Related papers: Estimation of sub-Gaussian random vectors using th…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components. Due to their broad expressive power, Gaussian mixture models…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for…
Approximating integrals is a fundamental task in probability theory and statistical inference, and their applied fields of signal processing, and Bayesian learning, as soon as expectations over probability distributions must be computed…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…
This paper is devoted to the numerical analysis of a piecewise constant discontinuous Galerkin method for time fractional subdiffusion problems. The regularity of weak solution is firstly established by using variational approach and…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
The stability of the Ghurye-Olkin (GO) characterization of Gaussian vectors is analyzed using a partition of the vectors into equivalence classes defined by their matrix factors. The sum of the vectors in each class is near-Gaussian in the…
The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the…