Related papers: Measuring Bayesian Robustness Using R\'enyi Diverg…

This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented…

Replication of scientific studies is important for assessing the credibility of their results. However, there is no consensus on how to quantify the extent to which a replication study replicates an original result. We propose a novel…

We propose an extension of the classical R\'enyi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured…

We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…

Diffusion models have emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. Likelihood misspecification…

When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…

External data borrowing in clinical trial designs has increased in recent years. This is accomplished in the Bayesian framework by specifying informative prior distributions. To mitigate the impact of potential inconsistency (bias) between…

In the Bayesian literature, a line of research called resolution of conflict is about the characterization of robustness against outliers of statistical models. The robustness characterization of a model is achieved by establishing the…

The R\'enyi information measures are characterized in terms of their Shannon counterparts, and properties of the former are recovered from first principle via the associated properties of the latter. Motivated by this characterization, a…

The quality of a Bayes factor crucially depends on the number of regressors, the sample size and the prior on the regression parameters, and hence it has to be established in a case-by-case basis. In this paper we analyze the consistency of…

For nonlinear supervised learning models, assessing the importance of predictor variables or their interactions is not straightforward because it can vary in the domain of the variables. Importance can be assessed locally with sensitivity…

Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…

We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of progressively Type-II censored data.…

The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…

Adversarial robustness is a critical property in a variety of modern machine learning applications. While it has been the subject of several recent theoretical studies, many important questions related to adversarial robustness are still…

We study diffusion control problems under parameter uncertainty. Controllers based on plug-in estimation can be brittle due to potential distribution shifts. Bayesian control with a prior on the parameters offers a formulation with beliefs…

In safety-critical deep learning applications, robustness measures the ability of neural models that handle imperceptible perturbations in input data, which may lead to potential safety hazards. Existing pre-deployment robustness assessment…

We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a…

In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior and likelihood, since this choice is made by 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…