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From MIM-Based GAN to Anomaly Detection:Event Probability Influence on Generative Adversarial Networks

Rui She, Pingyi Fan

TL;DR

This work introduces MIM-based GAN, a GAN variant that uses an exponential information metric to emphasize small-probability events during data generation. The authors derive theoretical properties including optimality when the real and generated distributions match, mode-collapse resistance, and enhanced gradient stability, alongside a small-probability-event analysis. They propose an unsupervised anomaly-detection method that leverages the MIM framework, enabling detection from entirely unlabeled data and showing how principal data components dominate the learning process. Experiments on ODDS IoT-related datasets demonstrate competitive data-generation quality and robust anomaly-detection performance, highlighting practical potential for IoT monitoring and security applications.

Abstract

In order to introduce deep learning technologies into anomaly detection, Generative Adversarial Networks (GANs) are considered as important roles in the algorithm design and realistic applications. In terms of GANs, event probability reflected in the objective function, has an impact on the event generation which plays a crucial part in GAN-based anomaly detection. The information metric, e.g. Kullback-Leibler divergence in the original GAN, makes the objective function have different sensitivity on different event probability, which provides an opportunity to refine GAN-based anomaly detection by influencing data generation. In this paper, we introduce the exponential information metric into the GAN, referred to as MIM-based GAN, whose superior characteristics on data generation are discussed in theory. Furthermore, we propose an anomaly detection method with MIM-based GAN, as well as explain its principle for the unsupervised learning case from the viewpoint of probability event generation. Since this method is promising to detect anomalies in Internet of Things (IoT), such as environmental, medical and biochemical outliers, we make use of several datasets from the online ODDS repository to evaluate its performance and compare it with other methods.

From MIM-Based GAN to Anomaly Detection:Event Probability Influence on Generative Adversarial Networks

TL;DR

This work introduces MIM-based GAN, a GAN variant that uses an exponential information metric to emphasize small-probability events during data generation. The authors derive theoretical properties including optimality when the real and generated distributions match, mode-collapse resistance, and enhanced gradient stability, alongside a small-probability-event analysis. They propose an unsupervised anomaly-detection method that leverages the MIM framework, enabling detection from entirely unlabeled data and showing how principal data components dominate the learning process. Experiments on ODDS IoT-related datasets demonstrate competitive data-generation quality and robust anomaly-detection performance, highlighting practical potential for IoT monitoring and security applications.

Abstract

In order to introduce deep learning technologies into anomaly detection, Generative Adversarial Networks (GANs) are considered as important roles in the algorithm design and realistic applications. In terms of GANs, event probability reflected in the objective function, has an impact on the event generation which plays a crucial part in GAN-based anomaly detection. The information metric, e.g. Kullback-Leibler divergence in the original GAN, makes the objective function have different sensitivity on different event probability, which provides an opportunity to refine GAN-based anomaly detection by influencing data generation. In this paper, we introduce the exponential information metric into the GAN, referred to as MIM-based GAN, whose superior characteristics on data generation are discussed in theory. Furthermore, we propose an anomaly detection method with MIM-based GAN, as well as explain its principle for the unsupervised learning case from the viewpoint of probability event generation. Since this method is promising to detect anomalies in Internet of Things (IoT), such as environmental, medical and biochemical outliers, we make use of several datasets from the online ODDS repository to evaluate its performance and compare it with other methods.
Paper Structure (35 sections, 8 theorems, 42 equations, 5 figures, 5 tables, 1 algorithm)

This paper contains 35 sections, 8 theorems, 42 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Related works
  4. Anomaly detection
  5. Models of GANs
  6. Contributions and organization
  7. Model of MIM-based GAN
  8. A general form of two-player game in GANs
  9. MIM-based GAN and its characteristics
  10. Optimality of $\mathbb{P}=\mathbb{P}_{g_{\theta}}$
  11. Resistance to mode collapse
  12. Interference on the gradient of generator
  13. Small probability event analysis
  14. Unsupervised anomaly detection with MIM-based GAN
  15. Principle analysis
  16. ...and 20 more sections

Key Result

Lemma 1

If the generator $g_{\bm \theta}$ is fixed, the optimal discriminator of MIM-based GAN is given by where $P(\cdot)$ and $P_{g_{\theta}}(\cdot)$ respectively denote the real probability density and the generative probability density for the corresponding distributions $\mathbb{P}$ and $\mathbb{P}_{g_{\theta}}$.

Figures (5)

  • Figure 1: The framework for the unsupervised anomaly detection with MIM-based GAN.
  • Figure 2: The diagram for MIM-based GAN anomaly detection in IoT applications.
  • Figure 3: Considering the unsupervised anomaly detection for the Cardio dataset, after randomly shuffling the data, $1,360$ samples (about $74.28 \%$ data) are used as training data and the rest are considered as the testing data. Especially, with respect to the GAN-based methods, we use the original GAN, WGAN, LSGAN and MIM-based GAN to produce the required generative data, which correspond to KL method, W method, LS method and MIM method, respectively, where the training iterations is $1000$. To show the performance on anomaly detection for each method, the ROC curve for the experiment with the median AUC as well as the boxplot of AUC for all the experiments are drawn as subfigures ($a$) and ($b$) respectively, where there are $20$ experiments.
  • Figure 4: As for the unsupvervised anomaly detection based on Thyroid dataset, $2800$ samples (about $74.23 \%$ data) are used as training data. Besides, the rest samples are regarded as the testing data. Especially, there are $1500$ training iterations for the GAN-based methods. To intuitively show the detection result for each method, the ROC curve for the experiment with the median AUC as well as the boxplot of AUC for all the experiments are drawn (as subfigures ($a$) and ($b$)), where $20$ experiments are taken.
  • Figure 5: In terms of the unsupervised anomaly detection for the Musk dataset, $2,200$ samples (about $71.85 \%$ data) are used as training data, while the rest samples are used as testing data. Moreover, the number of training iterations for the GAN-based methods is $50$. In order to intuitively show the different detection results, with respect to each method, the ROC curve for the experiment with the median AUC is shown as subfigure ($a$), as well as, the boxplot of AUC for all the experiments is drawn as subfigure ($b$), where the performance is evaluated on $20$ experiments.

Theorems & Definitions (17)

  • Definition 1: MIM-based GAN
  • Lemma 1: Optimal discriminator
  • proof
  • Proposition 1: Optimal solution of objective function
  • proof
  • Proposition 2: Mode collapse resistance
  • proof
  • Proposition 3: Generator gradient interfered by the discriminator
  • proof
  • Corollary 1
  • ...and 7 more