Integrating Statistical Depth Functions with Deep Learning for Explainable Multivariate Outlier Detection

Abstract

The process of identifying outliers in multiple variables stays as a major obstacle for data-driven modeling because researchers must handle expanding data dimensions and growing data complexities. The paper presents a new framework called Statistical Outlier Detection with Depth (SODD) which combines Statistical Depth Functions (SDFs) with Deep Learning systems to create an explainable multivariate outlier detection system that shows strong performance. The statistical depth functions establish a formal system which determines how far multivariate data points exist from their center point while maintaining their resistance to extreme values and their ability to show geometric characteristics. The proposed scheme utilizes a combination of four major approaches where depth scores are incorporated within deep neural networks to generate depth-enhanced feature extraction processes, depth-modulated losses, depth-guided regularizations, and depth-dependent architectures that generate better detection results along with higher levels of interpretability in models. The SODD framework utilizes the application of Tukey depth, Mahalanobis depth, Projection Depth, and Spatial depth in order to measure the extent to which an observation is an outlier under different data distributions. Experiments have been carried out on synthetic data as well as some standard real-world datasets, and the framework was implemented through a Python development environment. The results obtained are quite promising, with scores for AUC, Precision, and Recall of 0.94, 0.89, and 0.87, respectively, making the model perform comparably well relative to the baselines examined. Moreover, the inclusion of depth-based explanations enhances the interpretability aspect of the model.