Support Vector Machine-based Probability Density Estimation In The Estimation Of Distribution Algorithm

Probability density estimation is the focus of the traditional probability theory and mathematical statistics. It is also an important research of statistical learning theory. The estimation of probability density has a wide range of applications. It is the basis of information entropy theory and it is applied to the lossless compression of audio and video signals too. The distribution of the probability density is usually unknown, but the density can be estimated by the sample points which are from the unknown distribution. Density estimation is generally divided into parameter and non-parameter. Parameter estimation caculates the unknown parameters of the density when the distribution of the sample points is known. It has a strong dependence on the accuracy of the distribution function. Further more, parameter estimation also has some other limitations. Such as Gaussian distribution of unknown parameters can be estimated, but it can not get good results of mixed Gaussian density. The probability density based on support vector machine not only solves the problem that the traditional estimation is based on the samples of large number but also overcomes the limitations of parameter estimation.This paper combined with the insensitive loss function extends the one-dimensional probability density based on support vector machines to two-dimensional and has a simulation test of the results. Further more, it discusses the model of high-dimensional density. Now the estimation of probability density algorithms are based on the Gaussian model, while the actual distribution of probability density may be random. The density that is solved by Support Vector Machine and tested is applied to the estimation of distribution algorithm. In the estimation of distribution algorithm based on support vector machine solution corresponds to the probability density, this paper has extended the dimension of acceptance-rejection method and adjust the upper bound of the probability density that may exist local optimization value. Finally, the two-dimensional estimation of distribution algorithm based on support vector machine is compared with the standard PSO algorithm in the same condition.