Kalivas John H, Héberger Károly, Andries Erik
Department of Chemistry, Idaho State University, Pocatello, ID 83209, USA.
Research Centre for Natural Sciences, Hungarian Academy of Sciences, Pusztaszeri út 59-67, 1025 Budapest, Hungary.
Anal Chim Acta. 2015 Apr 15;869:21-33. doi: 10.1016/j.aca.2014.12.056. Epub 2015 Feb 7.
Most multivariate calibration methods require selection of tuning parameters, such as partial least squares (PLS) or the Tikhonov regularization variant ridge regression (RR). Tuning parameter values determine the direction and magnitude of respective model vectors thereby setting the resultant predication abilities of the model vectors. Simultaneously, tuning parameter values establish the corresponding bias/variance and the underlying selectivity/sensitivity tradeoffs. Selection of the final tuning parameter is often accomplished through some form of cross-validation and the resultant root mean square error of cross-validation (RMSECV) values are evaluated. However, selection of a "good" tuning parameter with this one model evaluation merit is almost impossible. Including additional model merits assists tuning parameter selection to provide better balanced models as well as allowing for a reasonable comparison between calibration methods. Using multiple merits requires decisions to be made on how to combine and weight the merits into an information criterion. An abundance of options are possible. Presented in this paper is the sum of ranking differences (SRD) to ensemble a collection of model evaluation merits varying across tuning parameters. It is shown that the SRD consensus ranking of model tuning parameters allows automatic selection of the final model, or a collection of models if so desired. Essentially, the user's preference for the degree of balance between bias and variance ultimately decides the merits used in SRD and hence, the tuning parameter values ranked lowest by SRD for automatic selection. The SRD process is also shown to allow simultaneous comparison of different calibration methods for a particular data set in conjunction with tuning parameter selection. Because SRD evaluates consistency across multiple merits, decisions on how to combine and weight merits are avoided. To demonstrate the utility of SRD, a near infrared spectral data set and a quantitative structure activity relationship (QSAR) data set are evaluated using PLS and RR.
大多数多元校准方法都需要选择调优参数，例如偏最小二乘法（PLS）或蒂霍诺夫正则化变体岭回归（RR）。调优参数值决定了各个模型向量的方向和大小，从而设定了模型向量的预测能力。同时，调优参数值还确定了相应的偏差/方差以及潜在的选择性/灵敏度权衡。最终调优参数的选择通常通过某种形式的交叉验证来完成，并对所得的交叉验证均方根误差（RMSECV）值进行评估。然而，仅依据这一个模型评估指标来选择“好的”调优参数几乎是不可能的。纳入额外的模型优点有助于调优参数的选择，以提供更好平衡的模型，同时也能对校准方法进行合理比较。使用多个优点需要就如何将这些优点组合并加权成一个信息准则做出决策。有大量的选择可能。本文提出的是排名差异总和（SRD），用于整合一系列随调优参数变化的模型评估优点。结果表明，模型调优参数的SRD共识排名允许自动选择最终模型，或者根据需要选择一组模型。从本质上讲，用户对偏差和方差之间平衡程度的偏好最终决定了用于SRD的优点，进而决定了SRD排名最低以供自动选择的调优参数值。还表明SRD过程允许在调优参数选择的同时，对特定数据集的不同校准方法进行同步比较。由于SRD评估多个优点之间的一致性，因此避免了关于如何组合和加权优点的决策。为了证明SRD的实用性，使用PLS和RR对一个近红外光谱数据集和一个定量构效关系（QSAR）数据集进行了评估。
