$L^p$ properties for Gaussian random series

L Properties for Gaussian Random Series

Let c = (cn)n∈N be an arbitrary sequence of l2(N ) and let Fc(ω) be a random series of the type Fc(ω) = ∑ n∈N gn(ω)cnen, where (gn)n∈N∗ is a sequence of independent NC(0, 1) Gaussian random variables and (en)n∈N an orthonormal basis of L2(Y,M, μ) (the finite measure space (Y,M, μ) being arbitrary). By using the equivalence of Gaussian moments and an integrability theorem due to Fernique, we sho...

Autoregressive Gaussian Random Vectors of First Order

Solving LP using random projections

A celebrated result of Johnson and Lindenstrauss asserts that, in high enough dimensional spaces, Euclidean distances defined by a finite set of points are approximately preserved when these points are projected to a certain lower dimensional space. We show that the distance from a point to a convex set is another approximate invariant, and leverage this result to approximately solve linear pro...

Utilizing Gaussian Markov random field properties of Bayesian animal models.

In this article, we demonstrate how Gaussian Markov random field properties give large computational benefits and new opportunities for the Bayesian animal model. We make inference by computing the posteriors for important quantitative genetic variables. For the single-trait animal model, a nonsampling-based approximation is presented. For the multitrait model, we set up a robust and fast Marko...

Robustness Properties of Dimensionality Reduction with Gaussian Random Matrices

In this paper we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the rob...