Related papers: High-Dimensional Bayesian Inference in Nonparametr…

Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual…

Finding the model that best describes a high-dimensional dataset is a daunting task, even more so if one aims to consider all possible high-order patterns of the data, going beyond pairwise models. For binary data, we show that this task…

High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected…

Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently…

Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. In this work,…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

Nonparametric empirical Bayes methods provide a flexible and attractive approach to high-dimensional data analysis. One particularly elegant empirical Bayes methodology, involving the Kiefer-Wolfowitz nonparametric maximum likelihood…

We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be…

We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…