Related papers: A note on Bayesian R-squared for generalized addit…

This paper concerns the robust regression model when the number of predictors and the number of observations grow in a similar rate. Theory for M-estimators in this regime has been recently developed by several authors [El Karoui et al.,…

Generalized additive models (GAMs, Hastie & Tibshirani, 1990; Wood, 2017) are an extension of the generalized linear model that allows the effects of covariates to be modelled as smooth functions. GAMs are increasingly used in many areas of…

We introduce the Group-R2 decomposition prior, a hierarchical shrinkage prior that extends R2-based priors to structured regression settings with known groups of predictors. By decomposing the prior distribution of the coefficient of…

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…

We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

In this letter, we present a unified Bayesian inference framework for generalized linear models (GLM) which iteratively reduces the GLM problem to a sequence of standard linear model (SLM) problems. This framework provides new perspectives…

One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…

We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. Thus far, GLMs are difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using…

A new approach for Bayesian model averaging (BMA) and selection is proposed, based on the mixture model approach for hypothesis testing in Kaniav et al., 2014. Inheriting from the good properties of this approach, it extends BMA to cases…

A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs…

Generalized additive models (GAM) have been successfully applied to high dimensional data analysis. However, most existing methods cannot simultaneously estimate the link function, the component functions and the variable interaction. To…

A novel method is proposed for the exact posterior mean and covariance of the random effects given the response in a generalized linear mixed model (GLMM) when the response does not follow normal. The research solves a long-standing problem…

This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…

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…

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

Gaussian variational approximations are widely used for summarizing posterior distributions in Bayesian models, especially in high-dimensional settings. However, a drawback of such approximations is the inability to capture skewness or more…