Related papers: Generalized modes in Bayesian inverse problems

Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to…

We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

Quantile estimation and regression within the Bayesian framework is challenging as the choice of likelihood and prior is not obvious. In this paper, we introduce a novel Bayesian nonparametric method for quantile estimation and regression…

We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…

Symmetries are known to improve the empirical performance of machine learning models, yet theoretical guarantees explaining these gains remain limited. Prior work has focused mainly on compact group symmetries and often assumes that the…

In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…

Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…

We investigate the frequentist coverage of Bayesian credible sets in a nonparametric setting. We consider a scale of priors of varying regularity and choose the regularity by an empirical Bayes method. Next we consider a central set of…

The nonparametric formulation of density-based clustering, known as modal clustering, draws a correspondence between groups and the attraction domains of the modes of the density function underlying the data. Its probabilistic foundation…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…

Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…

The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a…

This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…