Formal Analysis and Estimation of Chance in Datasets Based on Their Properties

Machine learning research, particularly in genomics, is often based on wide shaped datasets, i.e. datasets having a large number of features, but a small number of samples. Such configurations raise the possibility of chance influence (the increase of measured accuracy due to chance correlations) on the learning process and the evaluation results. Prior research underlined the problem of generalization of models obtained based on such data. In this paper, we investigate the influence of chance on prediction and show its significant effects on wide shaped datasets. First, we empirically demonstrate how significant the influence of chance in such datasets is by showing that prediction models trained on thousands of randomly generated datasets can achieve high accuracy. This is the case even when using cross-validation. We then provide a formal analysis of chance influence and design formal chance influence estimators based on the dataset parameters, namely its sample size, the number of features, the number of classes and the class distribution. Finally, we provide an in-depth discussion of the formal analysis including applications of the findings and recommendations on chance influence mitigation.