Related papers: A variational Bayesian method for inverse problems…

Outliers are ubiquitous in modern data sets. Distance-based techniques are a popular non-parametric approach to outlier detection as they require no prior assumptions on the data generating distribution and are simple to implement. Scaling…

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…

Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

We consider a standard distributed optimization problem in which networked nodes collaboratively minimize the sum of their locally known convex costs. For this setting, we address for the first time the fundamental problem of design and…

An efficient algorithm is proposed for Bayesian model calibration, which is commonly used to estimate the model parameters of non-linear, computationally expensive models using measurement data. The approach is based on Bayesian statistics:…

We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we…

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies…

This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…

This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise.…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…

Variational inference provides approximations to the computationally intractable posterior distribution in Bayesian networks. A prominent medical application of noisy-or Bayesian network is to infer potential diseases given observed…

Whether an extreme observation is an outlier or not, depends strongly on the corresponding tail behaviour of the underlying distribution. We develop an automatic, data-driven method to identify extreme tail behaviour that deviates from the…

In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…

In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…

We propose a robust and scalable variational Bayes (VB) framework designed to effectively handle contamination and outliers in dataset. Our approach partitions the data into $m$ disjoint subsets and formulates a joint optimization problem…

Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature…