Estimation of random accuracy and its use in validation of predictive quality of classification models within predictive challenges

Shortcomings of the correlation coefficient (Pearson's) as a measure for estimating and calculating the accuracy of predictive model properties are analysed. Here we discuss two such cases that can often occur in the application of the model in predicting properties of a new external set of compounds. The first problem in using the correlation coefficient is its insensitivity to the systemic error that must be expected in predicting properties of a novel external set of compounds, which is not a random sample selected from the training set. The second problem is that an external set can be arbitrarily large or small and have an arbitrary and uneven distribution of the measured value of the target variable, whose values are not known in advance. In these conditions, the correlation coefficient can be an overoptimistic measure of agreement of predicted values with the corresponding experimental values and can lead to a highly optimistic conclusion about the predictive ability of the model. Due to these shortcomings of the correlation coefficient, the use of standard error (root-mean-square-error) of prediction is suggested as a better quality measure of predictive capabilities of a model. In the case of classification models, the use of the difference between the real accuracy and the most probable random accuracy of the model shows very good characteristics in ranking different models according to predictive quality, having at the same time an obvious interpretation.