In this work, we analyze limited knowledge about likelihoods in traditional fusion as an uncertain Naïve Bayesian network whose conditional probabilities are known within posterior Dirichlet distributions reflected of limited training data. In prior work, we showed that inferences from these uncertain networks are confidently precise despite finite training data as the number of features goes to infinity for a uniform prior. The inference is usually correct except for pathological cases that diminish as the training data size goes to infinity. This work extends the analysis by studying how various priors affect asymptotic inference when the priors do or do not match the generative process for the conditional probabilities. Furthermore, the work analyzes how the prior affects the convergence rate of the inference.

We study the problem of quickest change detection (QCD) when the post-change distribution has parametric uncertainty. The generalized likelihood ratio (GLR) cumulative sum (CuSum) procedure is known to be asymptotically optimum in this setting. However, this rule requires significant memory and computational resources, making it difficult to implement in practice. To overcome this limitation, sliding window approaches, such as the window-limited GLR CuSum and window-limited adaptive CuSum tests, have been employed, where the test statistic is computed over a fixed window of the latest observations. We propose the K-Best rule which instead keeps track of K hypothesized change points that have the largest test statistic. This allows the hypothesized change points to reduce epistemic uncertainty over time, while restricting the number of hypothesized change points considered. We characterize the growth rate of the K-Best window necessary to achieve the detection performance of the GLR-CuSum rule and quantify the computational benefits over the existing windowing approaches.

State of the art methods for target tracking with sensor management (or controlled sensing) are model-based and are obtained through solutions to Partially Observable Markov Decision Process (POMDP) formulations. In this paper a Reinforcement Learning (RL) approach to the problem is explored for the setting where the motion model for the object/target to be tracked is unknown to the observer. It is assumed that the target dynamics are stationary in time, the state space and the observation space are discrete, and there is complete observability of the location of the target under certain (a priori unknown) sensor control actions. Then, a novel Markov Decision Process (MDP) rather than POMDP formulation is proposed for the tracking problem with controlled sensing, which is termed as Track-MDP. In contrast to the POMDP formulation, the Track-MDP formulation is amenable to an RL based solution. It is shown that the optimal policy for the Track-MDP formulation, which is approximated through RL, is guaranteed to track all significant target paths with certainty. The Track-MDP method is then compared with the optimal POMDP policy, and it is shown that the infinite horizon tracking reward of the optimal Track-MDP policy is the same as that of the optimal POMDP policy. In simulations it is demonstrated that Track-MDP based RL leads to a policy that can track the target with high accuracy.

We study the problem of Quickest Change Detection (QCD) in a complex networked system consisting of a set of heterogeneous agents that sequentially feed information to a central fusion center. At any unknown deterministic time, a persistent anomaly occurs, causing the distribution of observations from an unknown distinguishable subset of agents to simultaneously change from a nominal (pre-change) distribution to an anomalous (post-change) distribution, and the goal of the fusion center is to detect the change as quickly as possible subject to a false alarm constraint. Traditionally, various fusion rules have been proposed that assume that the distributions at each agent are either completely known or unknown and are locally solved using the Cumulative Sum (CuSum) and Generalized Likelihood Ratio (GLR) statistics, respectively. When an agent has access to training data, the Uncertain Likelihood Ratio (ULR) test generalizes distributional assumptions using uncertain distributions. However, the ULR has not been implemented for network change detection. This paper empirically studies incorporating the ULR statistics into the existing fusion rules for QCD and compares the average detection delay. Our results show that the ULR test can improve the average detection delay over the GLR tests using certain fusion techniques, while approaching the detection delay of the CuSum tests as the training data increases. Our results provide insights into future theoretical analysis to improve network QCD with imprecise knowledge of the distributions.

Likelihood fusion is a special case of Bayesian networks known as naïve Bayes. It is well known that as the number of observations goes to infinity with known likelihoods, the aleatoric uncertainty of the queried (or parent) variable goes to zero, and furthermore, the declared values are guaranteed to match the ground truth. This work considers the case that the conditional probabilities are learned with limited training data leading to uncertain likelihoods, and second-order probabilistic reasoning is incorporated to characterize the aleatoric and epistemic uncertainty. Remarkably, it is shown that both the aleatoric and epistemic uncertainty goes to zero despite limited knowledge of the likelihoods. The rate of convergence is dictated by a quasi-divergence value that is related to the Kullback-Liebler (KL) divergence. However, the quasi-divergence can be negative leading to false declarations. This paper investigates when false declarations can emerge and shows how such cases diminish as the amount of training data for the likelihoods increases.

Spatial reasoning tasks in multi-agent environments such as event prediction, agent type identification, or missing data imputation are important for multiple applications (e.g., autonomous surveillance over sensor networks and subtasks for reinforcement learning (RL)). StarCraft II game replays encode intelligent (and adversarial) multiagent behavior and could provide a testbed for these tasks; however, extracting simple and standardized representations for prototyping these tasks is laborious and hinders reproducibility. In contrast, MNIST and CIFAR10, despite their extreme simplicity, have enabled rapid prototyping and reproducibility of ML methods. Following the simplicity of these datasets, we construct a benchmark spatial reasoning dataset based on StarCraft II replays that exhibit complex multi-agent behaviors, while still being as easy to use as MNIST and CIFAR10. Specifically, we carefully summarize a window of 255 consecutive game states to create 3.6 million summary images from 60,000 replays, including all relevant metadata such as game outcome and player races. We develop three formats of decreasing complexity: Hyperspectral images that include one channel for every unit type (similar to multispectral geospatial images), RGB images that mimic CIFAR10, and grayscale images that mimic MNIST. We show how this dataset can be used for prototyping spatial reasoning methods. All datasets, code for extraction, and code for dataset loading can be found at https://starcraftdata.davidinouye.com/.

This paper studies the problem of event detection in highly dynamic and uncertain environments where training data is limited and the number of observations is small. The objective is to determine if the training data and observations are drawn from the same or different distributions. The traditional approach is to use the Generalized Likelihood Ratio (GLR) test statistic. However, with limited training data and observations, the GLR is suboptimal. To overcome this, we propose to use the Uncertain Likelihood Ratio (ULR) test statistic to accurately account for the uncertainty. We show that the ULR is the mean most powerful test and that it is asymptotically equivalent to the GLR under a Jeffreys Prior. Furthermore, a simulation study validates the theory that the performance of the ULR is superior to the GLR when testing in the small sample regime.

We consider the problem of distributed inference of a group of agents in a social network, where the agents construct, share, and update beliefs in a non-Bayesian framework to identify the underlying true state of the world. We build upon the concept of uncertain models that accurately represents each agents knowledge of the distribution of each hypothesis based on the amount of training data collected. Then, we propose an event-triggered communication protocol that only transmits a belief for a hypothesis if new information has been incorporated since the previous communication time. We show that the proposed solution allows the agents to achieve beliefs within the neighborhood of a full communication network, while significantly reducing the amount of transmissions.

The article presents a distributed algorithm, called Prediction-based Opportunistic Sensing for Resilient and Efficient Sensor Networks (POSE.R), where the sensor nodes utilize predictions of the targets' positions to probabilistically control their multi-modal operating states to track the targets. There are two desired features of the algorithm: energy efficiency and resilience. If the target is traveling through a high-node-density area, then an optimal sensor selection approach is employed that maximizes a joint cost function of remaining energy and geometric diversity around the target’s position. This provides energy efficiency and increases the network lifetime while preventing redundant nodes from tracking the target. However, if the target is traveling through a low-node-density area or in a coverage gap (e.g., formed by node failures or non-uniform node deployment), then a potential game is played amongst the surrounding nodes to optimally expand their sensing ranges via minimizing energy consumption and maximizing target coverage. This provides resilience, that is, the self-healing capability to track the target in the presence of low node densities and coverage gaps. The algorithm is comparatively evaluated against existing approaches through Monte Carlo simulations that demonstrate its superiority in terms of tracking performance, network-resilience, and network-lifetime.

This paper presents a distributed supervisory control algorithm that enables opportunistic sensing for energy-efficient target tracking in a sensor network. The algorithm called Prediction-based Opportunistic Sensing (POSE), is a distributed node-level energy management approach for minimizing energy usage. Distributed sensor nodes in the POSE network self-adapt to target trajectories by enabling high power consuming devices when they predict that a target is arriving in their coverage area, while enabling low power consuming devices when the target is absent. Each node has a Probabilistic Finite State Automaton which acts as a supervisor to dynamically control its various sensing and communication devices based on target's predicted position. The POSE algorithm is validated by extensive Monte Carlo simulations and compared with random scheduling schemes. The results show that the POSE algorithm provides significant energy savings while also improving track estimation via fusion-driven state initialization.

Border surveillance requires regular patrolling to prevent intruders from crossing across, emphasizing the need for an automated network of sensing devices that is capable of detecting and estimating multiple moving targets. This paper proposes a fusion-driven decentralized sensor scheduling scheme that enables dynamic space-time clustering around multiple moving targets for energy-efficient track estimation. Each sensor node runs a Probabilistic Finite State Automata (PFSA) that controls the sensing and communication devices in an energy-efficient manner. This decentralized scheduling scheme is validated and compared with traditional scheduling schemes. The results show that the proposed scheme conserves energy while maintaining accurate track estimation.

Human activity recognition has become an increasingly important field of research with many practical applications related to health care and leisure activities. The accessibility of inexpensive portable sensors, such as accelerometers, allows for a widespread use of this technology for both commercial and personal activity recognition. This paper develops a novel feature extraction approach to human activity recognition through the development of the Lempel-Ziv-Welch Coded Probabilistic Finite State Automata (LZW-Coded PFSA) to classify activities such as walking, jumping, running, waist rotations, and shoulder rotations. The PFSA reveal the underlying architecture of a given activity and classify it without making any a priori assumptions by inferring patterns from the sensor measurements. LZW-Coded PFSA select the optimal variable length state from the time-series data and compress it into class-separable state transition matrices π. This algorithm is robust to subject biases and is shown to be effective with a correct classification rate of 95.63%.