Related papers: Maximally Stable Gaussian Partitions with Discrete…
In this paper we prove two results related to the Gaussian optimizers conjecture for multimode bosonic system with gauge symmetry. First, we argue that the classical capacity of a Gaussian observable is attained on a Gaussian ensemble of…
This letter generalizes noise modulation by introducing two voltage biases and employing non-Gaussian noise distributions, such as Mixture of Gaussian (MoG) and Laplacian, in addition to traditional Gaussian noise. The proposed framework…
A theoretical approach for characterising the influence of asymmetry of noise distribution on the escape rate of a multi-stable system is presented. This was carried out via the estimation of an action, which is defined as an exponential…
We witness experimentally the presence of macroscopic coherence in Gaussian quantum states using a recently proposed criterion (E.G. Cavalcanti and M. Reid, Phys. Rev. Lett. 97, 170405 (2006)). The macroscopic coherence stems from…
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…
Let $\{\xi_n, n\in\Z^d\}$ be a $d$-dimensional array of i.i.d. Gaussian random variables and define $\SSS(A)=\sum_{n\in A} \xi_n$, where $A$ is a finite subset of $\Z^d$. We prove that the appropriately normalized maximum of…
This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…
We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to…
Many traditional algorithms applied in gravitational-wave astronomy rely on the assumption of Gaussian noise, a condition not always met. To meet this need, this study extends a robust statistical framework, advancing previous work on…
Black-box variational inference is widely used in situations where there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs: namely the challenge of…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
We prove that standard Gaussian random multipliers are expected to numerically stabilize both Gaussian elimination with no pivoting and block Gaussian elimination. Moreover we prove that such a multiplier (even without the customary…
We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…
In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even…
The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian noises. The noise term is…
It is common to model a deterministic response function, such as the output of a computer experiment, as a Gaussian process with a Mat\'ern covariance kernel. The smoothness parameter of a Mat\'ern kernel determines many important…
We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…
Benjamini, Kalai and Schramm (2001) showed that weighted majority functions of $n$ independent unbiased bits are uniformly stable under noise: when each bit is flipped with probability $\epsilon$, the probability $p_\epsilon$ that the…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…