Related papers: A New Bayesian Huberised Regularisation and Beyond

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

We propose a generalized formulation of the Huber loss. We show that with a suitable function of choice, specifically the log-exp transform; we can achieve a loss function which combines the desirable properties of both the absolute and the…

We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of…

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented…

Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…

We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…

In recent years, inconsistency in Bayesian deep learning has attracted significant attention. Tempered or generalized posterior distributions are frequently employed as direct and effective solutions. Nonetheless, the underlying mechanisms…

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…

Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…

We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…

This work describes a Bayesian framework for reconstructing the boundaries that represent targeted features in an image, as well as the regularity (i.e., roughness vs. smoothness) of these boundaries.This regularity often carries crucial…

Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and…

A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…