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首页> 外文会议>IFAC Symposium on System Identification >VARIANTS OF THE KULLBACK-LEIBLER DIVERGENCE AND THEIR ROLE IN MODEL SELECTION
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VARIANTS OF THE KULLBACK-LEIBLER DIVERGENCE AND THEIR ROLE IN MODEL SELECTION

机译：Kullback-Leibler分歧的变体及其在模型选择中的作用

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摘要

The Akaike information criterion, AIC, is a widely used tool for model selection. AIC is derived as an asymptotically unbiased estimator of a function used for ranking candidate models which is a variant of the Kullback-Leibler divergence between the true model and the approximating candidate model. Despite the Kullback-Leibler's computational and theoretical advantages, what can become a nuisance in model selection applications is its lack of symmetry. Simple examples can show that reversing the role of the arguments in the Kullback-Leibler divergence can yield substantially different results. In this paper, three new functions for ranking candidate models are proposed. These functions are constructed by symmetrizing the Kullback-Leibler divergence between the true model and the approximating candidate model. The operations used for symmetrizing are the average, geometric and harmonic means. It is found that the original AIC criterion is an asymptotically unbiased estimator of these three different functions. A simulation study based on polynomial regression is also provided to compare the different proposed ranking functions with the AIC asymptotic estimation.
机译：Akaike Information Criterion AIC是一种广泛使用的模型选择工具。 AIC衍生为用于排名候选模型的函数的渐近未偏见的估计器，其是真实模型与近似候选模型之间的kullback-leibler发散的变型。尽管Kullback-Leibler的计算和理论优势，但在模型选择应用中可能成为滋扰的是它缺乏对称性。简单的例子可以表明，反转Kullback-Leibler发散中的参数的作用可以产生显着不同的结果。在本文中，提出了三种排名候选模型的新功能。通过对称在真实模型和近似候选模型之间的kullback-leibler发散来构建这些功能。用于对称化的操作是平均值，几何和谐波装置。发现原始AIC标准是这三种不同功能的渐近无偏的估计器。还提供了一种基于多项式回归的仿真研究，以比较与AIC渐近估计的不同提出的排名功能。

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