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可能性线性模型中的参数选优与输入噪声间关系的研究

, PP. 42-47

Keywords: 可能性理论,可能性线性模型(PLM),最大后验估计(MAP)

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Abstract:

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.

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