to regression problems commonly encountered in scientific computing and various other…

There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

In many fields, and especially in the medical and social sciences and in recommender systems, data are gathered through clinical studies or targeted surveys. Participants are generally reluctant to respond to all questions in a survey or…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…

Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

In many applications, the training data for a machine learning task is partitioned across multiple nodes, and aggregating this data may be infeasible due to communication, privacy, or storage constraints. Existing distributed optimization…

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…

Sequencing-based technologies provide an abundance of high-dimensional biological datasets with skewed and zero-inflated measurements. Classification of such data with linear discriminant analysis leads to poor performance due to the…

Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…

In this paper, an alternative count distribution suitable for modeling over dispersed, zero vertex unimodality and monotonically decreasing data sets. Though the proposed probability model includes Gauss Hypergeometric special function, it…

A longstanding problem in machine learning is to find unsupervised methods that can learn the statistical structure of high dimensional signals. In recent years, GANs have gained much attention as a possible solution to the problem, and in…

Bounded continuous data on the unit interval frequently arise in applied fields and often exhibit a non-negligible proportion of observations at the boundaries. Inflated regression models address this feature by combining a continuous…

We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these…

We develop a new longitudinal count data regression model that accounts for zero-inflation and spatio-temporal correlation across responses. This project is motivated by an analysis of Iowa Fluoride Study (IFS) data, a longitudinal cohort…

In this paper, we propose two important extensions to cluster-weighted models (CWMs). First, we extend CWMs to have generalized cluster-weighted models (GCWMs) by allowing modeling of non-Gaussian distribution of the continuous covariates,…

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive…