We present the development of a bilinear regression model for multivariate calibration on the basis of maximum correntropy criteria (MCC) whose robustness can be easily controlled. MCC regression methods can be more effective when the assumption of normality does not hold or when data are contaminated with outliers. These methods are competitive when the degree of robustness against outliers should be controlled. By controlling the robustness, information from candidate outliers can be partially retained rather than completely included or discarded during calibration. Within the context of bilinear regression models, an MCC approach using statistically inspired modification of the partial least squares (SIMPLS) is proposed, which is named maximum correntropy‐weighted partial least squares (MCW‐PLS). Thanks to the controllable robustness of MCC models, observations are upweighted or downweighted during the calibration process, rendering robust models with soft discrimination of samples. Such a weighting represents an important advantage, especially for cases when samples are not drawn from a normal distribution. Applications to three real case studies are presented. These applications uncovered three main features of MCW‐PLS: robustness control between SIMPLS and robust SIMPLS (RSIMPLS), improvements in prediction performance of bilinear calibration models, and the possibility to detect the most informative samples in a calibration set.

中文翻译：

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基于最大相关熵的双线性建模鲁棒性控制

我们提出了基于最大相关熵准则 (MCC) 的多元校准双线性回归模型的开发，该模型的稳健性可以轻松控制。当正态性假设不成立或数据被异常值污染时，MCC 回归方法可能更有效。当应该控制对异常值的鲁棒性程度时，这些方法是有竞争力的。通过控制稳健性，可以在校准期间部分保留来自候选异常值的信息，而不是完全包括或丢弃。在双线性回归模型的背景下，提出了一种使用偏最小二乘法 (SIMPLS) 的统计启发修改的 MCC 方法，称为最大相关熵加权偏最小二乘法 (MCW-PLS)。由于 MCC 模型的可控鲁棒性，在校准过程中观测值会增加或减少，从而呈现具有样本软判别能力的稳健模型。这种加权代表了一个重要的优势，特别是对于样本不是从正态分布中抽取的情况。介绍了三个真实案例研究的应用。这些应用揭示了 MCW-PLS 的三个主要特征：SIMPLS 和鲁棒 SIMPLS（RSIPLS）之间的鲁棒性控制，双线性校准模型预测性能的改进，以及检测校准集中信息量最大的样本的可能性。特别是对于样本不是从正态分布中抽取的情况。介绍了三个真实案例研究的应用。这些应用揭示了 MCW-PLS 的三个主要特征：SIMPLS 和鲁棒 SIMPLS（RSIPLS）之间的鲁棒性控制，双线性校准模型预测性能的改进，以及检测校准集中信息量最大的样本的可能性。特别是对于样本不是从正态分布中抽取的情况。介绍了三个真实案例研究的应用。这些应用揭示了 MCW-PLS 的三个主要特征：SIMPLS 和鲁棒 SIMPLS（RSIPLS）之间的鲁棒性控制，双线性校准模型预测性能的改进，以及检测校准集中信息量最大的样本的可能性。