PRIMEX (PRIME-based Graph Encoding and Extraction for Information Fusion) is a novel framework designed to enhance distributed information fusion while minimizing communication overhead and computational complexity. Traditional information graph (IG)-based approaches require frequent synchronization and large-scale graph updates, leading to significant communication demands. PRIMEX overcomes these challenges by encoding information pedigree of state estimates as products of distinct prime numbers, allowing fusion to be performed using lightweight arithmetic operations such as greatest common divisor (GCD) for redundancy removal and least common multiple (LCM) for data integration. This eliminates the need for transmitting complex graph structures and instead leverages prime factorization-based queries to efficiently identify shared information, significantly improving scalability. PRIMEX is particularly well-suited for edge computing environments and decentralized systems, where reducing communication, computation, and memory overhead is crucial. By supporting federated learning principles, PRIMEX enhances system adaptability while preserving data privacy, making it a practical solution for scalable, distributed information fusion in applications such as autonomous systems, multi-agent networks, and large-scale sensing platforms.

This paper presents a methodology for predicting the fusion performance of multi-sensor systems in countering aerial threats (CAT). By integrating the ROC (Receiver Operating Characteristics) curves of individual sensors into a SOC (System Operating Characteristics) curve, we model the tradeoffs between various performance metrics, such as detection probability and false alarm rate, under different operating conditions. Our approach utilizes a grid-based method, dividing the Region of Interest (RoI) into small cells to evaluate system-level performance. This allows for the development of an objective function aimed at maximizing the RoI coverage rate, defined either as the average detection performance or as the percentage of cells where performance metrics exceed predefined thresholds. By applying optimization techniques such as mixed integer programming, we can strategically select and position sensors to enhance overall system performance while adhering to cost constraints. The proposed predictive fusion performance framework offers a comprehensive solution for improving situation assessment in aerial defense scenarios, leading to more effective and reliable detection, classification, and tracking of aerial targets.

Autonomous systems pose unique challenges for sensor fusion applications. In multi-sensor scenarios, a real-time data geometric alignment system, from initial online calibration to instant data consistency evaluation, is highly desirable for effective and efficient deployment of autonomy solutions. In this paper, we present an entropy-based real-time geometric alignment system for Radar-Lidar point cloud sensor fusion. The online alignment system is targetless and relies solely on multisensor point cloud measurements to form an entroy-based test statistics, requiring no prior information about the perception environment. Specifically, we design a finite mixture model (FMM) as empirical probability density function (PDF) to represent environment as a probabilistic world model. A proper entropy measure of the empirical PDF according to the perception world is then introduced to evaluate the FMM randomness. It can be observed that, even in a generally nonstationary environment, both Radar and Lidar point clouds can still converge to an optimal entropy. The gradual fluctuation of this entropy measure over time can serve as a data consistency metric, enabling the detection of sudden sensor drifts. A scenario study is carried out to evaluate and validate the effectiveness and efficiency of the proposed real-time point-cloud alignment system in real world environments.

In today's digital landscape, phishing attacks persist as a formidable challenge, highlighting the need for robust strategies to mitigate individual risk. While advanced machine learning techniques have excelled in identifying those most susceptible to phishing, existing research has primarily focused on refining prediction accuracy rather than leveraging this understanding to mitigate risk. To bridge this gap, we present a novel counterfactual explanation approach aimed at identifying the specific traits that heighten an individual's vulnerability to phishing. Our approach integrates uncertainties and causal insights from the data generation process, producing actionable intelligence to effectively lower individual susceptibility. This enables us to tailor personalized recommendations to reduce individual's vulnerability. Through experimentation, we assess the efficacy of our methodology and demonstrate capacity to reduce susceptibility to phishing. These findings emphasize the importance of personalized interventions, arming individuals with the knowledge necessary to improve their online security protocols.

This paper presents an eXplainable Deep Reinforcement Learning (XDRL) based strategy for solving the proposed problem of fleet-level aircraft maintenance scheduling (AMS) optimization. The XDRL-AMS considers various factors such as the aircraft’s initial status, mission requirements, maintenance resource capacity, and operational constraints to create a maintenance schedule for a specified period. The schedule aims to balance both mission readiness and cost reduction. We developed an RL environment, called AMS-Gym, using the OpenAI Gym toolkit specifically designed for this problem. AMS-Gym is highly flexible, allowing for easy extension to more complex scenarios and incorporating additional explanatory capabilities. The explainable RL capability was achieved by utilizing a decomposed reward Deep Q-Network (drDQN) algorithm. In the context of the AMS scenario, the drDQN consists of two parts: (i) a DQN that aims to maximize the mission accomplishment objective, and (ii) a DQN that aims to minimize the maintenance cost objective. As a result, the proposed drDQN strategy can generate real-time aircraft maintenance decisions, explain why those decisions were selected, and present the tradeoffs between the chosen action and non-selected alternatives. Experiment results show that the proposed drDQN performs well, providing an approximate solution to the vanilla DQN with a simpler structure while offering the ability to explain its decisions. In addition, a web-based prototype with an intuitive textual and visual user interface was developed to demonstrate the feasibility of the drDQN approach.

This paper reviews forty years of distributed estimation research since the first papers on decentralized filtering appeared in 1978. Starting with a formulation of the problem, it reviews the assumptions and objectives of the main approaches, including information decorrelation, cross-covariance fusion, channel filters, covariance intersection, maximum a posteriori probability fusion, best linear unbiased estimate, and distributed Kalman filters based on pseudo estimates and augmented state estimates. It also reviews algorithms motivated by sensor networks with flexible communication including consensus and diffusion filters. Suggestions for future research are provided.

Data fusion techniques are being regularly used for analysis in Operational Risk Management (ORM). A popular and commonly used risk metric of interest, Value-at-Risk (VaR), has always been difficult to robustly estimate for different data types. The classical Monte Carlo simulation (MCS) approach (denoted henceforth as classical approach) assumes the independence of loss severity and loss frequency. In practice, this assumption may not always hold. To overcome this limitation and handle cases with heavy-tail data and more robustly estimate the corresponding VaR, we adopt a new approach known as Mixture Copula-based Parametric Modeling of Frequency and Severity (MCPFS). The proposed approach is verified via large-scale MCS experiments and validated on four publicly available financial datasets. We compare MCPFS with the classical approach for robust VaR estimation. We observe that the classical approach estimates VaR poorly while the MCPFS methodologies attain better VaR estimates for real-world data. These studies provide real-world evidence that the MCPFS methodologies have merits for its use to accurately estimate VaR.

In this paper, we developed a pattern discovery and anomaly detection system using a knowledge graph constructed by integrating data from heterogeneous sources. Specifically, the knowledge graph is constructed based on data extracted from structured and unstructured sources. Besides the extracted entities and relations, the knowledge graph finds hidden relations via link prediction algorithms. Based on the constructed knowledge graph, the normalcy model for entity, action, and triplets are established. The information of the incoming streaming data is extracted and compared to the normalcy model in order to detect abnormal behaviors. In addition, we apply the lambda framework to enable a computationally scalable algorithm for pattern discovery and anomaly detection in a big data environment. Real time tweets data are used for evaluation and preliminary results show promising performance in detecting abnormal pattern and activities.

Dynamic construction of optimal portfolio is investigated. Multiple assets are allocated and rebalanced periodically based on different principles. We develop several dynamic allocation strategies to maximize long-term portfolio value based on Kelly's approach related to mutual information. We show that the resulting asset allocation strategy outperforms the traditional approaches and produces an excellent trade-off between risk and return. Out of sample simulation results are also provided to demonstrate the performance.

Predictive analytics and data fusion techniques are being regularly used for analysis in Quantitative Risk Management (QRM). The primary risk metric of interest, Value-at-Risk (VaR), has always been difficult to robustly estimate for different data types. The classical Monte Carlo simulation (MCS) approach (denoted henceforth as classical approach) assumes the independence of loss severity and loss frequency. In practice, this assumption may not always hold. To overcome this limitation and more robustly estimate the corresponding VaR, we propose a new approach known as Copula-based Parametric Modeling of Frequency and Severity (CPFS). The proposed approach is verified via large-scale MCS experiments and validated on three publicly available datasets. We compare CPFS with the classical approach and a Data-driven Partitioning of Frequency and Severity (DPFS) approach for robust VaR estimation. We observe that the classical approach estimates VaR poorly while both the DPFS and the CPFS methodologies attain VaR estimates for real-world data. These studies provide real-world evidence that the CPFS and DPFS methodologies have merits for its use to accurately estimate VaR.

Probabilistic reasoning applied to dynamic spectrum sharing systems enables them to characterize situational uncertainties and determine acceptable spectrum access behaviors. Spectrum sharing systems may use sensing data to reduce situational uncertainty and improve spectrum sharing potential. Probabilistic reasoning approaches enable risk-constrained spectrum access, a concept in which spectrum sharing is governed by maintaining acceptable levels of interference and spectrum access risks. Simulations show the potential for greater user density as a function of reduced situational uncertainty. This paper extends the risk-based spectrum access approach to secondary spectrum providers, who need to determine how to best allocate spectrum resources to users. A secondary spectrum provider revenue and cost model is developed that incorporates secondary user density, pricing models, and spectrum provider costs that are functions of interference risk and situational uncertainty. Simulations and analyses demonstrate the relationship among revenue, cost, risk, and situational uncertainty. Analysis shows significant variation in secondary spectrum provider revenue as a function of path loss uncertainty and interference risk.

Mixture distributions such as Gaussian mixture model (GMM) have been used in many applications for dynamic state estimation. These applications include robotics, image and acoustic processing, distributed tracking, and multisensor data fusion. However, the recursive processing of the mixture distributions incurs rapidly growing computational requirements. In particular, the number of components in the mixture distribution grows exponentially when multiple of them are combined. In order to keep the computational complexity tractable, it is necessary to approximate a mixture distribution by a reduced one with fewer components. Mixture reduction is traditionally done by iteratively removing insignificantly components or merging similar ones. However, a systematic procedure is needed in order to ensure scalability while trading-off performance. In this paper, we propose a recursive mixture reduction algorithm for Gaussian mixture distribution with a given error bound. To meet the error bound, we applied a constraint optimized weight adaptation to minimize the integrated squared error (ISE) between the reduced distribution and the original one. With extensive simulations, we showed that the proposed algorithm provides an efficient and effective mixture reduction performance in distributed fusion applications.

The traditional message passing algorithm developed by Pearl in 1980s provides exact inference for discrete poly-tree Bayesian networks. When there are multiple paths (loops) in the network, we can still apply Pearl's algorithm to provide approximate solutions and it is so-called "loopy propagation". However, when mixed random variables (continuous and discrete variables) are present in the network, there is no theoretical sound method so far for efficient message passing. In this paper, we propose a novel approach to compute, propagate and integrate the messages for hybrid models. Specifically, we propose to first partition the network into separate parts by introducing the concept of interface nodes. We then apply different algorithms for each sub-network. Finally we integrate the information through the channel of interface nodes and then calculate the posterior distributions for all hidden variables. The numerical experiment results show that the algorithm works well for hybrid Bayesian networks.

Uncertainty in communication channel characteristics is a significant factor for data fusion operations in wireless networks. Burst and random errors, message delays, user mobility, and link outages are significant factors that influence data fusion performance. These factors become even more significant in future mobile ad hoc networking environments. To date, however, those factors are not sufficiently addressed by formulations used for modeling and predicting data fusion performance. A stochastic-based fusion formulation that incorporates the effects of non-deterministic behaviors and stochastic communications characteristics is developed and proposed as a method for predicting estimation capabilities. The resulting stochastic fusion equations enable decentralized estimation capabilities to be evaluated in communication networks having non-idealized channel characteristics and ad hoc connectivity. The method is implemented in a simulation model for decentralized estimation in networks with time-varying ad hoc connectivity. The simulation results demonstrate the ability to closely predict expected fusion performance while greatly reducing model complexity and simulation time relative to current techniques. Those findings demonstrate the efficacy of a stochastic fusion formulation for prediction, and extending the approach to a wider range of data fusion domains and techniques is recommended.

In order to induct a Bayesian network from data, researchers proposed a variety of score metrics based on different assumptions. The score metric that performs best is of interest. In this paper, we compared the performance of five score metrics: uniform prior score metric (UPSM), conditional uniform prior score metric (CUPSM), Dirichlet prior score metric (DPSM), likelihood-equivalence Bayesian Dirichlet score metric (BDe), and minimum description length (MDL); resulting from five different assumptions: uniform prior, conditional uniform prior, Dirichlet prior, likelihood equivalence, and MDL. We used a three-node net, a five-node net, and the ALARM net to conduct several comparison experiments. The experimental results show that when they are applied to identify the true network structures, the DPSM yields the best discrimination score and BDe may fail to identify the true network if the equivalent sample size is not set properly. When they are applied to learn a network from data using the K2-like greedy search and the maximum likelihood (ML) parameter estimation, the network inducted by the K2D10, corresponding to the tenth-order DPSM, is most similar to the true network based on the cross-entropy criterion. It is concluded that the tenth-order DPSM is the best score metric and the corresponding K2D10 is the most reliable network learning algorithm.

During the past few years, a variety of methods have been developed for learning probabilistic networks from data, among which the heuristic single link forward or backward searches are widely adopted to reduce the search space. A major drawback of these search heuristics is that they can not guarantee to converge to the right networks even if a sufficiently large data set is available. This motivates us to explore an algorithm that will not suffer from this problem. We first identify an asymptotic property of different score metrics, based on which we then present a hybrid learning method that can be proved to be asymptotically convergent. We show that the algorithm, when employing the information criterion and the Bayesian metric, guarantees to converge in a very general way and is computationally feasible. Evaluation of the algorithm with simulated data is given to demonstrate the capability of the algorithm.

The importance of resolving general queries in Bayesian networks using the symbolic probabilistic inference (SPI) algorithm is considered. SPI applies the concept of dependency-directed backward search to probabilistic inference, and is incremental with respect to both queries and observations. Unlike traditional Bayesian network inferencing algorithms, the SPI algorithm is goal directed, performing only those calculations that are required to respond to queries. Research to date on SPI applies to Bayesian networks with only discrete-valued variables or only continuous variables (linear Gaussian) and does not address networks with both discrete and continuous variables. In this paper, we extend the SPI algorithm to handle Bayesian networks made up of both discrete and continuous variables (SPI-DC). The only topological constraint of the networks is that the successors of any continuous variable have to be continuous variables as well. In order to have exact analytical solution, the relationships between the continuous variables are restricted to be "linear Gaussian." With new representation, SPI-DC modifies the three basic SPI operations: multiplication, summation, and substitution. However, SPI-DC retains the framework of the SPI algorithm, namely building the search tree and recursive query mechanism and therefore retains the goal-directed and incrementality features of SPI.>

The authors present a Markov-chain-based performance evaluation technique for a two-stage sliding-window cascaded logic (2/2*m/n) for track formation in a cluttered environment. The main features of this technique are that it avoids the need for extensive simulations and it is more realistic than previous methods in that it accounts for the variation of the association gate size. The gates are obtained from a Kalman filter and fully account for its transient following the two-point initiation from the first stage of the logic. The proposed technique can also be used to select logic parameters that meet system requirements such as, for example, the true track detection and false track acceptance probabilities.>