arXiv subjects

Nagi Gebraeel

Publications and source records attributed to Nagi Gebraeel.

At least 19 recordsLinked to original sources

arXiv2026

Learning Unknown Interdependencies for Decentralized Root Cause Analysis in Nonlinear Dynamical Systems

Root cause analysis (RCA) in networked industrial systems, such as supply chains and power networks, is notoriously difficult due to unknown and dynamically evolving interdependencies among geographically distributed clients. These clients represent heterogeneous physical processes and industrial assets equipped with sensors that generate large volumes of nonlinear, high-dimensional, and heterogeneous IoT data. Classical RCA methods require partial or full knowledge of the system's dependency graph, which is rarely available in these complex networks. While federated learning (FL) offers a natural framework for decentralized settings, most existing FL methods assume homogeneous feature spaces and retrainable client models. These assumptions are not compatible with our problem setting. Different clients have different data features and often run fixed, proprietary models that cannot be modified. This paper presents a federated cross-client interdependency learning methodology for feature-partitioned, nonlinear time-series data, without requiring access to raw sensor streams or modifying proprietary client models. Each proprietary local client model is augmented with a Machine Learning (ML) model that encodes cross-client interdependencies. These ML models are coordinated via a global server that enforces representation consistency while preserving privacy through calibrated differential privacy noise. RCA is performed using model residuals and anomaly flags. We establish theoretical convergence guarantees and validate our approach on extensive simulations and a real-world industrial cybersecurity dataset.

cs.LG↗

arXiv2026

Federated Causal Representation Learning in State-Space Systems for Decentralized Counterfactual Reasoning

Networks of interdependent industrial assets (clients) are tightly coupled through physical processes and control inputs, raising a key question: how would the output of one client change if another client were operated differently? This is difficult to answer because client-specific data are high-dimensional and private, making centralization of raw data infeasible. Each client also maintains proprietary local models that cannot be modified. We propose a federated framework for causal representation learning in state-space systems that captures interdependencies among clients under these constraints. Each client maps high-dimensional observations into low-dimensional latent states that disentangle intrinsic dynamics from control-driven influences. A central server estimates the global state-transition and control structure. This enables decentralized counterfactual reasoning where clients predict how outputs would change under alternative control inputs at others while only exchanging compact latent states. We prove convergence to a centralized oracle and provide privacy guarantees. Our experiments demonstrate scalability, and accurate cross-client counterfactual inference on synthetic and real-world industrial control system datasets.

cs.LG↗

arXiv2026

Towards Uncertainty-Aware Federated Granger Causal Learning

Granger causality recovers directed interactions from time-series data, but in many distributed systems, the data are vertically partitioned across clients, with each client observing only the variables of its own subsystem. Federated Granger causality (FedGC) recovers cross-client interactions without sharing raw data. Existing FedGC methods, however, return deterministic point estimates with no calibrated measure of uncertainty, leaving operators without a principled basis for identifying reliable cross-client interactions. We address this limitation by characterizing how uncertainty propagates through the FedGC framework. We derive closed-form covariance recursions for the cross-covariances induced by the coupled client-server feedback loop, and establish spectral-radius-based convergence conditions yielding closed-form expressions for the steady-state variances at both the client and server. Under mild stability conditions, we prove that the steady-state uncertainty depends only on client data statistics (aleatoric) and is independent of the priors placed on the model parameters (epistemic). Building on this asymptotic characterization, we construct a post-training hypothesis testing procedure that separates genuine cross-client interactions from spurious edges. Experiments on synthetic and real-world datasets show that the predicted uncertainty propagation matches the theory across multiple operating regimes, while consistently outperforming the state-of-the-art federated causal structure learning baselines.

cs.LG↗

arXiv2026

Federated Learning of Nonlinear Temporal Dynamics with Graph Attention-based Cross-Client Interpretability

Networks of modern industrial systems are increasingly monitored by distributed sensors, where each system comprises multiple subsystems generating high dimensional time series data. These subsystems are often interdependent, making it important to understand how temporal patterns at one subsystem relate to others. This is challenging in decentralized settings where raw measurements cannot be shared and client observations are heterogeneous. In practical deployments each subsystem (client) operates a fixed proprietary model that cannot be modified or retrained, limiting existing approaches. Nonlinear dynamics further make cross client temporal interdependencies difficult to interpret because they are embedded in nonlinear state transition functions. We present a federated framework for learning temporal interdependencies across clients under these constraints. Each client maps high dimensional local observations to low dimensional latent states using a nonlinear state space model. A central server learns a graph structured neural state transition model over the communicated latent states using a Graph Attention Network. For interpretability we relate the Jacobian of the learned server side transition model to attention coefficients, providing the first interpretable characterization of cross client temporal interdependencies in decentralized nonlinear systems. We establish theoretical convergence guarantees to a centralized oracle and validate the framework through synthetic experiments demonstrating convergence, interpretability, scalability and privacy. Additional real world experiments show performance comparable to decentralized baselines.

cs.LG↗

arXiv2026

A Federated Generalized Expectation-Maximization Algorithm for Mixture Models with an Unknown Number of Components

We study the problem of federated clustering when the total number of clusters $K$ across clients is unknown, and the clients have heterogeneous but potentially overlapping cluster sets in their local data. To that end, we develop FedGEM: a federated generalized expectation-maximization algorithm for the training of mixture models with an unknown number of components. Our proposed algorithm relies on each of the clients performing EM steps locally, and constructing an uncertainty set around the maximizer associated with each local component. The central server utilizes the uncertainty sets to learn potential cluster overlaps between clients, and infer the global number of clusters via closed-form computations. We perform a thorough theoretical study of our algorithm, presenting probabilistic convergence guarantees under common assumptions. Subsequently, we study the specific setting of isotropic GMMs, providing tractable, low-complexity computations to be performed by each client during each iteration of the algorithm, as well as rigorously verifying assumptions required for algorithm convergence. We perform various numerical experiments, where we empirically demonstrate that our proposed method achieves comparable performance to centralized EM, and that it outperforms various existing federated clustering methods.

cs.LG↗

arXiv2025

Data-driven joint optimization of maintenance and spare parts provisioning: A distributionally robust approach

This paper investigates the joint optimization of condition-based maintenance and spare provisioning, incorporating insights obtained from sensor data. Prognostic models estimate components' remaining lifetime distributions (RLDs), which are integrated into an optimization model to coordinate maintenance and spare provisioning. The existing literature addressing this problem assumes that prognostic models provide accurate estimates of RLDs, thereby allowing a direct adoption of Stochastic Programming or Markov Decision Process methodologies. Nevertheless, this assumption often does not hold in practice since the estimated distributions can be inaccurate due to noisy sensors or scarcity of training data. To tackle this issue, we develop a Distributionally Robust Chance Constrained (DRCC) formulation considering general discrepancy-based ambiguity sets that capture potential distribution perturbations of the estimated RLDs. The proposed formulation admits a Mixed-Integer Linear Programming (MILP) reformulation, where explicit formulas are provided to simplify the general discrepancy-based ambiguity sets. Finally, for the numerical illustration, we test a type-$\infty$ Wasserstein ambiguity set and derive closed-form expressions for the parameters of the MILP reformulation. The efficacy of our methodology is showcased in a wind turbine case study, where the proposed DRCC formulation outperforms other benchmarks based on stochastic programming and robust optimization.

math.OC↗

arXiv2025

Federated Granger Causality Learning for Interdependent Clients with State Space Representation

Advanced sensors and IoT devices have improved the monitoring and control of complex industrial enterprises. They have also created an interdependent fabric of geographically distributed process operations (clients) across these enterprises. Granger causality is an effective approach to detect and quantify interdependencies by examining how one client's state affects others over time. Understanding these interdependencies captures how localized events, such as faults and disruptions, can propagate throughout the system, possibly causing widespread operational impacts. However, the large volume and complexity of industrial data pose challenges in modeling these interdependencies. This paper develops a federated approach to learning Granger causality. We utilize a linear state space system framework that leverages low-dimensional state estimates to analyze interdependencies. This addresses bandwidth limitations and the computational burden commonly associated with centralized data processing. We propose augmenting the client models with the Granger causality information learned by the server through a Machine Learning (ML) function. We examine the co-dependence between the augmented client and server models and reformulate the framework as a standalone ML algorithm providing conditions for its sublinear and linear convergence rates. We also study the convergence of the framework to a centralized oracle model. Moreover, we include a differential privacy analysis to ensure data security while preserving causal insights. Using synthetic data, we conduct comprehensive experiments to demonstrate the robustness of our approach to perturbations in causality, the scalability to the size of communication, number of clients, and the dimensions of raw data. We also evaluate the performance on two real-world industrial control system datasets by reporting the volume of data saved by decentralization.

cs.LG↗

arXiv2024

Prognostic Framework for Robotic Manipulators Operating Under Dynamic Task Severities

Robotic manipulators are critical in many applications but are known to degrade over time. This degradation is influenced by the nature of the tasks performed by the robot. Tasks with higher severity, such as handling heavy payloads, can accelerate the degradation process. One way this degradation is reflected is in the position accuracy of the robot's end-effector. In this paper, we present a prognostic modeling framework that predicts a robotic manipulator's Remaining Useful Life (RUL) while accounting for the effects of task severity. Our framework represents the robot's position accuracy as a Brownian motion process with a random drift parameter that is influenced by task severity. The dynamic nature of task severity is modeled using a continuous-time Markov chain (CTMC). To evaluate RUL, we discuss two approaches -- (1) a novel closed-form expression for Remaining Lifetime Distribution (RLD), and (2) Monte Carlo simulations, commonly used in prognostics literature. Theoretical results establish the equivalence between these RUL computation approaches. We validate our framework through experiments using two distinct physics-based simulators for planar and spatial robot fleets. Our findings show that robots in both fleets experience shorter RUL when handling a higher proportion of high-severity tasks.

cs.RO↗

arXiv2024

Prognostics for Autonomous Deep-Space Habitat Health Management under Multiple Unknown Failure Modes

Deep-space habitats (DSHs) are safety-critical systems that must operate autonomously for long periods, often beyond the reach of ground-based maintenance or expert intervention. Monitoring system health and anticipating failures are therefore essential. Prognostics based on remaining useful life (RUL) prediction support this goal by estimating how long a subsystem can operate before failure. Critical DSH subsystems, including environmental control and life support, power generation, and thermal control, are monitored by many sensors and can degrade through multiple failure modes. These failure modes are often unknown, and informative sensors may vary across modes, making accurate RUL prediction challenging when historical failure data are unlabeled. We propose an unsupervised prognostics framework for RUL prediction that jointly identifies latent failure modes and selects informative sensors using unlabeled run-to-failure data. The framework consists of two phases: an offline phase, where system failure times are modeled using a mixture of Gaussian regressions and an Expectation-Maximization algorithm to cluster degradation trajectories and select mode-specific sensors, and an online phase for real-time diagnosis and RUL prediction using low-dimensional features and a weighted functional regression model. The approach is validated on simulated DSH telemetry data and the NASA C-MAPSS benchmark, demonstrating improved prediction accuracy and interpretability.

stat.ML↗

arXiv2024

FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set

We study a federated classification problem over a network of multiple clients and a central server, in which each client's local data remains private and is subject to uncertainty in both the features and labels. To address these uncertainties, we develop a novel Federated Distributionally Robust Support Vector Machine (FDR-SVM), robustifying the classification boundary against perturbations in local data distributions. Specifically, the data at each client is governed by a unique true distribution that is unknown. To handle this heterogeneity, we develop a novel Mixture of Wasserstein Balls (MoWB) ambiguity set, naturally extending the classical Wasserstein ball to the federated setting. We then establish theoretical guarantees for our proposed MoWB, deriving an out-of-sample performance bound and showing that its design preserves the separability of the FDR-SVM optimization problem. Next, we rigorously derive two algorithms that solve the FDR-SVM problem and analyze their convergence behavior as well as their worst-case time complexity. We evaluate our algorithms on industrial data and various UCI datasets, whereby we demonstrate that they frequently outperform existing state-of-the-art approaches.

cs.LG↗

arXiv2024

Wasserstein Distributionally Robust Multiclass Support Vector Machine

We study the problem of multiclass classification for settings where data features $\mathbf{x}$ and their labels $\mathbf{y}$ are uncertain. We identify that distributionally robust one-vs-all (OVA) classifiers often struggle in settings with imbalanced data. To address this issue, we use Wasserstein distributionally robust optimization to develop a robust version of the multiclass support vector machine (SVM) characterized by the Crammer-Singer (CS) loss. First, we prove that the CS loss is bounded from above by a Lipschitz continuous function for all $\mathbf{x} \in \mathcal{X}$ and $\mathbf{y} \in \mathcal{Y}$, then we exploit strong duality results to express the dual of the worst-case risk problem, and we show that the worst-case risk minimization problem admits a tractable convex reformulation due to the regularity of the CS loss. Moreover, we develop a kernel version of our proposed model to account for nonlinear class separation, and we show that it admits a tractable convex upper bound. We also propose a projected subgradient method algorithm for a special case of our proposed linear model to improve scalability. Our numerical experiments demonstrate that our model outperforms state-of-the art OVA models in settings where the training data is highly imbalanced. We also show through experiments on popular real-world datasets that our proposed model often outperforms its regularized counterpart as the first accounts for uncertain labels unlike the latter.

cs.LG↗

arXiv2022

Large-Scale Maintenance and Unit Commitment: A Decentralized Subgradient Approach

Unit Commitment (UC) is a fundamental problem in power system operations. When coupled with generation maintenance, the joint optimization problem poses significant computational challenges due to coupling constraints linking maintenance and UC decisions. Obviously, these challenges grow with the size of the network. With the introduction of sensors for monitoring generator health and condition-based maintenance(CBM), these challenges have been magnified. ADMM-based decentralized methods have shown promise in solving large-scale UC problems, especially in vertically integrated power systems. However, in their current form, these methods fail to deliver similar computational performance and scalability when considering the joint UC and CBM problem. This paper provides a novel decentralized optimization framework for solving large-scale, joint UC and CBM problems. Our approach relies on the novel use of the subgradient method to temporally decouple various subproblems of the ADMM-based formulation of the joint problem along the maintenance horizon. By effectively utilizing multithreading, our decentralized subgradient approach delivers superior computational performance and eliminates the need to move sensor data thereby alleviating privacy and security concerns. Using experiments on large scale test cases, we show that our framework can provide a speedup of upto 50x as compared to various state of the art benchmarks without compromising on solution quality.

cs.DC↗

arXiv2021

Blockchain Based Decentralized Replay Attack Detection for Large Scale Power Systems

Large scale power systems are comprised of regional utilities with assets that stream sensor readings in real time. In order to detect cyberattacks, the globally acquired, real time sensor data needs to be analyzed in a centralized fashion. However, owing to operational constraints, such a centralized sharing mechanism turns out to be a major obstacle. In this paper, we propose a blockchain based decentralized framework for detecting coordinated replay attacks with full privacy of sensor data. We develop a Bayesian inference mechanism employing locally reported attack probabilities that is tailor made for a blockchain framework. We compare our framework to a traditional decentralized algorithm based on the broadcast gossip framework both theoretically as well as empirically. With the help of experiments on a private Ethereum blockchain, we show that our approach achieves good detection quality and significantly outperforms gossip driven approaches in terms of accuracy, timeliness and scalability.

cs.DC↗

arXiv2021

An Online Approach to Cyberattack Detection and Localization in Smart Grid

Complex interconnections between information technology and digital control systems have significantly increased cybersecurity vulnerabilities in smart grids. Cyberattacks involving data integrity can be very disruptive because of their potential to compromise physical control by manipulating measurement data. This is especially true in large and complex electric networks that often rely on traditional intrusion detection systems focused on monitoring network traffic. In this paper, we develop an online detection algorithm to detect and localize covert attacks on smart grids. Using a network system model, we develop a theoretical framework by characterizing a covert attack on a generator bus in the network as sparse features in the state-estimation residuals. We leverage such sparsity via a regularized linear regression method to detect and localize covert attacks based on the regression coefficients. We conduct a comprehensive numerical study on both linear and nonlinear system models to validate our proposed method. The results show that our method outperforms conventional methods in both detection delay and localization accuracy.

stat.AP↗

arXiv2020

Decentralized and Secure Generation Maintenance with Differential Privacy

Decentralized methods are gaining popularity for data-driven models in power systems as they offer significant computational scalability while guaranteeing full data ownership by utility stakeholders. However, decentralized methods still require sharing information about network flow estimates over public facing communication channels, which raises privacy concerns. In this paper we propose a differential privacy driven approach geared towards decentralized formulations of mixed integer operations and maintenance optimization problems that protects network flow estimates. We prove strong privacy guarantees by leveraging the linear relationship between the phase angles and the flow. To address the challenges associated with the mixed integer and dynamic nature of the problem, we introduce an exponential moving average based consensus mechanism to enhance convergence, coupled with a control chart based convergence criteria to improve stability. Our experimental results obtained on the IEEE 118 bus case demonstrate that our privacy preserving approach yields solution qualities on par with benchmark methods without differential privacy. To demonstrate the computational robustness of our method, we conduct experiments using a wide range of noise levels and operational scenarios.

cs.DC↗

arXiv2020

Deep Learning based Covert Attack Identification for Industrial Control Systems

Cybersecurity of Industrial Control Systems (ICS) is drawing significant concerns as data communication increasingly leverages wireless networks. A lot of data-driven methods were developed for detecting cyberattacks, but few are focused on distinguishing them from equipment faults. In this paper, we develop a data-driven framework that can be used to detect, diagnose, and localize a type of cyberattack called covert attacks on smart grids. The framework has a hybrid design that combines an autoencoder, a recurrent neural network (RNN) with a Long-Short-Term-Memory (LSTM) layer, and a Deep Neural Network (DNN). This data-driven framework considers the temporal behavior of a generic physical system that extracts features from the time series of the sensor measurements that can be used for detecting covert attacks, distinguishing them from equipment faults, as well as localize the attack/fault. We evaluate the performance of the proposed method through a realistic simulation study on the IEEE 14-bus model as a typical example of ICS. We compare the performance of the proposed method with the traditional model-based method to show its applicability and efficacy.

cs.LG↗

arXiv2019

Adaptive Two-stage Stochastic Programming with an Analysis on Capacity Expansion Planning Problem

Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a number of planning periods. Two-stage stochastic programming might be better suited to such settings, where the decisions for all periods are made here-and-now and do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, where the stages are not predetermined but part of the optimization problem. Each component of the decision policy has an associated revision point, a period prior to which the decision is predetermined and after which it is revised to adjust to the uncertainty realized thus far. We motivate this setting using the multi-period newsvendor problem by deriving an optimal adaptive policy. We label the proposed approach as adaptive two-stage stochastic programming and provide a generic mixed-integer programming formulation for finite stochastic processes. We show that adaptive two-stage stochastic programming is NP-hard in general. Next, we derive bounds on the value of adaptive two-stage programming in comparison to the two-stage and multi-stage approaches for a specific problem structure inspired by the capacity expansion planning problem. Since directly solving the mixed-integer linear program associated with the adaptive two-stage approach might be very costly for large instances, we propose several heuristic solution algorithms based on the bound analysis. We provide approximation guarantees for these heuristics. Finally, we present an extensive computational study on an electricity generation capacity expansion planning problem and demonstrate the computational and practical impacts of the proposed approach from various perspectives.

math.OC↗

arXiv2019

An Asynchronous, Decentralized Solution Framework for the Large Scale Unit Commitment Problem

With increased reliance on cyber infrastructure, large scale power networks face new challenges owing to computational scalability. In this paper we focus on developing an asynchronous decentralized solution framework for the Unit Commitment(UC) problem for large scale power networks. We exploit the inherent asynchrony in a region based decomposition arising out of imbalance in regional subproblems to boost computational efficiency. A two phase algorithm is proposed that relies on the convex relaxation and privacy preserving valid inequalities in order to deliver algorithmic improvements. Our algorithm employs a novel interleaved binary mechanism that locally switches from the convex subproblem to its binary counterpart based on consistent local convergent behavior. We develop a high performance computing (HPC) oriented software framework that uses Message Passing Interface (MPI) to drive our benchmark studies. Our simulations performed on the IEEE 3012 bus case are benchmarked against the centralized and a state of the art synchronous decentralized method. The results demonstrate that the asynchronous method improves computational efficiency by a significant amount and provides a competitive solution quality rivaling the benchmark methods.

cs.DC↗