Related papers: Bayesian inference of sparsity in stable vector au…

In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution…

We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…

In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide…

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to…

The emergence of Big Data raises the question of how to model economic relations when there is a large number of possible explanatory variables. We revisit the issue by comparing the possibility of using dense or sparse models in a Bayesian…

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…

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…

We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…