Predictive modeling on data streams plays an important role in modern data analysis, where data arrives continuously and needs to be mined in real time. In the stream setting the data distribution is often evolving over time, and models that update themselves during operation are becoming the state-of-the-art. This paper formalizes a learning and evaluation scheme of such predictive models. We theoretically analyze evaluation of classifiers on streaming data with temporal dependence. Our findings suggest that the commonly accepted data stream classification measures, such as classification accuracy and Kappa statistic, fail to diagnose cases of poor performance when temporal dependence is present, therefore they should not be used as sole performance indicators. Moreover, classification accuracy can be misleading if used as a proxy for evaluating change detectors with datasets that have temporal dependence. We formulate the decision theory for streaming data classification with temporal dependence and develop a new evaluation methodology for data stream classification that takes temporal dependence into account. We propose a combined measure for classification performance, that takes into account temporal dependence, and we recommend using it as the main performance measure in classification of streaming data.
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