We propose a family of non-uniform sampling strategies to provably speed up a class of stochastic optimization algorithms with linear convergence including Stochastic Variance Reduced Gradient (SVRG) and Stochastic Dual Coordinate Ascent (SDCA). For a large family of penalized empirical risk minimization problems, our methods exploit data dependent local smoothness of the loss functions near th...

Variance swaps now trade actively over-the-counter (OTC) on both stocks and stock indices. Also trading OTC are variations on variance swaps which localize the payoff in time, in the underlying asset price, or both. Given that the price of the underlying asset evolves continuously over time, it is well known that there exists a semi-robust hedge for these localized variance contracts. Remarkabl...

We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue −1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X∗X, where the variances of the entries of X may vary.

The present work deals with the development of a framework dedicated to construction constitutive models non-local internal variables. Such variables allow considering impact microstructural changes on current state material point. Non-locality is introduced by considering, not only spatial average, but also variance an variable in relations. proposed relies continuum thermodynamics construct s...

We use IGETS absolute gravitational acceleration measurement data to study the variance. The relative variance of $\delta g /g$ in 22 years is less than $4\times 10^{-8}$. Since G /G\lessapprox\delta /g $, this implies Newtonian constant $3\times 10^{-9}$ based on an sine-like oscillation hypothesis. This limit at least 4 orders magnitude better existing $G$ measurements. scattered values repor...