The Steady State variants of the Multi-Objective Covariance Matrix Adaptation Evolution Strategy (SS-MO-CMA-ES) generate one offspring from a uniformly selected parent. Some other parental selection operators for SS-MO-CMA-ES are investigated in this paper. These operators involve the definition of multi-objective rewards, estimating the expectation of the offspring survival and its Hypervolume...

Using the geometric properties of Sobolev spaces of integer order and a duality condition, the covariance operators of a generalized random field and its dual can be factorized. Via this covariance factorization, a representation of the generalized random field is obtained as a stochastic equation driven by generalized white noise. This stochastic equation becomes a differential equation under ...

Many spatial processes in environmental applications, such as climate variables and climate model errors on a global scale, exhibit complex nonstationary dependence structure, in not only their marginal covariance but also their cross-covariance. Flexible crosscovariance models for processes on a global scale are critical for an accurate description of each spatial process as well as the cross-...

This work studies finite sample approximations of the exact and entropic regularized Wasserstein distances between centered Gaussian processes and, more generally, covariance operators functional random processes. We first show that these distances/divergences are fully represented by reproducing kernel Hilbert space (RKHS) cross-covariance associated with corresponding functions. Using this re...

It is demonstrated that the Schrödinger operator in Ĥ | ψk >= Ek | ψk > can be associated with a covariance matrix whose eigenvalues are the squares of the spectrum σ(Ĥ + Iζ) where ζ is an arbitrarily chosen shift. An efficient method for extracting σ(Ĥ) components, in the vicinity of ζ, from a few specially selected eigenvectors of the inverse of the covariance matrix is derived. The method en...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

This paper deals with two-sample tests for functional time series data, which have become widely available in conjunction the advent of modern complex observation systems. Here, particular interest is evaluating whether two sets observations share shape their primary modes variation as encoded by eigenfunctions respective covariance operators. To this end, a novel testing approach introduced th...

We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ...