arXiv subjects

Rick S. Blum

Publications and source records attributed to Rick S. Blum.

At least 19 recordsLinked to original sources

arXiv2026

Statistical Analysis of using the Shapley Value for Sensor Anomaly Localization with Accurate Classifiers

Recent publications have suggested using the Shap- ley value for sensor anomaly/attack localization. We study the performance of such an approach by using mathematically de- fined optimum binary classifiers in the Shapley value calculation. To judge localization performance, we study the ability of the Shapley value of a given sensor observation to determine if that observation is anomalous. First, we prove that for cases with independent sensor observations, an optimized anomaly test using the Shapley value is equivalent to an optimized lower-complexity anomaly test using a single term in the Shapley value calculation, yielding the exact same probability of error. For some popular dependent observation cases involving two sensors, including correlated bivariate Gaussian/Laplacian probability density functions and constant/Gaussian at- tacks/anomalies, we prove that these two tests are fundamentally different, yielding different decision regions and error probabil- ities. Further, we prove that the Shapley value test is sometimes strictly inferior to the other (single term in Shapley calculation) test in certain statistically dependent bivariate Gaussian scenarios with large correlation magnitude and additive attacks/anomalies, while it is strictly superior in others, depending on the sign of the correlation. One can combine these two approaches to obtain a strictly better approach in these cases. These results, which provide the first theoretical statistical analysis of Shapley-based localization, seem very interesting based on the wide acceptance of the Shapley value by many researchers and should encourage further research on this topic. Numerical results are provided which illustrate our findings.

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arXiv2026

Cyber Security of Sensor Systems for State Sequence Estimation: A Machine Learning Approach

Due to possible devastating consequences, counteracting sensor data attacks is an extremely impor- tant topic, which has not seen sufficient study. To the best of our knowledge, this paper develops the first meth- ods that accurately identify/eliminate only the problem- atic attacked sensor data presented to a sequence es- timation/regression algorithm under any attack from our attack model. The approach does not assume a known form for the statistical model of the sensor data, allow- ing data-driven and machine learning sequence estima- tion/regression algorithms to be protected. A simple pro- tection approach for attackers not endowed with knowledge of the details of our protection approach is first developed, followed by additional processing for attacks based on pro- tection system knowledge. Experimental results show that the simple approach achieves performance indistinguish- able from that for an approach which knows which sensors are attacked. For cases where the attacker has knowledge of the protection approach, experimental results indicate the additional processing can be configured so that the worst-case degradation under the additional processing and a large number of sensors attacked can be made signif- icantly smaller than the worst-case degradation of the sim- ple approach, and close to an approach which knows which sensors are attacked, with just a slight degradation under no attacks. Mathematical descriptions of the worst-case attacks are used to demonstrate the additional processing will provide similar advantages for cases for which we do not have numerical results. All the data-driven/machine learning processing used in our approaches employ only unattacked training data.

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arXiv2026

On Using the Shapley Value for Anomaly Localization: A Statistical Investigation

Recent publications have suggested using the Shapley value for anomaly localization for sensor data systems. Using a reasonable mathematical anomaly model for full control, experiments indicate that using a single fixed term in the Shapley value calculation achieves a lower complexity anomaly localization test, with the same probability of error, as a test using the Shapley value for all cases tested. A proof demonstrates these conclusions must be true for all independent observation cases. For dependent observation cases, no proof is available.

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arXiv2026

Receding Horizon Multi-Agent Deceptive Path Planner

Deceptive path planning enables autonomous agents to obscure their true goals from observers by deviating from an expected optimal path. Prior work largely solves full-horizon, end-to-end optimization for single agents, which is expensive to recompute online and difficult to scale or adapt en route. We propose a unified framework for deceptive path planning using a Boltzmann distribution, computing over short-horizon candidate trajectories within a receding-horizon loop. By param- By iterating a user-defined cost that captures deception, resources, and smoothness, and optionally includes coupling terms between agents, the framework yields stochastic policies that balance the tradeoff between optimal paths and deceptive deviation. Policies are updated locally and do not require training. The level of deception and adherence to constraints can be dynamically tuned, enabling online adaptation to changes in goals and constraints such as obstacles. This step-by-step tuning opens the door to new forms of dynamic deception. Simulation studies demonstrate the flexibility of our approach, maintaining deception while adapting to environmental and constraint updates, avoiding the recomputation required by full-horizon methods, and supporting intuitive tuning via a small set of parameters

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arXiv2026

Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systems

Anomaly detection and root cause analysis (RCA) are critical for ensuring the safety and resilience of cyber-physical systems such as power grids. However, existing machine learning models for time series anomaly detection often operate as black boxes, offering only binary outputs without any explanation, such as identifying anomaly type and origin. To address this challenge, we propose Power Interpretable Causality Ordinary Differential Equation (PICODE) Networks, a unified, causality-informed architecture that jointly performs anomaly detection along with the explanation why it is detected as an anomaly, including root cause localization, anomaly type classification, and anomaly shape characterization. Experimental results in power systems demonstrate that PICODE achieves competitive detection performance while offering improved interpretability and reduced reliance on labeled data or external causal graphs. We provide theoretical results demonstrating the alignment between the shape of anomaly functions and the changes in the weights of the extracted causal graphs.

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arXiv2025

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.

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arXiv2025

Spectrum Optimization of Dynamic Networks for Reduction of Vulnerability Against Adversarial Resonance Attacks

Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant frequency by an adversarial agent with the aim of saturating the network with the signal. Towards this goal, we develop the notion of network vulnerability, which is measured by the expected resonance amplitude on the network under a stochastically modeled adversarial attack. Assuming a second order dynamics model based on the network graph Laplacian matrix and a known stochastic model for the adversarial attack, we propose two methods for minimizing the network vulnerability through optimization of the spectrum of the network graph. We provide extensive numerical results analyzing the effects of both methods.

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arXiv2024

Adaptive Regulated Sparsity Promoting Approach for Data-Driven Modeling and Control of Grid-Connected Solar Photovoltaic Generation

This paper aims to introduce a new statistical learning technique based on sparsity promoting for data-driven modeling and control of solar photovoltaic (PV) systems. Compared with conventional sparse regression techniques that might introduce computational complexities when the number of candidate functions increases, an innovative algorithm, named adaptive regulated sparse regression (ARSR) is proposed that adaptively regulates the hyperparameter weights of candidate functions to best represent the dynamics of PV systems. Utilizing this algorithm, open-loop and closed-loop models of single-stage and two-stage PV systems are obtained from measurements and are utilized for control design purposes. Moreover, it is demonstrated that the proposed data-driven approach can successfully be employed for fault analysis studies, which distinguishes its capabilities compared with other data-driven techniques. Finally, the proposed approach is validated through real-time simulations.

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arXiv2024

Data-Driven Dynamic State Estimation of Photovoltaic Systems via Sparse Regression Unscented Kalman Filter

Dynamic state estimation (DSE) is vital in modern power systems with numerous inverter-based distributed energy resources including solar and wind, ensuring real-time accuracy for tracking system variables and optimizing grid stability. This paper proposes a data-driven DSE approach designed for photovoltaic (PV) energy conversion systems (single stage and two stage) that are subjected to both process and measurement noise. The proposed framework follows a two-phase methodology encompassing ``data-driven model identification" and ``state-estimation." In the initial model identification phase, state feedback is gathered to elucidate the dynamics of the photovoltaic systems using nonlinear sparse regression technique. Following the identification of the PV dynamics, the nonlinear data-driven model will be utilized to estimate the dynamics of the PV system for monitoring and protection purposes. To account for incomplete measurements, inherent uncertainties, and noise, we employ an ``unscented Kalman filter," which facilitates state estimation by processing the noisy output data. Ultimately, the paper substantiates the efficacy of the proposed sparse regression-based unscented Kalman filter through simulation results, providing a comparative analysis with a physics-based DSE.

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arXiv2024

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.

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arXiv2022

Communication-Efficient {Federated} Learning Using Censored Heavy Ball Descent

Distributed machine learning enables scalability and computational offloading, but requires significant levels of communication. Consequently, communication efficiency in distributed learning settings is an important consideration, especially when the communications are wireless and battery-driven devices are employed. In this paper we develop a censoring-based heavy ball (CHB) method for distributed learning in a server-worker architecture. Each worker self-censors unless its local gradient is sufficiently different from the previously transmitted one. The significant practical advantages of the HB method for learning problems are well known, but the question of reducing communications has not been addressed. CHB takes advantage of the HB smoothing to eliminate reporting small changes, and provably achieves a linear convergence rate equivalent to that of the classical HB method for smooth and strongly convex objective functions. The convergence guarantee of CHB is theoretically justified for both convex and nonconvex cases. In addition we prove that, under some conditions, at least half of all communications can be eliminated without any impact on convergence rate. Extensive numerical results validate the communication efficiency of CHB on both synthetic and real datasets, for convex, nonconvex, and nondifferentiable cases. Given a target accuracy, CHB can significantly reduce the number of communications compared to existing algorithms, achieving the same accuracy without slowing down the optimization process.

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arXiv2022

Route Discovery and Capacity of Ad hoc Networks

Throughput capacity of large ad hoc networks has been shown to scale adversely with the size of network $n$. However the need for the nodes to find or repair routes has not been analyzed in this context. In this paper, we explicitly take route discovery into account and obtain the scaling law for the throughput capacity under general assumptions on the network environment, node behavior, and the quality of route discovery algorithms. We also discuss a number of possible scenarios and show that the need for route discovery may change the scaling for the throughput capacity dramatically.

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arXiv2022

Distributed Learning With Sparsified Gradient Differences

A very large number of communications are typically required to solve distributed learning tasks, and this critically limits scalability and convergence speed in wireless communications applications. In this paper, we devise a Gradient Descent method with Sparsification and Error Correction (GD-SEC) to improve the communications efficiency in a general worker-server architecture. Motivated by a variety of wireless communications learning scenarios, GD-SEC reduces the number of bits per communication from worker to server with no degradation in the order of the convergence rate. This enables larger-scale model learning without sacrificing convergence or accuracy. At each iteration of GD-SEC, instead of directly transmitting the entire gradient vector, each worker computes the difference between its current gradient and a linear combination of its previously transmitted gradients, and then transmits the sparsified gradient difference to the server. A key feature of GD-SEC is that any given component of the gradient difference vector will not be transmitted if its magnitude is not sufficiently large. An error correction technique is used at each worker to compensate for the error resulting from sparsification. We prove that GD-SEC is guaranteed to converge for strongly convex, convex, and nonconvex optimization problems with the same order of convergence rate as GD. Furthermore, if the objective function is strongly convex, GD-SEC has a fast linear convergence rate. Numerical results not only validate the convergence rate of GD-SEC but also explore the communication bit savings it provides. Given a target accuracy, GD-SEC can significantly reduce the communications load compared to the best existing algorithms without slowing down the optimization process.

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arXiv2022

Communication Efficient Federated Learning via Ordered ADMM in a Fully Decentralized Setting

The challenge of communication-efficient distributed optimization has attracted attention in recent years. In this paper, a communication efficient algorithm, called ordering-based alternating direction method of multipliers (OADMM) is devised in a general fully decentralized network setting where a worker can only exchange messages with neighbors. Compared to the classical ADMM, a key feature of OADMM is that transmissions are ordered among workers at each iteration such that a worker with the most informative data broadcasts its local variable to neighbors first, and neighbors who have not transmitted yet can update their local variables based on that received transmission. In OADMM, we prohibit workers from transmitting if their current local variables are not sufficiently different from their previously transmitted value. A variant of OADMM, called SOADMM, is proposed where transmissions are ordered but transmissions are never stopped for each node at each iteration. Numerical results demonstrate that given a targeted accuracy, OADMM can significantly reduce the number of communications compared to existing algorithms including ADMM. We also show numerically that SOADMM can accelerate convergence, resulting in communication savings compared to the classical ADMM.

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arXiv2021

Training Robust Graph Neural Networks with Topology Adaptive Edge Dropping

Graph neural networks (GNNs) are processing architectures that exploit graph structural information to model representations from network data. Despite their success, GNNs suffer from sub-optimal generalization performance given limited training data, referred to as over-fitting. This paper proposes Topology Adaptive Edge Dropping (TADropEdge) method as an adaptive data augmentation technique to improve generalization performance and learn robust GNN models. We start by explicitly analyzing how random edge dropping increases the data diversity during training, while indicating i.i.d. edge dropping does not account for graph structural information and could result in noisy augmented data degrading performance. To overcome this issue, we consider graph connectivity as the key property that captures graph topology. TADropEdge incorporates this factor into random edge dropping such that the edge-dropped subgraphs maintain similar topology as the underlying graph, yielding more satisfactory data augmentation. In particular, TADropEdge first leverages the graph spectrum to assign proper weights to graph edges, which represent their criticality for establishing the graph connectivity. It then normalizes the edge weights and drops graph edges adaptively based on their normalized weights. Besides improving generalization performance, TADropEdge reduces variance for efficient training and can be applied as a generic method modular to different GNN models. Intensive experiments on real-life and synthetic datasets corroborate theory and verify the effectiveness of the proposed method.

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arXiv2020

Inter-cluster Transmission Control Using Graph Modal Barriers

In this paper we consider the problem of transmission across a graph and how to effectively control/restrict it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus across a computer network, or spread of an infectious disease across communities. The key insight is to assign proper weights to bottleneck edges of the graph based on their role in reducing the connection between two or more strongly-connected clusters within the graph. Selectively reducing the weights (implying reduced transmission rate) on the critical edges helps limit the transmission from one cluster to another. We refer to these as barrier weights and their computation is based on the eigenvectors of the graph Laplacian. Unlike other work on graph partitioning and clustering, we completely circumvent the associated computational complexities by assigning weights to edges instead of performing discrete graph cuts. This allows us to provide strong theoretical results on our proposed methods. We also develop approximations that allow low complexity distributed computation of the barrier weights using only neighborhood communication on the graph.

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arXiv2020

Ordering for Communication-Efficient Quickest Change Detection in a Decomposable Graphical Model

A quickest change detection problem is considered in a sensor network with observations whose statistical dependency structure across the sensors before and after the change is described by a decomposable graphical model (DGM). Distributed computation methods for this problem are proposed that are capable of producing the optimum centralized test statistic. The DGM leads to the proper way to collect nodes into local groups equivalent to cliques in the graph, such that a clique statistic which summarizes all the clique sensor data can be computed within each clique. The clique statistics are transmitted to a decision maker to produce the optimum centralized test statistic. In order to further improve communication efficiency, an ordered transmission approach is proposed where transmissions of the clique statistics to the fusion center are ordered and then adaptively halted when sufficient information is accumulated. This procedure is always guaranteed to provide the optimal change detection performance, despite not transmitting all the statistics from all the cliques. A lower bound on the average number of transmissions saved by ordered transmissions is provided and for the case where the change seldom occurs the lower bound approaches approximately half the number of cliques provided a well behaved distance measure between the distributions of the sensor observations before and after the change is sufficiently large. We also extend the approach to the case when the graph structure is different under each hypothesis. Numerical results show significant savings using the ordered transmission approach and validate the theoretical findings.

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arXiv2020

A Statistical Learning-Based Algorithm for Topology Verification in Natural Gas Networks Based on Noisy Sensor Measurements

Accurate knowledge of natural gas network topology is critical for the proper operation of natural gas networks. Failures, physical attacks, and cyber attacks can cause the actual natural gas network topology to differ from what the operator believes to be present. Incorrect topology information misleads the operator to apply inappropriate control causing damage and lack of gas supply. Several methods for verifying the topology have been suggested in the literature for electrical power distribution networks, but we are not aware of any publications for natural gas networks. In this paper, we develop a useful topology verification algorithm for natural gas networks based on modifying a general known statistics-based approach to eliminate serious limitations for this application while maintaining good performance. We prove that the new algorithm is equivalent to the original statistics-based approach for a sufficiently large number of sensor observations. We provide new closed-form expressions for the asymptotic performance that are shown to be accurate for the typical number of sensor observations required to achieve reliable performance.

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