Unifying Explainable Anomaly Detection and Root Cause Analysis in Dynamical Systems

Dynamical systems, prevalent in various scientific and engineering domains, are susceptible to anomalies that can significantly impact their performance and reliability. This paper addresses the critical challenges of anomaly detection, root cause localization, and anomaly type classification in dynamical systems governed by ordinary differential equations (ODEs). We define two categories of anomalies: cyber anomalies, which propagate through interconnected variables, and measurement anomalies, which remain localized to individual variables. To address these challenges, we propose the Interpretable Causality Ordinary Differential Equation (ICODE) Networks, a model-intrinsic explainable learning framework. ICODE leverages Neural ODEs for anomaly detection while employing causality inference through an explanation channel to perform root cause analysis (RCA), elucidating why specific time periods are flagged as anomalous. ICODE is designed to simultaneously perform anomaly detection, RCA, and anomaly type classification within a single, interpretable framework. Our approach is grounded in the hypothesis that anomalies alter the underlying ODEs of the system, manifesting as changes in causal relationships between variables. We provide a theoretical analysis of how perturbations in learned model parameters can be utilized to identify anomalies and their root causes in time series data. Comprehensive experimental evaluations demonstrate the efficacy of ICODE across various dynamical systems, showcasing its ability to accurately detect anomalies, classify their types, and pinpoint their origins.

Incorporating Domain Differential Equations into Graph Convolutional Networks to Lower Generalization Discrepancy

Ensuring both accuracy and robustness in time series prediction is critical to many applications, ranging from urban planning to pandemic management. With sufficient training data where all spatiotemporal patterns are well-represented, existing deep-learning models can make reasonably accurate predictions. However, existing methods fail when the training data are drawn from different circumstances (e.g., traffic patterns on regular days) compared to test data (e.g., traffic patterns after a natural disaster). Such challenges are usually classified under domain generalization. In this work, we show that one way to address this challenge in the context of spatiotemporal prediction is by incorporating domain differential equations into Graph Convolutional Networks (GCNs). We theoretically derive conditions where GCNs incorporating such domain differential equations are robust to mismatched training and testing data compared to baseline domain agnostic models. To support our theory, we propose two domain-differential-equation-informed networks called Reaction-Diffusion Graph Convolutional Network (RDGCN), which incorporates differential equations for traffic speed evolution, and Susceptible-Infectious-Recovered Graph Convolutional Network (SIRGCN), which incorporates a disease propagation model. Both RDGCN and SIRGCN are based on reliable and interpretable domain differential equations that allow the models to generalize to unseen patterns. We experimentally show that RDGCN and SIRGCN are more robust with mismatched testing data than the state-of-the-art deep learning methods.

Robust Conformal Prediction under Distribution Shift via Physics-Informed Structural Causal Model

Uncertainty is critical to reliable decision-making with machine learning. Conformal prediction (CP) handles uncertainty by predicting a set on a test input, hoping the set to cover the true label with at least $(1-\alpha)$ confidence. This coverage can be guaranteed on test data even if the marginal distributions $P_X$ differ between calibration and test datasets. However, as it is common in practice, when the conditional distribution $P_{Y|X}$ is different on calibration and test data, the coverage is not guaranteed and it is essential to measure and minimize the coverage loss under distributional shift at \textit{all} possible confidence levels. To address these issues, we upper bound the coverage difference at all levels using the cumulative density functions of calibration and test conformal scores and Wasserstein distance. Inspired by the invariance of physics across data distributions, we propose a physics-informed structural causal model (PI-SCM) to reduce the upper bound. We validated that PI-SCM can improve coverage robustness along confidence level and test domain on a traffic speed prediction task and an epidemic spread task with multiple real-world datasets.

RQP-SGD: Differential Private Machine Learning through Noisy SGD and Randomized Quantization

The rise of IoT devices has prompted the demand for deploying machine learning at-the-edge with real-time, efficient, and secure data processing. In this context, implementing machine learning (ML) models with real-valued weight parameters can prove to be impractical particularly for large models, and there is a need to train models with quantized discrete weights. At the same time, these low-dimensional models also need to preserve privacy of the underlying dataset. In this work, we present RQP-SGD, a new approach for privacy-preserving quantization to train machine learning models for low-memory ML-at-the-edge. This approach combines differentially private stochastic gradient descent (DP-SGD) with randomized quantization, providing a measurable privacy guarantee in machine learning. In particular, we study the utility convergence of implementing RQP-SGD on ML tasks with convex objectives and quantization constraints and demonstrate its efficacy over deterministic quantization. Through experiments conducted on two datasets, we show the practical effectiveness of RQP-SGD.

Spectral-DP: Differentially Private Deep Learning through Spectral Perturbation and Filtering

Differential privacy is a widely accepted measure of privacy in the context of deep learning algorithms, and achieving it relies on a noisy training approach known as differentially private stochastic gradient descent (DP-SGD). DP-SGD requires direct noise addition to every gradient in a dense neural network, the privacy is achieved at a significant utility cost. In this work, we present Spectral-DP, a new differentially private learning approach which combines gradient perturbation in the spectral domain with spectral filtering to achieve a desired privacy guarantee with a lower noise scale and thus better utility. We develop differentially private deep learning methods based on Spectral-DP for architectures that contain both convolution and fully connected layers. In particular, for fully connected layers, we combine a block-circulant based spatial restructuring with Spectral-DP to achieve better utility. Through comprehensive experiments, we study and provide guidelines to implement Spectral-DP deep learning on benchmark datasets. In comparison with state-of-the-art DP-SGD based approaches, Spectral-DP is shown to have uniformly better utility performance in both training from scratch and transfer learning settings.

NeuGuard: Lightweight Neuron-Guided Defense against Membership Inference Attacks

Membership inference attacks (MIAs) against machine learning models can lead to serious privacy risks for the training dataset used in the model training. In this paper, we propose a novel and effective Neuron-Guided Defense method named NeuGuard against membership inference attacks (MIAs). We identify a key weakness in existing defense mechanisms against MIAs wherein they cannot simultaneously defend against two commonly used neural network based MIAs, indicating that these two attacks should be separately evaluated to assure the defense effectiveness. We propose NeuGuard, a new defense approach that jointly controls the output and inner neurons' activation with the object to guide the model output of training set and testing set to have close distributions. NeuGuard consists of class-wise variance minimization targeting restricting the final output neurons and layer-wise balanced output control aiming to constrain the inner neurons in each layer. We evaluate NeuGuard and compare it with state-of-the-art defenses against two neural network based MIAs, five strongest metric based MIAs including the newly proposed label-only MIA on three benchmark datasets. Results show that NeuGuard outperforms the state-of-the-art defenses by offering much improved utility-privacy trade-off, generality, and overhead.

Data-Driven Contract Design for Multi-Agent Systems with Collusion Detection

In applications such as participatory sensing and crowd sensing, self-interested agents exert costly effort towards achieving an objective for the system operator. We study such a setup where a principal incentivizes multiple agents of different types who can collude with each other to derive rent. The principal cannot observe the efforts exerted directly, but only the outcome of the task, which is a noisy function of the effort. The type of each agent influences the effort cost and task output. For a duopoly in which agents are coupled in their payments, we show that if the principal and the agents interact finitely many times, the agents can derive rent by colluding even if the principal knows the types of the agents. However, if the principal and the agents interact infinitely often, the principal can disincentivize agent collusion through a suitable data-driven contract.

Modeling and Detection of Future Cyber-Enabled DSM Data Attacks using Supervised Learning

Demand-Side Management (DSM) is a vital tool that can be used to ensure power system reliability and stability. In future smart grids, certain portions of a customers load usage could be under automatic control with a cyber-enabled DSM program which selectively schedules loads as a function of electricity prices to improve power balance and grid stability. In such a case, the security of DSM cyberinfrastructure will be critical as advanced metering infrastructure, and communication systems are susceptible to hacking, cyber-attacks. Such attacks, in the form of data injection, can manipulate customer load profiles and cause metering chaos and energy losses in the grid. These attacks are also exacerbated by the feedback mechanism between load management on the consumer side and dynamic price schemes by independent system operators. This work provides a novel methodology for modeling and simulating the nonlinear relationship between load management and real-time pricing. We then investigate the behavior of such a feedback loop under intentional cyber-attacks using our feedback model. We simulate and examine load-price data under different levels of DSM participation with three types of additive attacks: ramp, sudden, and point attacks. We apply change point and supervised learning methods for detection of DSM attacks. Results conclude that while higher levels of DSM participation can exacerbate attacks they also lead to better detection of such attacks. Further analysis of results shows that point attacks are the hardest to detect and supervised learning methods produce results on par or better than sequential detectors.