Prediction sets

After selection of descriptors/NN training, the best networks were applied to the prediction of 259 chemical shifts from 31 molecules (prediction set), which were not used for training. The mean absolute error obtained for the whole prediction set was 0.25 ppm, and for 90% of the cases the mean absolute error was 0.19 ppm. Some stereochemical effects could be correctly predicted. In terms of speed, the neural network method is very fast - the whole process to predict the NMR shifts of 30 protons in a molecule with 56 atoms, starting from an MDL Molfile, took less than 2 s on a common workstation. 

More recently (2006) we performed and reported quantitative structure-activity relationship (QSAR) modeling of the same compounds based on their atomic linear indices, for finding fimctions that discriminate between the tyrosinase inhibitor compounds and inactive ones [50]. Discriminant models have been applied and globally good classifications of 93.51 and 92.46% were observed for nonstochastic and stochastic hnear indices best models, respectively, in the training set. The external prediction sets had accuracies of 91.67 and 89.44% [50]. In addition to this, these fitted models have also been employed in the screening of new cycloartane compounds isolated from herbal plants. Good behavior was observed between the theoretical and experimental results. These results provide a tool that can be used in the identification of new tyrosinase inhibitor compounds [50]. 

The success rate of every prediction set was greater than the value of 50% expected by chance. Specifically, the various sets of predictions differed from the 50% value by about 3 standard deviations (for the lowest success rate, which was for the merged data) to about 12 standard deviations (for the highest success rates, which were for the medium and long regions of disorder). Overall, these data provided very strong support for our hypothesis that disorder is encoded by the amino acid sequence (Romero et al., 1997b). 

If data from many objects are available, a split into three sets is best into a Training set (ca. 50% of the objects) for creating models, a Validation set (ca. 25% of the objects) for optimizing the model to obtain good prediction performance, and a Test set (prediction set, approximately 25%) for testing the final model to obtain a realistic estimation of the prediction performance for new cases. The three sets are treated separately. Applications in chemistry rarely allow this strategy because of a too small number of objects available. 

The data set is split into a calibration set used for model creation and optimization and a test set (prediction set) to obtain a realistic estimation... 

As you study the thought processes of great men and women, you will realize they have a predictable set of beliefs and values that run their lives. Likewise, miserable angry criminals who create pain and torment in the world have a very different set of values, beliefs and purpose. In the coming section, you will have an opportunity to elicit the beliefs and values that you currently hold. Then, you will be given the opportunity to decide if these are beliefs that will take you where you really want to go. 

In the second approach we used the information contained in the whole dataset of 49 molecules to build a training set using a classical random method. Every third compound was withdrawn from the list of compounds sorted by increasing activity, thus creating a prediction set of 16 molecules (Prediction Set PS 3.2) and a training set of 33 molecules (Training Set TS 3.2). The PLS-OSC model computed with this reduced training set retained its efficiency of prediction (Table 5 ... 

The musk database was divided into a training set of 312 compounds and a prediction set of 19 compounds (see Table 2). Compounds in the prediction set were randomly chosen. Discriminating relationships uncovered in the training set could be validated using the compounds from the prediction set. 

A prediction set of 19 compounds (see Table 2) was used to assess the predictive ability of the 15 molecular descriptors identified by the pattern recognition GA. We chose to map the 19 compounds directly onto the principal component plot defined by the 312 compounds and 15 descriptors. Figure 5 shows the prediction set samples projected onto the principal component map. Each projected compound lies in a region of the map with compounds that bare the same class label. Evidently, the pattern-recognition GA can identify molecular descriptors that are correlated to musk odor quality. 

Fig. 5. A plot of the two largest principal components of the training set developed from the 312 compounds and 15 molecular descriptors identified by the pattern-recognition GA. The plane defined by the two largest principal components accounts for 35% of the total cumulative variance. Circles are the musks inverted triangles are the nonmusks M = musks from the prediction set projected onto the principal component plot N = nonmusks from the prediction set projected onto the principal component plot.

The third reason to add a third tier to the diagnostic process is that it provides insight in the fundamental abilities of the patients. The fourth reason is the most important. From its inception as a scientific discipline, the nosological model has been, and still is, taken for granted in psychiatry. Psychiatric disorders are viewed as discrete entities, with a fixed and predictable set of attributes and distinguishable from adjacent disorders. Within the framework of this model, biological psychiatry searches for markers and, eventually, causes of true disease entities. 

Two methods are used to evaluate the predictive ability for LDA and for all other classification techniques. One method consists of dividing the objects of the whole data set into two subsets, the training and the prediction or evaluation set. The objects of the training set are used to obtain the covariance matrix and the discriminant scores. Then, the objects of the training set are classified, so obtaining the apparent error rate and the classification ability, and the objects of the evaluation set are classified to obtain the actual error rate and the predictive ability. The subdivision into the training and prediction sets can be randomly repeated many times, and with different percentages of the objects in the two sets, to obtain a better estimate of the predictive ability. 

A similar method, stepwise bayesian analysis, selects the variables giving the minimum number of classification plus prediction errors. When the error rate does not show further decrease, the procedure stops. The whole process is repeated with random subdivisions between the training and prediction sets. Only the variables that are selected independently of the subdivision are retained. This method has been used with the data set of Fig. 4 only 5 variables were selected and a very high prediction ability was obtained. 

Different spectral preprocessing and transformations available in SIMCA P-p (version 10.0, Umetrics, Sweden) were evaluated and the best approach for data handling and manipulation was determined. Data collected on the surrogate tablets were divided into a training set to generate the PLS models, and prediction set to test the PLS models. MCC powder, equilibrated at different RH, was also roller compacted at different roll speeds on a Fitzpatrick IR220 roller compactor fitted with smooth rolls. Powder feed rate and roll pressure were kept constant for all experiments. The key sample attributes measured on the surrogate tablets were also measured for the samples prepared by roller compaction. 

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