Statistics and Its Interface

Volume 17 (2024)

Number 1

Special issue in honor of Professor Lincheng Zhao

Abnormal sample detection based on robust Mahalanobis distance estimation in adversarial machine learning

Pages: 91 – 106



Wan Tian (Capital Normal University, Beijing, China)

Lingyue Zhang (Capital Normal University, Beijing, China)

Hengjian Cui (Capital Normal University, Beijing, China)


This paper addresses the problem of abnormal sample detection in deep learning-based computer vision, focusing on two types of abnormal samples: outlier samples and adversarial samples. The presence of these abnormal samples can significantly degrade the performance and robustness of deep learning models, posing security risks in critical areas. To address this, we propose a method that combines robust Mahalanobis distance (RMD) estimation with a pretrained convolutional neural networks (CNNs) model. The RMD estimation involves using minimum covariance matrix determinant (MCD), $T$-type, and $S$ estimators. Furthermore, we theoretically analyze the breakdown point and influence function of the $T$-type estimator. To evaluate the effectiveness and robustness of our method, we utilize public datasets, CNN models, and adversarial sample generation algorithms commonly employed in the field. The experimental results demonstrate the effectiveness of our algorithm in detecting abnormal samples.


abnormal sample detection, MCD estimator, $T$-type estimator, breakdown point, influence function

2010 Mathematics Subject Classification

Primary 62G35, 62H30. Secondary 62H35.

Received 3 November 2022

Accepted 24 August 2023

Published 27 November 2023