相关论文: Riemannian Laplace approximations for Bayesian neu…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…

The generalized Gauss-Newton (GGN) approximation is often used to make practical Bayesian deep learning approaches scalable by replacing a second order derivative with a product of first order derivatives. In this paper we argue that the…

Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…

In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…

We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…

The Laplace approximation provides a scalable and efficient means of quantifying weight-space uncertainty in deep neural networks, enabling the application of Bayesian tools such as predictive uncertainty and model selection via Occam's…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…