可能性线性模型中的参数选优与输入噪声间关系的研究

Research on the Dependency between Optimal Parameter and the Input Noise in Possibilistic Linear Model

基于可能性理论的可能性线性模型(PLM)在模糊建模等应用中有重要的作用.本文首先借鉴统计学习理论将此模型扩展为正则化(regularized)的可能性线性模型(RPLM),以提高其泛化能力.然后利用将其优化问题转换为最大后验估计问题的新方法,研究当数据含有噪声时,模型中的拟合门限值λ和输入噪声均方差σ之间的关系.理论推导和仿真实验均证明,当输入噪声为高斯模型时,λ和σ成近似的线性反比关系.该结论对 PLM 和RPLM 均有借鉴意义,为已知输入噪声均方差时,合理选择λ提供理论依据.

Possibilistic linear model （PLM） based on possibility theory plays a pivotal role in fuzzy modeling. In order to enhance the generalization capability of the linear model, the regularized version is firstly extended, i.e. the regularized possibilistic linear model （RPLM）. Then the RPLM is transformed into the corresponding equivalent MAP problem. Accordingly, with a series of mathematical derivation, the inversely proportional dependency between the parameter and the standard deviation of Gaussian noisy input is revealed. In the meanwhile, the simulation result has proved this conclusion. Obviously, the conclusion is helpful for the practical applications of both PLM and RPLM.