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Nandan Sriranga, Saikiran Bulusu, Baocheng Geng, Pramod K. Varshney

In this work, we consider a binary sequential hypothesis testing problem with distributed and asynchronous measurements. The aim is to analyze the effect of sampling times of jointly \textit{wide-sense stationary} (WSS) Gaussian observation processes at distributed sensors on the expected stopping time of the sequential test at the fusion center (FC). The distributed system is such that the sensors and the FC sample observations periodically, where the sampling times are not necessarily synchronous, i.e., the sampling times at different sensors and the FC may be different from each other. \color{black} The sampling times, however, are restricted to be within a time window and a sample obtained within the window is assumed to be \textit{uncorrelated} with samples outside the window. We also assume that correlations may exist only between the observations sampled at the FC and those at the sensors in a pairwise manner (sensor pairs not including the FC have independent observations). The effect of \textit{asynchronous} sampling on the SPRT performance is analyzed by obtaining bounds for the expected stopping time. We illustrate the validity of the theoretical results with numerical results.

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Chen Quan, Yunghsiang S. Han, Baocheng Geng, Pramod K. Varshney

This paper investigates distributed detection of sparse stochastic signals with quantized measurements under Byzantine attacks. Under this type of attack, sensors in the networks might send falsified data to degrade system performance. The Bernoulli-Gaussian (BG) distribution in terms of the sparsity degree of the stochastic signal is utilized for modeling the sparsity of signals. Several detectors with improved detection performance are proposed by incorporating the estimated attack parameters into the detection process. First, we propose the generalized likelihood ratio test with reference sensors (GLRTRS) and the locally most powerful test with reference sensors (LMPTRS) detectors with adaptive thresholds, given that the sparsity degree and the attack parameters are unknown. Our simulation results show that the LMPTRS and GLRTRS detectors outperform the LMPT and GLRT detectors proposed for an attack-free environment and are more robust against attacks. The proposed detectors can achieve the detection performance close to the benchmark likelihood ratio test (LRT) detector, which has perfect knowledge of the attack parameters and sparsity degree. When the fraction of Byzantine nodes are assumed to be known, we can further improve the system's detection performance. We propose the enhanced LMPTRS (E-LMPTRS) and enhanced GLRTRS (E-GLRTRS) detectors by filtering out potential malicious sensors with the knowledge of the fraction of Byzantine nodes in the network. Simulation results show the superiority of proposed enhanced detectors over LMPTRS and GLRTRS detectors.

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Chen Quan, Baocheng Geng, Yunghsiang S. Han, Pramod K. Varshney

This paper proposes a belief-updating scheme in a human-machine collaborative decision-making network to combat Byzantine attacks. A hierarchical framework is used to realize the network where local decisions from physical sensors act as reference decisions to improve the quality of human sensor decisions. During the decision-making process, the belief that each physical sensor is malicious is updated. The case when humans have side information available is investigated, and its impact is analyzed. Simulation results substantiate that the proposed scheme can significantly improve the quality of human sensor decisions, even when most physical sensors are malicious. Moreover, the performance of the proposed method does not necessarily depend on the knowledge of the actual fraction of malicious physical sensors. Consequently, the proposed scheme can effectively defend against Byzantine attacks and improve the quality of human sensors' decisions so that the performance of the human-machine collaborative system is enhanced.

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Nandan Sriranga, Baocheng Geng, Pramod K. Varshney

In this work, we consider a binary hypothesis testing problem involving a group of human decision-makers. Due to the nature of human behavior, each human decision-maker observes the phenomenon of interest sequentially up to a random length of time. The humans use a belief model to accumulate the log-likelihood ratios until they cease observing the phenomenon. The belief model is used to characterize the perception of the human decision-maker towards observations at different instants of time, i.e., some decision-makers may assign greater importance to observations that were observed earlier, rather than later and vice-versa. The global decision-maker is a machine that fuses human decisions using the Chair-Varshney rule with different weights for the human decisions, where the weights are determined by the number of observations that were used by the humans to arrive at their respective decisions.

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Baocheng Geng, Chen Quan, Tianyun Zhang, Makan Fardad, Pramod K. Varshney

This work considers a Bayesian signal processing problem where increasing the power of the probing signal may cause risks or undesired consequences. We employ a market based approach to solve energy management problems for signal detection while balancing multiple objectives. In particular, the optimal amount of resource consumption is determined so as to maximize a profit-loss based expected utility function. Next, we study the human behavior of resource consumption while taking individuals' behavioral disparity into account. Unlike rational decision makers who consume the amount of resource to maximize the expected utility function, human decision makers act to maximize their subjective utilities. We employ prospect theory to model humans' loss aversion towards a risky event. The amount of resource consumption that maximizes the humans' subjective utility is derived to characterize the actual behavior of humans. It is shown that loss attitudes may lead the human to behave quite differently from a rational decision maker.

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Baocheng Geng, Pramod K. Varshney

Recently, modeling of decision making and control systems that include heterogeneous smart sensing devices (machines) as well as human agents as participants is becoming an important research area due to the wide variety of applications including autonomous driving, smart manufacturing, internet of things, national security, and healthcare. To accomplish complex missions under uncertainty, it is imperative that we build novel human machine collaboration structures to integrate the cognitive strengths of humans with computational capabilities of machines in an intelligent manner. In this paper, we present an overview of the existing works on human decision making and human machine collaboration within the scope of signal processing and information fusion. We review several application areas and research domains relevant to human machine collaborative decision making. We also discuss current challenges and future directions in this problem domain.

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Chen Quan, Nandan Sriranga, Haodong Yang, Yunghsiang S. Han, Baocheng Geng, Pramod K. Varshney

In distributed detection systems, energy-efficient ordered transmission (EEOT) schemes are able to reduce the number of transmissions required to make a final decision. In this work, we investigate the effect of data falsification attacks on the performance of EEOT-based systems. We derive the probability of error for an EEOT-based system under attack and find an upper bound (UB) on the expected number of transmissions required to make the final decision. Moreover, we tighten this UB by solving an optimization problem via integer programming (IP). We also obtain the FC's optimal threshold which guarantees the optimal detection performance of the EEOT-based system. Numerical and simulation results indicate that it is possible to reduce transmissions while still ensuring the quality of the decision with an appropriately designed threshold.

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Chen Quan, Yunghsiang S. Han, Baocheng Geng, Pramod K. Varshney

In this paper, two reputation based algorithms called Reputation and audit based clustering (RAC) algorithm and Reputation and audit based clustering with auxiliary anchor node (RACA) algorithm are proposed to defend against Byzantine attacks in distributed detection networks when the fusion center (FC) has no prior knowledge of the attacking strategy of Byzantine nodes. By updating the reputation index of the sensors in cluster-based networks, the system can accurately identify Byzantine nodes. The simulation results show that both proposed algorithms have superior detection performance compared with other algorithms. The proposed RACA algorithm works well even when the number of Byzantine nodes exceeds half of the total number of sensors in the network. Furthermore, the robustness of our proposed algorithms is evaluated in a dynamically changing scenario, where the attacking parameters change over time. We show that our algorithms can still achieve superior detection performance.

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Shan Zhang, Pranay Sharma, Baocheng Geng, Pramod K. Varshney

We consider the problem of collaborative distributed estimation in a large scale sensor network with statistically dependent sensor observations. In collaborative setup, the aim is to maximize the overall estimation performance by modeling the underlying statistical dependence and efficiently utilizing the deployed sensors. To achieve greater sensor transmission and estimation efficiency, we propose a two step group-based collaborative distributed estimation scheme, where in the first step, sensors form dependence driven groups such that sensors in the same group are highly dependent, while sensors from different groups are independent, and perform a copula-based maximum a posteriori probability (MAP) estimation via intragroup collaboration. In the second step, the estimates generated in the first step are shared via inter-group collaboration to reach an average consensus. A merge based K-medoid dependence driven grouping algorithm is proposed. Moreover, we further propose a group-based sensor selection scheme using mutual information prior to the estimation. The aim is to select sensors with maximum relevance and minimum redundancy regarding the parameter of interest under certain pre-specified energy constraint. Also, the proposed group-based sensor selection scheme is shown to be equivalent to the global/non-group based selection scheme with high probability, but computationally more efficient. Numerical experiments are conducted to demonstrate the effectiveness of our approach.

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Chen Quan, Saikiran Bulusu, Baocheng Geng, Pramod K. Varshney

The ordered transmission (OT) scheme reduces the number of transmissions needed in the network to make the final decision, while it maintains the same probability of error as the system without using OT scheme. In this paper, we investigate the performance of the system using OT scheme in the presence of Byzantine attacks for binary hypothesis testing problem. We analyze the probability of error for the system under attack and evaluate the number of transmissions saved using Monte Carlo method. We also derive the bounds for the number of transmissions saved in the system under attack. The optimal attacking strategy for the OT-based system is investigated. Simulation results show that the Byzantine attacks have significant impact on the number of transmissions saved even when the signal strength is sufficiently large.

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