关键词: 概率密度估计, 支持向量机（SVM）, 多核学习, 非平坦函数

Abstract: Aiming at the probability density estimation problem for non-flat functions, this paper constructs a single slack factor multi-scale kernel support vector machine (SVM) probability density estimation model, by improving the form of constraint condition of the traditional SVM model and introducing the multi-scale kernel method. In the model, a single slack factor instead of two types of slack factors is used to control the learning error of SVM, which reduces the computational complexity of model. At the same time, by introducing the multi-scale kernel method, the model can well fit the functions with both the fiercely changed region and the flatly changed region. Through several probability density estimation experiments with typical non-flat functions, the results show that the single slack probability density estimation model has faster learning speed than the common SVM model. And compared with the single kernel method, the multi-scale kernel SVM probability density estimation model has better estimation precision.

Key words: probability density estimation, support vector machine (SVM), multiple kernel learning, non-flat function