Applications of Bayesian Neural Networks in Outlier Detection.

Anomaly detection is crucial in a variety of domains, such as fraud detection, disease diagnosis, and equipment defect detection. With the development of deep learning, anomaly detection with Bayesian neural networks (BNNs) becomes a novel research topic in recent years. This article aims to propose a widely applicable method of outlier detection (a category of anomaly detection) using BNNs based on uncertainty measurement. There are three kinds of uncertainties generated in the prediction of BNNs: epistemic uncertainty, aleatoric uncertainty, and (model) misspecification uncertainty. Although the approaches in previous studies are adopted to measure epistemic and aleatoric uncertainty, a new method of utilizing loss functions to quantify misspecification uncertainty is proposed in this article. Then, these three uncertainty sources are merged together by specific combination models to construct total prediction uncertainty. In this study, the key idea is that the observations with high total prediction uncertainty should correspond to outliers in the data. The method of this research is applied to the experiments on Modified National Institute of Standards and Technology (MNIST) dataset and Taxi dataset, respectively. From the results, if the network is appropriately constructed and well-trained and model parameters are carefully tuned, most anomalous images in MNIST dataset and all the abnormal traffic periods in Taxi dataset can be nicely detected. In addition, the performance of this method is compared with the BNN anomaly detection methods proposed before and the classical Local Outlier Factor and Density-Based Spatial Clustering of Applications with Noise methods. This study links the classification of uncertainties in essence with anomaly detection and takes the lead to consider combining different uncertainty sources to reform detection outcomes instead of using only single uncertainty each time.