A diversified and heterogeneous ensemble learning framework with predictive uncertainty calibration for explainable anomaly analysis

Abstract Ensemble methods have been the norm for anomaly detection. However, existing ensemble methods for anomaly detection have three main issues: (1) Lack of diversity, the base classifiers are of the same algorithm with different initializations, for example, decision trees or neural networks, achieving only sub-optimal results. (2) The predictive uncertainty is not well calibrated for reliable and explainable anomaly detection, where overconfident predictions for both correct and erroneous classifications are made, making the results unreliable and hard to explain. (3) Traditional ensemble methods (e.g., bagging) cannot effectively capture the distinct distributions of predictions from diverse base models. In this paper, we propose a D iversified and H eterogeneous E nsemble learning framework with C alibrated predictive U ncertainty estimation (DHE-CU). We utilize a multi-layer perceptron (MLP) as the meta-classifier to combine the confidence of diverse base models, thereby achieving more explainable anomaly detection. We devise a global diversity loss that considers a global measure of diversity for the selection and pruning of the base models. The MLP meta-classifier can capture the diverse and distinct distributions of predictions from base classifiers. We use a simple yet effective method to quantify the predictive uncertainty of the meta-classifier. We propose a weighted accuracy-uncertainty calibration loss for class-imbalanced data to effectively calibrate predictive uncertainties. Various datasets are used to perform experimental evaluation extensively. The proposed DHE-CU framework demonstrates strong ensemble learning ability, achieving an average improvement of 8.8% in classification accuracy across 27 UCR time series datasets and other anomaly detection benchmark datasets.