Related papers: Variational inference for count response semiparam…
The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…
One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
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…
Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
Being in the era of big data, modeling and prediction of count data have become significantly important in many fields including health, finance, social, etc. Although linear Poisson regression has been widely used to model count and rate…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…
We study the properties of variational Bayes approximations for exponential family models with missing values. It is shown that the iterative algorithm for obtaining the variational Bayesian estimator converges locally to the true value…
Beta-binomial/Poisson models have been used by many authors to model multivariate count data. Lora and Singer (Statistics in Medicine, 2008) extended such models to accommodate repeated multivariate count data with overdipersion in the…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…