Related papers: Sparse Bayesian Inference with Regularized Gaussia…

The recovery of sparse generative models from few noisy measurements is an important and challenging problem. Many deterministic algorithms rely on some form of $\ell_1$-$\ell_2$ minimization to combine the computational convenience of the…

Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…

For propensity score analysis and sparse estimation, we develop an information criterion for determining the regularization parameters needed in variable selection. First, for Gaussian distribution-based causal inference models, we extend…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

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…

Gaussian mixture models are a popular tool for model-based clustering, and mixtures of factor analyzers are Gaussian mixture models having parsimonious factor covariance structure for mixture components. There are several recent extensions…

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…

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 multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. Inference is made tractable by…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial…

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…

Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…

Reconstructing lens potentials and lensed sources can easily become an underconstrained problem, even when the degrees of freedom are low, due to degeneracies, particularly when potential perturbations superimposed on a smooth lens are…

We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…