Overfitting

At present, the data base used for the fit was not specially selected to avoid homologous proteins. Thus, a further improvement can be expected from using data for one of the specially prepared lists of PDB files (cf. Hobohm et al. [9]). We also expect further improvements from replacing the polynomial fits in the potential estimation procedure by piecewise cubic fits though at the moment it is not clear how to select the number of nodes needed to get a good but not overfitting approximation to the density. Finally, we are considering... 

Another method of detection of overfitting/overtraining is cross-validation. Here, test sets are compiled at run-time, i.e., some predefined number, n, of the compounds is removed, the rest are used to build a model, and the objects that have been removed serve as a test set. Usually, the procedure is repeated several times. The number of iterations, m, is also predefined. The most popular values set for n and m are, respectively, 1 and N, where N is the number of the objects in the primary dataset. This is called one-leave-out cross-validation. 

Evaluating the model in tenns of how well the model fits the data, including the use of posterior predictive simulations to determine whether data predicted from the posterior distribution resemble the data that generated them and look physically reasonable. Overfitting the data will produce unrealistic posterior predictive distributions. 

In all modeling techniques, and neural networks in particular, care must be taken not to overtrain or overfit the model. 

Equations (24) and (25) are adequate for designing decision trees. The feature that minimizes the information content is selected as a node. This procedure is repeated for every leaf node until adequate classification is obtained. Techniques for preventing overfitting of training data, such as cross validation are then applied. 

We chose the number of PCs in the PCR calibration model rather casually. It is, however, one of the most consequential decisions to be made during modelling. One should take great care not to overfit, i.e. using too many PCs. When all PCs are used one can fit exactly all measured X-contents in the calibration set. Perfect as it may look, it is disastrous for future prediction. All random errors in the calibration set and all interfering phenomena have been described exactly for the calibration set and have become part of the predictive model. However, all one needs is a description of the systematic variation in the calibration data, not the... 

Leaving out one object at a time represents only a small perturbation to the data when the number (n) of observations is not too low. The popular LOO procedure has a tendency to lead to overfitting, giving models that have too many factors and a RMSPE that is optimistically biased. Another approach is k-fold cross-validation where one applies k calibration steps (5 < k < 15), each time setting a different subset of (approximately) n/k samples aside. For example, with a total of 58 samples one may form 8 subsets (2 subsets of 8 samples and 6 of 7), each subset tested with a model derived from the remaining 49 or 50 samples. In principle, one may repeat this / -fold cross-validation a number of times using a different splitting [20]. 

In practice, the choice of parameters to be refined in the structural models requires a delicate balance between the risk of overfitting and the imposition of unnecessary bias from a rigidly constrained model. When the amount of experimental data is limited, and the model too flexible, high correlations between parameters arise during the least-squares fit, as is often the case with monopole populations and atomic displacement parameters [6], or with exponents for the various radial deformation functions [7]. 

Zhang et al.14 develop a neural network approach to bacterial classification using MALDI MS. The developed neural network is used to classify bacteria and to classify culturing time for each bacterium. To avoid the problem of overfitting a neural network to the large number of channels present in a raw MALDI spectrum, the authors first normalize and then reduce the dimensionality of the spectra by performing a wavelet transformation. 

Overfitting arises when the network learns for too long. For most students, the longer they are trained the more they learn, but artificial neural networks are different. Since networks grow neither bored nor tired, it is a little odd that their performance can begin to degrade if training is excessive. To understand this apparent paradox, we need to consider how a neural network learns. 

Overfitting is a potentially serious problem in neural networks. It is tackled in two ways (1) by continually monitoring the quality of training as it occurs using a test set, and (2) by ensuring that the geometry of the network (its size and the way the nodes are connected) is appropriate for the size of the dataset. 

This method for preventing overfitting requires that there are enough samples so that both training and test sets are representative of the dataset. In fact, it is desirable to have a third set known as a validation set, which acts as a secondary test of the quality of the network. The reason is that, although the test set is not used to train the network, it is nevertheless used to determine at what point training is stopped, so to this extent the form of the trained network is not completely independent of the test set. 

A quite different way to reduce overfitting is to use random noise. A random signal is added to each data point as it is presented to the network, so that a data pattern ... 

The number of latent variables (PLS components) must be determined by some sort of validation technique, e.g., cross-validation [42], The PLS solution will coincide with the corresponding MLR solution when the number of latent variables becomes equal to the number of descriptors used in the analysis. The validation technique, at the same time, also serves the purpose to avoid overfitting of the model. 

With PCR and PLS we introduced the extra parameter of the number of factors one extra parameter. With wavelets we introduce the order and the locality of each wavelet two extra parameters. With neural nets, we have the number of nodes in each layer n extra parameters, and then there is even a metaparameter the number of layers. No wonder reports of overfitting abound (and don t forget those are only the ones that are recognized) And nary a diagnostic in sight. 

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