Related papers: Robustness in the Poisson Boolean model with conve…
This paper proposes normative criteria for voting rules under uncertainty about individual preferences. The criteria emphasize the importance of responsiveness, i.e., the probability that the social outcome coincides with the realized…
Granular materials are involved in most industrial and environmental processes, as well as many civil engineering applications. Although significant advances have been made in understanding the statics and dynamics of cohesionless grains…
Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly,…
Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ-grain model.…
The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum…
Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…
A stationary Boolean model is the union set of random compact particles which are attached to the points of a stationary Poisson point process. For a stationary Boolean model with convex grains we consider a recently developed collection of…
We determine the non-equilibrium grain size distribution during the crystallization of a solid in $d$ dimensions at fixed thermodynamic conditions, for the random nucleation and growth model, and in absence of grain coalescence. Two…
In a previous work, two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
Grain boundary roughness can affect electronic and mechanical properties of two-dimensional materials. This roughness depends crucially on the growth process by which the two-dimensional material is formed. To investigate the key mechanisms…
We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K $\subset$ R d with non empty interior. In a first setting, the Boolean model is a…
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…
Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case…
The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an…
The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do…
Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D…
While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…
A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two…
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…