Related papers: Being Bayesian about Network Structure
The well-known Bayes theorem assumes that a posterior distribution is a probability distribution. However, the posterior distribution may no longer be a probability distribution if an improper prior distribution (non-probability measure)…
We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be…
Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…
Bayesian network structure learning is often performed in a Bayesian setting, evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an…
In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
This paper deals with some computational aspects in the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent…
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…
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…
Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…
This paper studies a Bayesian estimation procedure for single-hidden-layer neural networks using $\ell_{1}$ controlled weights. We study the structure of the posterior density and provide a representation that makes it amenable to rapid…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…