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 model adopts the use of Tukey depth, Mahalanobis depth, Projection Depth, and Spatial depth in order to assess the degree of outlierness of observations across different data distributions. AUC, Precision, and Recall scores of 0.94, 0.89, and 0.87, respectively, were achieved, demonstrating superior performance over baseline methods on both synthetic and real-world datasets. Furthermore, the integration of depth-based explanations provides local and global interpretability mechanisms, enabling practitioners to understand the rationale behind outlier classifications. This work bridges the gap between classical statistical robustness and modern deep learning representational power, offering a theoretically grounded yet practically applicable solution for explainable anomaly detection in high-dimensional spaces.