Related papers: Simple proof of robustness for Bayesian heavy-tail…
The robustness to the prior of Bayesian inference procedures based on a measure of statistical evidence are considered. These inferences are shown to have optimal properties with respect to robustness. Furthermore, a connection between…
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…
Real-world data is often unbalanced and long-tailed, but deep models struggle to recognize rare classes in the presence of frequent classes. To address unbalanced data, most studies try balancing the data, the loss, or the classifier to…
A large body of work in the statistics and computer science communities dating back to Huber (Huber, 1960) has led to statistically and computationally efficient outlier-robust estimators. Two particular outlier models have received…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
Out-of-distribution (OOD) generalization is a complicated problem due to the idiosyncrasies of possible distribution shifts between training and test domains. Most benchmarks employ diverse datasets to address this issue; however, the…
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…
Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…
Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…
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…
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…
In this paper we criticize the robustness measure traditionally employed to assess the performance of machine learning models deployed in adversarial settings. To mitigate the limitations of robustness, we introduce a new measure called…
Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…
Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…
Adversarial robustness refers to a model's ability to resist perturbation of inputs, while distribution robustness evaluates the performance of the model under data shifts. Although both aim to ensure reliable performance, prior work has…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…
The vulnerability of machine learning models to adversarial attacks remains a critical security challenge. Traditional defenses, such as adversarial training, typically robustify models by minimizing a worst-case loss. However, these…
In astronomical observations, the estimation of distances from parallaxes is a challenging task due to the inherent measurement errors and the non-linear relationship between the parallax and the distance. This study leverages ideas from…