查看更多>>摘要：In the realm of large-scale machine learning,it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization per-formance.Additionally,since the collected data may contain some sensitive information,it is also of great significance to study privacy-preserving machine learning algorithms.This paper focuses on the performance of the differentially private stochastic gradient descent(SGD)algo-rithm based on random features.To begin,the algorithm maps the original data into a low-dimensional space,thereby avoiding the traditional kernel method for large-scale data storage requirement.Subsequently,the algorithm iteratively optimizes parameters using the stochastic gradient descent approach.Lastly,the output perturbation mechanism is employed to introduce random noise,ensuring algorithmic privacy.We prove that the proposed algorithm satisfies the differential privacy while achieving fast convergence rates under some mild conditions.
查看更多>>摘要：Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction.The proposed technique consists of two steps:testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model.Examples are presented to demonstrate how the method is implemented and to verify its effectiveness.
查看更多>>摘要：The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow.The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid.The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model.The problem formulated in dimensionless form is solved by NDSolve MATHEMATIC A.The graphical analysis for parameters governed by the problem is performed with physical applications.The affiliation of entropy generation and Bejan number for different parameters is inspected in detail.The numerical data for illustrating skin friction,heat and mass transfer rate is also reported.The motion of the fluid is highest for the viscosity ratio parameter.The temperature of the fluid rises via thermal Biot number.Entropy generation rises for greater Brinkman number and diffusion parameter.
查看更多>>摘要：In this paper,Let Mn denote the maximum of logarithmic general error distribution with parameter v ≥ 1.Higher-order expansions for distributions of powered extremes Mpn are derived under an optimal choice of normalizing constants.It is shown that Mpn,when v=1,converges to the Fréchet extreme value distribution at the rate of 1/n,and if v＞1 then Mpn converges to the Gumbel extreme value distribution at the rate of(log log n)2/(log n)1-1/v.
查看更多>>摘要：In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.
查看更多>>摘要：On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].
查看更多>>摘要：This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equiva-lence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.
查看更多>>摘要：Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily depen-dent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
查看更多>>摘要：The paper generalizes the direct method of moving planes to the Logarithmic Lapla-cian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Loga-rithmic Laplacian system is obtained.
查看更多>>摘要：In this paper,we study spatial cross-sectional data models in the form of matrix exponential spatial specification(MESS),where MESS appears in both dependent and error terms.The empirical likelihood(EL)ratio statistics are established for the parameters of the MESS model.It is shown that the limiting distributions of EL ratio statistics follow chi-square distributions,which are used to construct the confidence regions of model parameters.Simula-tion experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method.
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