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We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…

A polycrystalline solid is modelled as an ensemble of random irregular polyhedra filling the entire space occupied by the solid body, leaving no voids or flaws between them. Adjacent grains can slide with a relative velocity proportional to…

Porosity is one of the key properties of dense particle packings like sediment deposits and is influenced by a multitude of grain characteristics such as their size distribution and shape. In the present work, we focus on the form, a…

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…

A machine learning model that generalizes well should obtain low errors on unseen test examples. Thus, if we learn an optimal model in training data, it could have better generalization performance in testing tasks. However, learning such a…

Distributional robustness is a promising framework for training deep learning models that are less vulnerable to adversarial examples and data distribution shifts. Previous works have mainly focused on exploiting distributional robustness…

We conduct a large empirical evaluation to investigate the landscape of distributional robustness in question answering. Our investigation spans over 350 models and 16 question answering datasets, including a diverse set of architectures,…

To ensure trust in AI models, it is becoming increasingly apparent that evaluation of models must be extended beyond traditional performance metrics, like accuracy, to other dimensions, such as fairness, explainability, adversarial…

Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

We study the robustness of Bayesian persuasion to uncertainty about the receiver's preferences. We analyze two conceptually distinct notions: continuity, in which only the modeler lacks precise knowledge, but where the model's predictions…

Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…

In random systems consisting of grains with size distributions the transport properties are difficult to explore by network models. However, the concentration dependence of effective conductivity and its critical properties can be…

We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poisson's ratio with…

Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…

A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…

We use confocal microscopy and time-resolved light scattering to investigate plasticity in a col- loidal polycrystal, following the evolution of the network of grain boundaries as the sample is submitted to thousands of shear deformation…