Sparse Bayesian Mixture of Experts and Its Application to Spectral Multivariate Calibration
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摘要: 在光谱数据的多元校正中, 光谱数据通常是在多种不同的环境条件下收集的. 为了建模来源于不同环境中的高维光谱数据, 本文提出了一种新的稀疏贝叶斯混合专家模型, 并将其用来选择多元校正模型的稀疏特征. 混合专家模型能够把训练数据划分到不同的子类, 之后使用不同的预测模型来分别对划分后的数据进行预测, 因此这种方法适合于建模来自于多种环境下的光谱数据. 本文提出的稀疏的混合专家模型利用稀疏贝叶斯的方法来进行特征选择, 不依赖于事先指定的参数; 同时利用probit模型作为门函数以得到解析的后验分布, 避免了在门函数分类模型中进行特征提取时需要的近似. 本文提出的模型与其他几种常用的回归模型在人工数据集和几个公开的光谱数据集上进行了比较, 比较结果显示本文提出的模型对多个来源的光谱数据进行浓度预测时精度比传统的回归方法有一定的提高.Abstract: In spectral multivariate calibration, high dimensional spectral data are often measured on different conditions. To predict the property value of a spectrum without knowing its source, a new sparse Bayesian mixture experts (ME) model is proposed and applied to the multivariate calibration model for selecting the sparse features. The technique of mixture of experts can divide the training data into some different classes and estimate the different predictive functions for each class. Therefore, ME is suitable for prediction of multiple-source spectral data. To analyze high dimensional spectral data, the new ME model employs the sparse Bayesian method to select certain features without tuning parameters. Moreover, the multinomial probit model is used as the gate function to obtain the analytic posterior distribution in this model. This new method is compared with some classical multivariate calibration methods on artificial and some real-world datasets. Experimental results show the advantage of proposed model for high dimensional spectral data.
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Key words:
- Multivariate calibration /
- mixture of experts /
- feature selection /
- variational inference
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图 5 根据玉米数据集的全部样本训练的三个专家的SME 模型的专家模型回归系数的均值
Fig. 5 The means of the coe±cients of the three expert models of SME trained with the corn data set
表 1 在人工数据集上的预测结果
Table 1 The prediction results in the arti-cial data set
Method RMSECV PLS 5.1617 ± 0.7679 SVR 4.9164 ± 0.5646 LASSO 5.2411 ± 0.4112 Ridge 5.0103 ± 0.5044 ME 10.236 ± 1.5720 SME 1.5130 ± 0.3117 
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表 2 玉米光谱数据集的预测结果
Table 2 The prediction results in corn data set
Method RMSECV PLS 0.1480±0.0093 SVR 0.1504±0.0084 LASSO 0.1510±0.0114 Ridge 0.1511±0.0083 Bagging-ridge 0.1239±0.0113 SME 0.1124±0.0034 Multi-task 0.1145±0.0094
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表 3 温度数据集的预测结果
Table 3 The prediction results in temperature data set
Method RMSECV PLS 0.0148±0.0026 SVR 0.0180±0.0019 LASSO 0.0208±0.0031 Ridge 0.0345±0.0013 Bagging-ridge 0.0143±0.0018 SME 0.0106±0.0008 Multi-task 0.0225±0.0032
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表 4 药片光谱数据集的预测结果
Table 4 The prediction results in pharmaceutical data set
Method RMSECV PLS 0.0148±0.0026 SVR 0.0180±0.0019 LASSO 0.0208±0.0031 Ridge 0.0345±0.0013 Bagging-ridge 0.0143±0.0018 SME 0.0106±0.0008 Multi-task 0.0225±0.0032
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