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There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a…

We introduce a new copula-based correction for generalized linear mixed models (GLMMs) within the integrated nested Laplace approximation (INLA) approach for approximate Bayesian inference for latent Gaussian models. While INLA is usually…

Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…

We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…

We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…

Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution…

As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption…

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…

Generalized linear models (GLMs) are routinely used for modeling relationships between a response variable and a set of covariates. The simple form of a GLM comes with easy interpretability, but also leads to concerns about model…

Motivated by big data and the vast parameter spaces in modern machine learning models, optimisation approaches to Bayesian inference have seen a surge in popularity in recent years. In this paper, we address the connection between the…

The generalized linear model (GLM), where a random vector $\boldsymbol{x}$ is observed through a noisy, possibly nonlinear, function of a linear transform output $\boldsymbol{z}=\boldsymbol{Ax}$, arises in a range of applications such as…

Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear…

It is a challenging problem that solving the \textit{multivariate linear model} (MLM) $\mathbf{A}\mathbf{x}=\mathbf{b}$ with the $\ell_1 $-norm approximation method such that $||\mathbf{A}\mathbf{x}-\mathbf{b}||_1$, the $\ell_1$-norm of the…

Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is to account for within-subject correlation in longitudinal data analysis. They are also the standard vehicle…

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive…