The energy scaling laws of multihop data fusion networks for distributed inference are considered. The fusion network consists of randomly located sensors distributed i.i.d. according to a general spatial distribution in an expanding region. Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field (MRF) hypotheses, the scheme with minimum average energy consumption is bounded below by average energy of fusion along the minimum spanning tree, and above by a suboptimal scheme, referred to as Data Fusion for Markov Random Fields (DFMRF). Scaling laws are derived for the optimal and suboptimal fusion policies. It is shown that the average asymptotic energy of the DFMRF scheme is finite for a class of MRF models.
Regret-weighted Bayes Fusion for Distributed Experimental Design
Fariborz Maseeh Department of Mathematics and Statistics, Portland State University（波特兰州立大学）；AI Innovation Institute, Stony Brook University（石溪大学人工智能创新研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Department of Electrical Engineering and Computer Science, Syracuse University（雪城大学）
This paper studies the impact of interactive fusion on detection performance in tandem fusion networks with conditionally independent observations. Within the Neyman-Pearson framework, two distinct regimes are considered: the fixed sample size test and the large sample test. For the former, it is established that interactive distributed detection may strictly outperform the one-way tandem fusion structure. However, for the large sample regime, it is shown that interactive fusion has no improvement on the asymptotic performance characterized by the Kullback-Leibler (KL) distance compared with t…
Distributed Experimental Design: Bayes-optimal Fusion of Local Designs
Portland State University（波特兰州立大学）；AI Innovation Institute, Stony Brook University（石溪大学人工智能创新研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Syracuse University（雪城大学）
We develop a new algorithm for activity detection for grant-free multiple access in distributed multiple-input multiple-output (MIMO). The algorithm is a distributed version of the approximate message passing (AMP) based on a soft combination of likelihood ratios computed independently at multiple access points. The underpinning theoretical basis of our algorithm is a new observation that we made about the state evolution in the AMP. Specifically, with a minimum mean-square error denoiser, the state maintains a block-diagonal structure whenever the covariance matrices of the signals have such …
We consider the problem of soft decision fusion in a bandwidth-constrained wireless sensor network (WSN). The WSN is tasked with the detection of an intruder transmitting an unknown signal over a fading channel. A binary hypothesis testing is performed using the soft decision of the sensor nodes (SNs). Using the likelihood ratio test, the optimal soft fusion rule at the fusion center (FC) has been shown to be the weighted distance from the soft decision mean under the null hypothesis. But as the optimal rule requires a-priori knowledge that is difficult to attain in practice, suboptimal fusion…
In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learni…
Finding optimal weights for the problem of Fastest Distributed Consensus on networks with different topologies has been an active area of research for a number of years. Here in this work we present an analytical solution for the problem of Fastest Distributed Consensus for a network formed from fusion of two different symmetric star networks or in other words a network consists of two different symmetric star networks which share the same central node. The solution procedure consists of stratification of associated connectivity graph of network and Semidefinite Programming (SDP), particularly…
A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. It is shown that for zero-mean c…
This paper considers the problem of binary distributed detection of a known signal in correlated Gaussian sensing noise in a wireless sensor network, where the sensors are restricted to use likelihood ratio test (LRT), and communicate with the fusion center (FC) over bandwidth-constrained channels that are subject to fading and noise. To mitigate the deteriorating effect of fading encountered in the conventional parallel fusion architecture, in which the sensors directly communicate with the FC, we propose new fusion architectures that enhance the detection performance, via harvesting cooperat…
In this paper, we disclose the statistical behavior of the max-product algorithm configured to solve a maximum a posteriori (MAP) estimation problem in a network of distributed agents. Specifically, we first build a distributed hypothesis test conducted by a max-product iteration over a binary-valued pairwise Markov random field and show that the decision variables obtained are linear combinations of the local log-likelihood ratios observed in the network. Then, we use these linear combinations to formulate the system performance in terms of the false-alarm and detection probabilities. Our fin…
We study the utility of social learning in a distributed detection model with agents sharing the same goal: a collective decision that optimizes an agreed upon criterion. We show that social learning is helpful in some cases but is provably futile (and thus essentially a distraction) in other cases. Specifically, we consider Bayesian binary hypothesis testing performed by a distributed detection and fusion system, where all decision-making agents have binary votes that carry equal weight. Decision-making agents in the team sequentially make local decisions based on their own private signals an…
Distributed detection fusion with high-dimension conditionally dependent observations is known to be a challenging problem. When a fusion rule is fixed, this paper attempts to make progress on this problem for the large sensor networks by proposing a new Monte Carlo framework. Through the Monte Carlo importance sampling, we derive a necessary condition for optimal sensor decision rules in the sense of minimizing the approximated Bayesian cost function. Then, a Gauss-Seidel/person-by-person optimization algorithm can be obtained to search the optimal sensor decision rules. It is proved that the…
Cooperative spectrum sensing is a robust strategy that enhances the detection probability of primary licensed users. However, a large number of detectors reporting to a fusion center for a final decision causes significant delay and also presumes the availability of unreasonable communication resources at the disposal of a network searching for spectral opportunities. In this work, we employ the idea of sequential detection to obtain a quick, yet reliable, decision regarding primary activity. Local detectors take measurements, and only a few of them transmit the log likelihood ratios (LLR) to …
This paper proposes an energy-efficient counting rule for distributed detection by ordering sensor transmissions in wireless sensor networks. In the counting rule-based detection in an $N-$sensor network, the local sensors transmit binary decisions to the fusion center, where the number of all $N$ local-sensor detections are counted and compared to a threshold. In the ordering scheme, sensors transmit their unquantized statistics to the fusion center in a sequential manner; highly informative sensors enjoy higher priority for transmission. When sufficient evidence is collected at the fusion ce…
We study distributed coding of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a distributed framework for realizing optimized quantizer that enables encoding CS measurements of correlated sparse sources followed by joint decoding at a fusion center. The optimality of VQ encoder-decoder pairs is addressed by minimizing the sum of mean-square errors between the sparse sources and their reconstruction vectors at the fusion center. We derive a lower-bound on the end-to-end performance of the studied distributed system, and propose a practical encoder-decoder design th…
Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion
School of Sciences, University of Salamanca（萨拉曼卡大学理学院）；Institute of Telecommunications, Vienna University of Technology（维也纳工业大学电信研究所）；School of Mechanical Engineering, Northwestern Polytechnical University（西北工业大学机械工程学院）
In a multicell multiuser MIMO downlink employing random beamforming as the transmission scheme, the heterogeneous large scale channel effects of intercell and intracell interference complicate analysis of distributed scheduling based systems. In this paper, we extend the analysis in [1] and [2] to study the aforementioned challenging scenario. The cumulative distribution function (CDF)-based scheduling policy utilized in [1] and [2] is leveraged to maintain fairness among users and simultaneously obtain multiuser diversity gain. The closed form expression of the individual sum rate for each us…
In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions (pdf) are not exactly known. The observations are quantized and are sent to the fusion center. The fusion center fuses the current quantized observations and makes a final decision. It also designs (updated) quantizers to be used at the sensors and the fusion rule based on all previous quantized observations. Information regarding updated quantizers is sent b…
As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar generalization performance metrics must be sacrificed in order to gain interpretability. Such arguments, however, fail to acknowledge that the overall decision-making system is composed of two entities: the learned model and a human who fuses together model outputs with his or her own information. As such, the relevant performance criteria should be for the entire s…
This paper is concerned with decentralized estimation of a Gaussian source using multiple sensors. We consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center, using the analog amplify and forwarding technique. The fusion centre reconstructs an MMSE estimate of the source based on the received measurements. A distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered. We derive asymptotic expressions for the expected distort…
Consider a distributed detection problem in which the underlying distributions of the observations are unknown; instead of these distributions, noisy versions of empirically observed statistics are available to the fusion center. These empirically observed statistics, together with source (test) sequences, are transmitted through different channels to the fusion center. The fusion center decides which distribution the source sequence is sampled from based on these data. For the binary case, we derive the optimal type-II error exponent given that the type-I error decays exponentially fast. The …
In this paper, we consider a distributed reception scenario where a transmitter broadcasts a signal to multiple geographically separated receive nodes over fading channels, and each node forwards a few bits representing a processed version of the received signal to a fusion center. The fusion center then tries to decode the transmitted signal based on the forwarded information from the receive nodes and possible channel state information. We show that there is a strong connection between the problem of minimizing a symbol error probability at the fusion center in distributed reception and chan…
This paper considers cooperative spectrum sensing algorithms for Cognitive Radios which focus on reducing the number of samples to make a reliable detection. We develop an energy efficient detector with low detection delay using decentralized sequential hypothesis testing. Our algorithm at the Cognitive Radios employs an asynchronous transmission scheme which takes into account the noise at the fusion center. We start with a distributed algorithm, DualSPRT, in which Cognitive Radios sequentially collect the observations, make local decisions using SPRT (Sequential Probability Ratio Test) and s…
The scaling laws of the achievable communication rates and the corresponding upper bounds of distributed reception in the presence of an interfering signal are investigated. The scheme includes one transmitter communicating to a remote destination via two relays, which forward messages to the remote destination through reliable links with finite capacities. The relays receive the transmission along with some unknown interference. We focus on three common settings for distributed reception, wherein the scaling laws of the capacity (the pre-log as the power of the transmitter and the interferenc…
In this paper we tackle distributed detection of a non-cooperative target with a Wireless Sensor Network (WSN). When the target is present, sensors observe an unknown random signal with amplitude attenuation depending on the distance between the sensor and the target (unknown) positions, embedded in white Gaussian noise. The Fusion Center (FC) receives sensors decisions through error-prone Binary Symmetric Channels (BSCs) and is in charge of performing a (potentially) more-accurate global decision. The resulting problem is a one-sided testing with nuisance parameters present only under the tar…
This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control. Each secondary user executes the derived power control policy in a distributed fashion by using local knowledge of its direct and interference channel gains such that the resulting aggregate (average) interference does not disrupt primary's communication. Then, the tight sum-rate scaling laws are derived as a function of the number of secondary users $N$ under…
Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame of subspaces) theory is a new area that has potential to be applied to problems in such fields as distributed sensing and parallel processing. Grassmannian fusion frames combine elements from both theories. A simple, novel construction of Grassmannian fusion frames with an extension to Grassmannian fusion frames with local frames shall be presented. Some co…
Motivated by sensor networks and other distributed settings, several models for distributed learning are presented. The models differ from classical works in statistical pattern recognition by allocating observations of an independent and identically distributed (i.i.d.) sampling process amongst members of a network of simple learning agents. The agents are limited in their ability to communicate to a central fusion center and thus, the amount of information available for use in classification or regression is constrained. For several basic communication models in both the binary classificatio…
Fusion of finite set distributions: Pointwise consistency and global cardinality
University of Edinburgh（爱丁堡大学）；National University of Singapore（新加坡国立大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University College London（伦敦大学学院）；Telecom-SudParis（巴黎电信学院）
Distributed estimation in the context of sensor networks is considered, where distributed agents are given a set of sensor measurements, and are tasked with estimating a target variable. A subset of sensors are assumed to be faulty. The objective is to minimize i) the mean square estimation error at each node (accuracy objective), and ii) the mean square distance between the estimates at each pair of nodes (consensus objective). It is shown that there is an inherent tradeoff between the former and latter objectives. Assuming a general stochastic model, the sensor fusion algorithm optimizing th…
