Related papers: Fisher-Riemann geometry for nonparametric probabil…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
The aim of this paper is to derive explicit formulae for the Riemannian Bures metric on the manifold of (finite dimensional) nondegenerate density matrices. The computation of the Bures metric using the presented equations does not require…
In this paper, we study the geometry of non-Archimedean Gromov-Hausdorff metric. This is the first part of our series work, which we try to establish some facts about the counterpart of Gromov-Hausdorff metric in the non-Archimedean spaces.…
In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution,…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
In this talk the possibility of constructing geodesically complete inhomogeneous stiff fluid cosmologies is discussed. A family with infinite parameters is derived. A wide and easy to implement sufficient condition for geodesic completeness…
We study systems of parameters over finite fields from a probabilistic perspective, and use this to give the first effective Noether normalization result over a finite field. Our central technique is an adaptation of Poonen's closed point…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
Short geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers' theorem gives a global bound on the length of the first $3g-3$ geodesics. We use the construction of Brooks and Makover of random Riemann…
The notion of partial geodesic was introduced by Jamshidpey et al. in "Sets of medians in the non-geodesic pseudometric space of unsigned genomes with breakpoints", 2014. In this paper, we study the density of points on non-trivial partial…
We consider a class of nonlocal generalized perimeters which includes fractional perimeters and Riesz type potentials. We prove a general isoperimetric inequality for such functionals, and we discuss some applications. In particular we…
We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic…
The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the…
We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behavior. We give sufficient conditions for the continuous variation (in the $L^1$-norm) of the densities of absolutely continuous…
A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…
This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…
We introduce Riemannian First-Passage Percolation (Riemannian FPP) as a new model of random differential geometry, by considering a random, smooth Riemannian metric on $\mathbb R^d$. We are motivated in our study by the random geometry of…