Related papers: Inference on High-Dimensional Sparse Count Data
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…
This paper discusses predictive densities under the Kullback--Leibler loss for high-dimensional Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive…
In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…
Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like…
In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number…
Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion,…
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…
This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable…
Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions, although it is generally the least accurate approach,…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…
Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable…
The emergence of Big Data raises the question of how to model economic relations when there is a large number of possible explanatory variables. We revisit the issue by comparing the possibility of using dense or sparse models in a Bayesian…
Global-local shrinkage prior has been recognized as useful class of priors which can strongly shrink small signals towards prior means while keeping large signals unshrunk. Although such priors have been extensively discussed under Gaussian…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
We focus on the increasingly important area of sparse regression problems where there are many variables and the effects of a large subset of these are negligible. This paper describes the construction of hierarchical prior distributions…