Deep Structured Energy Based Models for Anomaly Detection (1605.07717v2)

Abstract: In this paper, we attack the anomaly detection problem by directly modeling the data distribution with deep architectures. We propose deep structured energy based models (DSEBMs), where the energy function is the output of a deterministic deep neural network with structure. We develop novel model architectures to integrate EBMs with different types of data such as static data, sequential data, and spatial data, and apply appropriate model architectures to adapt to the data structure. Our training algorithm is built upon the recent development of score matching \cite{sm}, which connects an EBM with a regularized autoencoder, eliminating the need for complicated sampling method. Statistically sound decision criterion can be derived for anomaly detection purpose from the perspective of the energy landscape of the data distribution. We investigate two decision criteria for performing anomaly detection: the energy score and the reconstruction error. Extensive empirical studies on benchmark tasks demonstrate that our proposed model consistently matches or outperforms all the competing methods.

• The paper introduces DSEBMs that integrate energy-based models with deep neural networks by parameterizing the energy function as a negative log probability estimator.
• The approach employs score matching for training, simplifying the process with stochastic gradient descent without relying on complex sampling methods.
• DSEBMs robustly detect anomalies using energy score and reconstruction error criteria, outperforming traditional methods on high-dimensional benchmarks.

Deep Structured Energy Based Models for Anomaly Detection

The paper "Deep Structured Energy Based Models for Anomaly Detection" investigates the application of energy-based models (EBMs) within deep learning frameworks to facilitate anomaly detection. The proposed Deep Structured Energy Based Models (DSEBMs) leverage the structural advantages of deep networks to improve their effectiveness in identifying anomalies across different types of data. The authors specifically paper the capacity of DSEBMs to handle static, sequential, and spatial data by employing various neural network architectures—fully connected networks for static data, recurrent neural networks (RNNs) for sequential data, and convolutional neural networks (CNNs) for spatial data.

Core Methodology

1. Model Architecture: The authors integrate EBMs with deep neural network architectures by parameterizing the energy function using these networks. The energy function, represented as a deterministic neural network, performs as a negative log probability estimator. This incorporation allows the DSEBMs to model complex data patterns effectively, making them suitable for high-dimensional anomaly detection tasks.
2. Training via Score Matching: Rather than relying on traditional maximum likelihood estimation (MLE), which often involves complex sampling techniques, the authors utilize score matching. This method connects EBMs with regularized autoencoders and simplifies the training of DSEBMs using straightforward stochastic gradient descent (SGD).
3. Anomaly Detection Criteria: The paper introduces two statistically derived decision criteria based on the energy landscape for detecting anomalies: the energy score and the reconstruction error.

• Energy Score: Anomalies are identified as data points assigned a higher energy relative to a threshold, signifying low probability under the model.
• Reconstruction Error: Relating to autoencoder-like models, this defines anomalies as those data points that produce significant discrepancies when reconstructed by the model.

Empirical Evaluation

The authors conducted extensive empirical evaluations on benchmark datasets, covering static, sequential, and image data. DSEBMs consistently performed on par with or better than established methods, such as PCA, Kernel PCA, and One-Class SVMs, demonstrating robustness across different domains and data types. Notably, DSEBMs showed outstanding performance on high-dimensional datasets, underlining the enhanced capability of deep models.

Implications and Future Directions

The scalability of DSEBMs and their applicability to varied data structures suggest practical utility in diverse fields, from cybersecurity (e.g., intrusion detection) to healthcare (e.g., anomaly detection in medical imaging). The integration of score matching also highlights potential advancements in the training efficiency of deep probabilistic models. Future research may explore optimizing model architectures further or extending this framework to handle hybrid data types encountered in real-world applications.

The theoretical implications extend to the broader understanding of model expressiveness in deep learning. The capacity of DSEBMs to generalize across data structures underscores the potential of deep models in capturing intricate data distributions, opening avenues for enhanced representation learning and probabilistic modeling in machine learning.