Challenging the Deployment of Fiducial Points in Minimum Error Entropy
Challenging the Deployment of Fiducial Points in Minimum Error Entropy
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DOI：
10.1109/isit50566.2022.9834419
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发表时间：
2022-06
期刊：
影响因子：
--
通讯作者：
Sajjad Bahrami;E. Tuncel
中科院分区：
文献类型：
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作者：
Sajjad Bahrami;E. Tuncel
本文研究了非高斯噪声下的鲁棒自适应线性滤波问题。更准确地说，著名的稳健自适应学习算法--带基准点的最小误差熵(MEEF)受到了挑战。误差熵和误差相关熵是两个可用于有监督学习问题的信息论代价函数。它们结合了标签和系统输出之间的误差的高阶统计量，因此是数据的综合描述符，与传统的成本函数相比，对环境的非高斯表现出更强的稳健性。这种稳健性使它们成为传统均方误差(MSE)的有力替代，后者只考虑误差的方差(二阶矩)。具体地，在最小误差熵(MEE)中，误差熵被最小化，以提取关于数据生成系统的尽可能多的信息。然而，由于熵是移位不变的，所以对于不位于原点的其他误差PDF也可以出现该最小熵。在这些情况下，获得系统参数的不希望的估计。因此，必须采取额外的步骤将误差样本集中在原点周围。为此，最著名的方法是MEEF，在这种方法中，一些外部和人为的零误差样本被添加到成本函数中作为参考点，以迫使实际误差样本集中在它们周围。使用这些基准点将最大似然估计转化为最大似然估计和最大相关熵准则(MCC)的加权组合。文中指出，将这些基准点加入到MEE中甚至可以降低稳态失调和/或收敛速度。
In this paper, robust linear adaptive filtering in presence of non-Gaussian noise is addressed. More precisely, the well-known algorithm for robust adaptive learning called minimum error entropy with fiducial points (MEEF) is challenged. Error entropy and error correntropy are two information theoretic cost functions that can be used in a supervised learning problem. They incorporate higher-order statistics of the error between labels and system outputs and therefore are comprehensive descriptors of data that show more robustness against non-Gaussianity of the environment compared to the conventional cost functions. This robustness makes them strong substitutions for classical mean square error (MSE) that only considers the variance (second-order moment) of the error. In minimum error entropy (MEE) specifically, error entropy is minimized to extract as much information as possible about the data generating system. However, this minimum entropy can also occur for other error PDFs not located at the origin inasmuch as entropy is shift-invariant. In these cases, an undesired estimate of the system parameters is obtained. Therefore, an extra step must be taken to concentrate error samples around the origin. The most celebrated approach towards that end is MEEF, in which some external and artificial zero error samples, called fiducial points (not generated by the underlying system), are added to the cost function as the reference points to force actual error samples to get concentrated around them. Using these fiducial points translates MEEF into a weighted combination of MEE and maximum correntropy criterion (MCC). In this paper, it is shown that incorporating these fiducial points into MEE can even degrade the steady state misalignment and/or convergence speed.