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Follow-up observations at high-angular resolution of submillimeter galaxies showed that the single-dish sources are comprised of a blend of several galaxies. Consequently, number counts derived from low and high angular resolution…
This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several…
We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…
We prove that for Gaussian random normal matrices the correlation function has universal behavior. Using the technique of orthogonal polynomials and identities similar to the Christoffel-Darboux formula, we find that in the limit, as the…
Three-dimensional molecular dynamics simulations of dissipative particles (~ 10^6) are carried out for studying the clustering kinetics of granular media during cooling. The inter-connected high particle density regions are identified,…
We extend some recent results on the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. Dimensions higher than two and measurements in Banach spaces are considered. We investigate the relation…
We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
We study potential biases of popular cluster quality metrics, such as conductance or modularity. We propose a method that uses both stochastic and preferential attachment block models construction to generate networks with preset community…
We introduce and carefully study a natural probability measure over the numerical range of a complex matrix $A \in M_n(\C)$. This numerical measure $\mu_A$ can be defined as the law of the random variable $<AX,X> \in \C$ when the vector $X…
Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of…
We study the packing dimension of Borel measures under orthogonal projections. We give a necessary and sufficient condition such that typical projections of Borel probability measures have full packing dimension and derive general lower…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
The generalized density is a product of a density function and a weight function. For example, the average local brightness of an astronomical image is the probability of finding a galaxy times the mean brightness of the galaxy. We propose…
Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n\leq d$ in spaces of…
We study thermodynamics properties of a one dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in two-dimensional space. Correlations between orientations of the objects are…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…