Related papers: Expectation Propagation for Poisson Data
Laplace approximations are a standard tool for computationally efficient inference in latent Gaussian models, but they fail for quantile regression with the asymmetric Laplace likelihood because the observed Hessian vanishes almost…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian…
One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance…
In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special…
Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as…
In employing spatial regression models for counts, we usually meet two issues. First, ignoring the inherent collinearity between covariates and the spatial effect would lead to causal inferences. Second, real count data usually reveal over…
This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local approximations…
In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…
This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the…
Expectation Propagation (EP) is a widely used message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions (beliefs) using intermediate functions (messages). While…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…