An evolutionary sampling approach with adaptive Levy probability distribution

In classical learning methods, sampling is a process of acquiring training data, which can select the representative samples from the original data and offer a solution to some intractable optimization problems. In this paper, we investigate how to acquire accurate samples from an arbitrary distribution. Based on our previous work and the principles of evolutionary computation, we propose an improved evolutionary sampling approach (ES). In order to obtain the performance of the ES, we propose a general method to set the smoothing parameter and thus employ an adaptive Levy probability distribution to control the parameter in the Markov chain. In the whole evolution sampling process, a support sample model (SSM) is firstly built to approximate an original density function, and then the proposed evolutionary sampling approach can converge to the optimal solution by minimizing the total distance through seeking the accurate model parameters of the SSM. The proposed algorithm is applied to some probability density functions with different numbers of the peaks to obtain optimal sample set that can represent the solutions of related problems. The experimental results show that the proposed variant of evolutionary sampling approach obtains accurate sample set with high efficiency, and that the method can be suitable for any other machine learning problems that can be transformed into density function estimation problems with a probabilistic framework.