Avoided crossing robustness

The R-RMSECV values are rather time consuming because, for every choice of k, they require the whole RPCR procedure to be performed n times. Faster algorithms for cross validation are described [80], They avoid the complete recomputation of resampling methods, such as the MCD, when one observation is removed from the data set. Alternatively, one could also compute a robust R2-value [61], For q= 1 it equals ... 

By coupling the Chromarod separation technique described in Section 11.4 with the reliable and robust NDIR (nondispersive infrared) technique for detecting the CO2 formed in the combustion, completely new ways of analyzing hydrocarbons are opened up. This principle of detection has the advantage that it is specific for CO2, i.e. cross-sensitivities are largely avoided. 

Cross-validation estimates model robustness and predictivity to avoid overfitting in QSAR [27]. In 3D-QSAR models, PLS and NN model complexity are established by testing the significance of adding a new dimension to the current QSAR, i.e., a PLS component or a hidden neuron, respectively. The optimal number of PLS components or hidden neurons is usually chosen from the analysis with the highest q2 (cross-validated r2) value, Eq. (3). The most popular cross-validation technique is leave-one-out (LOO), where each compound is left out of the model once and only once, yielding reproducible results. An extremely fast LOO method, SAMPLS [42], which evaluates the covariance matrix only, allows the end user to rapidly estimate the robustness of 3D-QSAR models. Randomly repeated cross-validation rounds using leave 20% out (L5G), or leave 50% out (L2G), are routinely used to check internal... 

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