Related papers: A Graphical View of Bayesian Variable Selection
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…
A substantial focus of research in molecular biology are gene regulatory networks: the set of transcription factors and target genes which control the involvement of different biological processes in living cells. Previous statistical…
Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…
Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…
An important aspect of Bayesian model selection is how to deal with huge model spaces, since exhaustive enumeration of all the models entertained is unfeasible and inferences have to be based on the very small proportion of models visited.…
Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs…
We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…
We propose a novel Bayesian model selection technique on linear mixed-effects models to compare multiple treatments with a control. A fully Bayesian approach is implemented to estimate the marginal inclusion probabilities that provide a…
We address the problem of providing inference from a Bayesian perspective for parameters selected after viewing the data. We present a Bayesian framework for providing inference for selected parameters, based on the observation that…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
We introduce a new Ising-type framework for opinion dynamics that explicitly separates private preferences from publicly expressed binary opinions and naturally incorporates neutral agents. Each individual is endowed with an immutable…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
Variable fusion in linear regression models is a statistical method that identifies covariates making similar contributions to the response variable and imposes the same coefficient values on them. Many methods for variable fusion also…
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction…
We aim to incorporate variable selection routines into variable-by-variable (or sequential) imputation in clustered data to achieve computational improvement in applications with large-scale health data. Specifically, we utilize variable…
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…
The choice of tuning parameters in Bayesian variable selection is a critical problem in modern statistics. In particular, for Bayesian linear regression with non-local priors, the scale parameter in the non-local prior density is an…