Related papers: Concentration of Measure for Radial Distributions …
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also…
Future large scale structure surveys will provide increasingly tight constraints on our cosmological model. These surveys will report results on the distance scale and growth rate of perturbations through measurements of Baryon Acoustic…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
We study frequentist risk properties of predictive density estimators for mean mixtures of multivariate normal distributions, involving an unknown location parameter $\theta \in \mathbb{R}^d$, and which include multivariate skew normal…
The concentration of measure phenomena were discovered as the mathematical background of statistical mechanics at the end of the XIX - beginning of the XX century and were then explored in mathematics of the XX-XXI centuries. At the…
Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing…
We suggest that the curse of dimensionality affecting the similarity-based search in large datasets is a manifestation of the phenomenon of concentration of measure on high-dimensional structures. We prove that, under certain geometric…
Packing density is a permutation occurrence statistic which describes the maximal number of permutations of a given type that can occur in another permutation. In this article we focus on containment of sets of permutations. Although this…
We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…
This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite…
In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…
If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy…