This paper deals with the problem of estimation in the parametric case for discrete random variables Their study is facilitated by the powerful method of probability generating function

https://documat.unirioja.es/descarga/articulo/118523.pdf

The integrated squared error estimation of parameters.

A kernelized non-parametric classifier based on feature ranking in anisotropic Gaussian kernel

An efficient Global Particle Swarm Optimization (GPSO) is proposed in order to overcome the concern of trapping in the local optimal point especially in high dimensional while using ordinary Particle Swarm Optimization (PSO). GPSO is able to bring all the particles to be closely clumped together faster than PSO. In this paper, an improved GPSO is proposed in order to get a closely clumped particles group faster than using GPSO. The original GPSO is improved by taking into account the global best fitness error and particle fitness clumping size of every iteration. The improved GPSO is simulated by using several two dimension mathematical function and benchmarked with the original GPSO. The improved GPSO is shown to be able to obtain closely clumped particles much more faster than the original GPSO up to 62%. The performances are also evaluated by comparing the standard deviation, average, best particle and worst particles obtained through a 50 independent runs. In term of the four factors mentioned, the improved GPSO performance is shown to be as good of the original GPSO.

An Improved Global Particle Swarm Optimization for Faster Optimization Process

Combining multiple classifiers to achieve better performance than any single classifier is one of the most important research areas in machine learning. In this paper, we focus on combining different classifiers to form an effective ensemble system. By introducing a novel framework operated on outputs of different classifiers, our aim is to build a powerful model which is competitive to other well-known combining algorithms such as Decision Template, Multiple Response Linear Regression (MLR), SCANN and fixed combining rules. Our approach is difference from the traditional approaches in that we use Gaussian Mixture Model (GMM) to model distribution of Level1 data and to predict the label of an observation based on maximizing the posterior probability realized through Bayes model. We also apply Principle Component Analysis (PCA) to output of base classifiers to reduce its dimension of what before GMM modeling. Experiments were evaluated on 21 datasets coming from University of California Irvine (UCI) Machine Learning Repository to demonstrate the benefits of our framework compared with several benchmark algorithms.

Machine Learning and Cybernetics

The determination of bandwidth parameter is a critical factor for the performance of probability density estimation method. The advanced parameter selection methods, such as the bootstrap method, the least-squares cross-validation (LSCV) method and the biased cross-validation (BCV) method, always need the help of the brute-force search or exhaustive search to find the optimal bandwidth parameters. In this paper, we apply five particle swarm optimization (PSO) algorithms-standard PSO (SPSO), PSO with a constriction factor (PSOCF), Gaussian PSO (GPSO), Gaussian PSO with Gaussian jump (GPSOGJ) and Gaussian PSO with Cauchy jump (GPSOCJ)-to determine the optimal bandwidths. In order to experimentally validate the feasibility and effectiveness of selecting the optimal parameters by using PSO algorithms, we carry out some numerical simulations on four univariate artificial datasets: Uniform dataset, Normal dataset, Exponential dataset and Rayleigh dataset. The finally comparative results show that our strategies are well-performed and Gaussian PSO with jump methods can obtain the better estimations than other PSO algorithms.

Applying particle swarm optimization to determine the bandwidth parameter in probability density estimation

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Applying particle swarm optimization to determine the bandwidth parameter in probability density estimation