相关论文: A new data fitting method for stretched Gaussian n…
This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, L\'evy and stretched Gaussian noises, to exact value of the selected…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
In gravitational wave astronomy, non-Gaussian noise, such as scattered light noise disturbs stable interferometer operation, limiting the interferometer's sensitivity, and reducing the reliability of the analyses. In scattered light noise,…
In light of recent advances in time-step independent stochastic integrators for Langevin equations, we revisit the considerations for using non-Gaussian distributions for the thermal noise term in discrete-time thermostats. We find that the…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
A distributed adaptive algorithm for estimation of sparse unknown parameters in the presence of nonGaussian noise is proposed in this paper based on normalized least mean fourth (NLMF) criterion. At the first step, local adaptive NLMF…
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of the subordinated killed Brownian motion. The tempered…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index $H>1/2$, it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
A popular class of problem in statistics deals with estimating the support of a density from $n$ observations drawn at random from a $d$-dimensional distribution. The one-dimensional case reduces to estimating the end points of a univariate…
We present a simple variant of the Gaussian mechanism for answering differentially private queries when the sensitivity space has a certain common structure. Our motivating problem is the fundamental task of answering $d$ counting queries…
In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
The trimming scheme with a prefixed cutoff portion is known as a method of improving the robustness of statistical models such as multivariate Gaussian mixture models (MG- MMs) in small scale tests by alleviating the impacts of outliers.…
We study Gaussian approximations to the distribution of a diffusion. The approximations are easy to compute: they are defined by two simple ordinary differential equations for the mean and the covariance. Time correlations can also be…