Balancing Gaussian Vectors

Autoregressive Gaussian Random Vectors of First Order

A Probabilistic Approach to the Geometry of the `p Ball

This article investigates, by probabilistic methods, various geometric questions on B p , the unit ball of ` n p . We propose realizations in terms of independent random variables of several distributions on B p , including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B p . As another applicati...

Novel Radial Basis Function Neural Networks based on Probabilistic Evolutionary and Gaussian Mixture Model for Satellites Optimum Selection

In this study, two novel learning algorithms have been applied on Radial Basis Function Neural Network (RBFNN) to approximate the functions with high non-linear order. The Probabilistic Evolutionary (PE) and Gaussian Mixture Model (GMM) techniques are proposed to significantly minimize the error functions. The main idea is concerning the various strategies to optimize the procedure of Gradient ...

A Probabilistic Approach to the Geometry of the lp Ball

This article investigates, by probabilistic methods, various geometric questions on B p , the unit ball of l p . We propose realizations in terms of independent random variables of several distributions on B p , including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B p . As another application...

Towards a Constructive Version of Banaszczyk's Vector Balancing Theorem

An important theorem of Banaszczyk (Random Structures & Algorithms ‘98) states that for any sequence of vectors of `2 norm at most 1/5 and any convex body K of Gaussian measure 1/2 in R, there exists a signed combination of these vectors which lands inside K. A major open problem is to devise a constructive version of Banaszczyk’s vector balancing theorem, i.e. to find an efficient algorithm wh...