Consistency Analysis of an Empirical Minimum Error Entropy Algorithm
Consistency Analysis of an Empirical Minimum Error Entropy Algorithm
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DOI：
10.1016/j.acha.2014.12.005
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Jun Fan;Ting Hu;Qiang Wu;Ding-Xuan Zhou
中科院分区：
文献类型：
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作者：
Jun Fan;Ting Hu;Qiang Wu;Ding-Xuan Zhou
在本文中，我们研究的经验最小误差熵（EML）算法在回归设置的一致性。我们介绍两种类型的一致性。误差熵的一致性，这需要学习函数的误差熵近似最小误差熵，示出总是真的，如果带宽参数以适当的速率趋于0。然而，回归一致性要求学习函数逼近回归函数，这是一个复杂的问题。证明了当噪声与输入变量无关时，误差熵的一致性蕴涵着回归的一致性。但对于异方差模型，一个反例被用来表明，这两种类型的一致性不重合。一个令人惊讶的结果是，回归一致性总是真的，只要带宽参数以适当的速率趋于无穷大。证明了两类特殊模型的回归一致性在带宽参数固定的情况下仍然成立，进一步说明了MEE回归一致性的复杂性。傅里叶变换在我们的分析中起着至关重要的作用。
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the bandwidth parameter tends to 0 at an appropriate rate. The regression consistency, which requires the learned function to approximate the regression function, however, is a complicated issue. We prove that the error entropy consistency implies the regression consistency for homoskedastic models where the noise is independent of the input variable. But for heteroskedastic models, a counterexample is used to show that the two types of consistency do not coincide. A surprising result is that the regression consistency is always true, provided that the bandwidth parameter tends to infinity at an appropriate rate. Regression consistency of two classes of special models is shown to hold with fixed bandwidth parameter, which further illustrates the complexity of regression consistency of MEE. Fourier transform plays crucial roles in our analysis.