Moments for Hawkes Processes with Gamma Decay Kernel Functions

Author(s):  
Lirong Cui ◽  
Bei Wu ◽  
Juan Yin
2019 ◽  
Vol 3 (1) ◽  
pp. 391-412
Author(s):  
Jiancang Zhuang

AbstractThe Hawkes self-exciting model has become one of the most popular point-process models in many research areas in the natural and social sciences because of its capacity for investigating the clustering effect and positive interactions among individual events/particles. This article discusses a general nonparametric framework for the estimation, extensions, and post-estimation diagnostics of Hawkes models, in which we use the kernel functions as the basic smoothing tool.


2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.


Author(s):  
Khalid AA Abakar ◽  
Chongwen Yu

This work demonstrated the possibility of using the data mining techniques such as artificial neural networks (ANN) and support vector machine (SVM) based model to predict the quality of the spinning yarn parameters. Three different kernel functions were used as SVM kernel functions which are Polynomial and Radial Basis Function (RBF) and Pearson VII Function-based Universal Kernel (PUK) and ANN model were used as data mining techniques to predict yarn properties. In this paper, it was found that the SVM model based on Person VII kernel function (PUK) have the same performance in prediction of spinning yarn quality in comparison with SVM based RBF kernel. The comparison with the ANN model showed that the two SVM models give a better prediction performance than an ANN model.


2019 ◽  
Author(s):  
Kylie-Anne Richards ◽  
William Dunsmuir ◽  
Gareth W. Peters
Keyword(s):  

2019 ◽  
Vol 14 (6) ◽  
pp. 480-490 ◽  
Author(s):  
Tuncay Bayrak ◽  
Hasan Oğul

Background: Predicting the value of gene expression in a given condition is a challenging topic in computational systems biology. Only a limited number of studies in this area have provided solutions to predict the expression in a particular pattern, whether or not it can be done effectively. However, the value of expression for the measurement is usually needed for further meta-data analysis. Methods: Because the problem is considered as a regression task where a feature representation of the gene under consideration is fed into a trained model to predict a continuous variable that refers to its exact expression level, we introduced a novel feature representation scheme to support work on such a task based on two-way collaborative filtering. At this point, our main argument is that the expressions of other genes in the current condition are as important as the expression of the current gene in other conditions. For regression analysis, linear regression and a recently popularized method, called Relevance Vector Machine (RVM), are used. Pearson and Spearman correlation coefficients and Root Mean Squared Error are used for evaluation. The effects of regression model type, RVM kernel functions, and parameters have been analysed in our study in a gene expression profiling data comprising a set of prostate cancer samples. Results: According to the findings of this study, in addition to promising results from the experimental studies, integrating data from another disease type, such as colon cancer in our case, can significantly improve the prediction performance of the regression model. Conclusion: The results also showed that the performed new feature representation approach and RVM regression model are promising for many machine learning problems in microarray and high throughput sequencing analysis.


2019 ◽  
Vol 61 ◽  
pp. 161
Author(s):  
Lucas Amaral ◽  
Andrew Papanicolaou

Author(s):  
Po Ting Lin ◽  
Wei-Hao Lu ◽  
Shu-Ping Lin

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.


2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Chunhui Wang ◽  
Chunyu Guo ◽  
Fenglei Han

Modified 3D Moving Particle Semi-Implicit (MPS) method is used to complete the numerical simulation of the fluid sloshing in LNG tank under multidegree excitation motion, which is compared with the results of experiments and 2D calculations obtained by other scholars to verify the reliability. The cubic spline kernel functions used in Smoothed Particle Hydrodynamics (SPH) method are adopted to reduce the deviation caused by consecutive two times weighted average calculations; the boundary conditions and the determination of free surface particles are modified to improve the computational stability and accuracy of 3D calculation. The tank is under forced multidegree excitation motion to simulate the real conditions of LNG ships, the pressures and the free surfaces at different times are given to verify the accuracy of 3D simulation, and the free surface and the splashed particles can be simulated more exactly.


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