Related papers: Numerical differentiation by the polynomial-expone…
In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…
We consider linearizations of stochastic differential equations with additive noise using the Karhunen-Lo\`eve expansion. We obtain our linearizations by truncating the expansion and writing the solution as a series of matrix-vector…
In this letter, we delve into a scenario where a user aims to compute polynomial functions using their own data as well as data obtained from distributed sources. To accomplish this, the user enlists the assistance of $N$ distributed…
Shannon in his 1949 paper suggested the use of derivatives to increase the W*T product of the sampled signal. Use of derivatives enables improved reconstruction particularly in the case of non-uniformly sampled signals. An FM-AM…
We have presented a new and alternative algorithm for noise reduction using the methods of discrete wavelet transform and numerical differentiation of the data. In our method the threshold for reducing noise comes out automatically. The…
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…
To capture and simulate geometric surface evolutions, one effective approach is based on the phase field methods. Among them, it is important to design and analyze numerical approximations whose error bound depends on the inverse of the…
We derived the formulae of central differentiation for the finding of the first and second derivatives of functions given in discrete points, with the number of points being arbitrary. The obtained formulae for the derivative calculation do…
We consider an approximation scheme for multivariate information assuming that synergistic information only appearing in higher order joint distributions is suppressed, which may hold in large classes of systems. Our approximation scheme…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method,…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
In this paper we present a data-driven approach for uncertainty propagation. In particular, we consider stochastic differential equations with parametric uncertainty. Solution of the differential equation is approximated using maximum…
We revisit the task of releasing marginal queries under differential privacy with additive (correlated) Gaussian noise. We first give a construction for answering arbitrary workloads of weighted marginal queries, over arbitrary domains. Our…
We study the problem of reconstructing a multivariate trigonometric polynomial having only few non-zero coefficients from few random samples. Inspired by recent work of Candes, Romberg and Tao we propose to recover the polynomial by Basis…
Differentially private (DP) mechanisms face the challenge of providing accurate results while protecting their inputs: the privacy-utility trade-off. A simple but powerful technique for DP adds noise to sensitivity-bounded query outputs to…