Related papers: Bayesian matrix completion: prior specification

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…

We present a Bayesian tomography framework operating with prior-knowledge-based parametrization that is accelerated by surrogate models. Standard high-fidelity forward solvers solve wave equations with natural spatial parametrizations based…

An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph…

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…

We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…

Many inverse problems arising in engineering and applied sciences involve unknown quantities with pronounced spatial inhomogeneity, such as localized defects or spatially varying material properties, making reliable uncertainty…

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…

The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates…

Dirichlet distribution and Dirichlet process as its infinite dimensional generalization are primarily used conjugate prior of categorical and multinomial distributions in Bayesian statistics. Extensions have been proposed to broaden…

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…

This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…

We obtain the optimal Bayesian minimax rate for the unconstrained large covariance matrix of multivariate normal sample with mean zero, when both the sample size, n, and the dimension, p, of the covariance matrix tend to infinity.…

Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors.…

Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric…

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum $\gamma$-divergence estimator is well-known to work well estimation against heavy contamination. The robust Bayesian…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

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…

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…