Cross validation time-consuming

Unfortunately, the ANN method is probably the most susceptible to overfitting of the methods discussed thus far. For similar N and M, ANNs reqnire many more parameters to be estimated in order to define the model. In addition, cross validation can be very time-consuming, as models with varying complexity (nnmber of hidden nodes) mnst be trained individually before testing. Also, the execntion of an ANN model is considerably more elaborate than a simple dot product, as it is for MLR, CLS, PCR and PLS (Eqnations 12.34, 12.37, 12.43 and 12.46). Finally, there is very little, or no, interpretive value in the parameters of an ANN model, which eliminates one nseful means for improving the confidence of a predictive model. 

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 ... 

With three-way methods such as Tucker3 and PARAFAC (see Section 3.3) cross-validation is less trivial compared to cross-validation in two-way models, since sub-sampling may be performed in more ways. Furthermore, cross-validation of three-way models may be rather time-consuming and may therefore not be the optimal method to choose. 

Validation without an independent test set. Each application of the adaptive wavelet algorithm has been applied to a training set and validated using an independent test set. If there are too few observations to allow for an independent testing and training data set, then cross validation could be used to assess the prediction performance of the statistical method. Should this be the situation, it is necessary to mention that it would be an extremely computational exercise to implement a full cross-validation routine for the AWA. That is. it would be too time consuming to leave out one observation, build the AWA model, predict the deleted observation, and then repeat this leave-one-out procedure separately. In the absence of an independent test set, a more realistic approach would be to perform cross-validation using the wavelet produced at termination of the AWA, but it is important to mention that this would not be a full validation. 

Moreover, the experimental measurements presented in Section 4 can faithfully capture the effect of the microorganisms size, shape, and polydisper-sity. However, the experimental setup can be cosdy and the experimental procedure is time consuming. Thus, it may be difficult to implement in actual production systems. In addition, measurements ate valid only for specific growth conditions and need to be repeated each time conditions change including pH, temperature, illumination, medium composition, etc. Thus, it would be beneficial to develop a simplified experimental method to determine the radiation characteristics and in particular the absorption cross-section which is the most influence on light transfer in PBRs (Kandilian, 2014). 

Unfortunately, cross-validation is a very time-consuming process. It requires recalculating the models for every sample left out. However, there are a few somewhat acceptable shortcuts. If the number of samples in the training set is large enough, the number of samples rotated out in each pass... 

In practice, the soft margin versions of the standard SVM (also known as C-SVM) described in the previous sections often suffer from the following problems. Firstly, there is a problem of how to determine the error penalty parameter C. Although the cross-validation technique can be used to determine this parameter, it is still hard to explain. Secondly, the time taken for a support vector classifier to compute the class of a new sample is proportional to the number of support vectors, so if that number is large, the computation is time-consuming. 

It is often necessary to include at least 50 samples in the calibration and prediction sets. Sometimes, measurement of the primary analytical data of so many samples is excessively time consuming. The number of samples can be approximately halved, at the cost of computation time, by using only one calibration set and calculating the root-mean-square error of cross validation (RMSECV), as described in Section 9.9. In general, however, it is preferable to use an independent prediction set to investigate the validity of the calibration but the leave-one-out method significantly reduces the number of samples for which primary analytical data are required. 

The ANN cross-validation results show that using more than one hidden neuron results in decreased predictive power. Because it is very time consuming, the LOO procedure was not tested with ANN. Therefore, as the best model for the neural network QSAR, we selected the one with a single hidden neuron and with tanh functions for both hidden and output neurons tcai = 0.934, RMSEcai = 0.38 fL5%o=0.906, 5% =0.820, RMSEl5%o = 0-44 and... 

Selecting an optimum group of descriptors is both an important and time-consuming phase in developing a predictive QSAR model. Frohlich, Wegner, and Zell introduced the incremental regularized risk minimization procedure for SVM classification and regression models, and they compared it with recursive feature elimination and with the mutual information procedure. Their first experiment considered 164 compounds that had been tested for their human intestinal absorption, whereas the second experiment modeled the aqueous solubility prediction for 1297 compounds. Structural descriptors were computed by those authors with JOELib and MOE, and full cross-validation was performed to compare the descriptor selection methods. The incremental... 

Lin, is a very efficient leave-one-out model selection for SVM two-class classification. Although LOO cross-validation is usually too time consuming to be performed for large datasets, looms implements numerical procedures that make LOO accessible. Given a range of parameters, looms automatically returns the parameter and model with the best LOO statistics. It is available as C source code and Windows binaries. 

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