Tailored Bayes: a risk modelling framework under unequal classification costs
Risk prediction models are widely used. Some areas include medical diagnosis and prognosis, fraud detection, financial crisis prediction, spam email filtering, text/image categorization, object detection from satellite images, classification of protein databases, among others. Risk prediction models are prevalently based on binary outcomes, constructed to minimise the expected classification error; that is the proportion of incorrect classifications. The disadvantage of this approach is to implicitly assume that all errors cost equally. However, equality is but one choice, and an arbitrary one, which we suspect is in fact rarely appropriate. For example, in cancer diagnosis, a false negative (that is, misdiagnosing a cancer patient as healthy) may have more severe consequences than a false positive (that is, misdiagnosing a healthy patient with cancer); the latter may lead to extra medical costs and unnecessary patient anxiety but will not result in loss of life. For these applications, a prioritised control of asymmetric classification errors is desirable. In this work, we present Tailored Bayes (TB), a novel Bayesian inference framework which “tailors” model fitting to optimise predictive performance with respect to unbalanced misclassification costs. We demonstrate using synthetic and real-world data that under certain scenarios TB outperforms standard off-the-shelf statistical/machine learning models.
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