2,901 research outputs found
Distributed Detection of Cycles
Distributed property testing in networks has been introduced by Brakerski and
Patt-Shamir (2011), with the objective of detecting the presence of large dense
sub-networks in a distributed manner. Recently, Censor-Hillel et al. (2016)
have shown how to detect 3-cycles in a constant number of rounds by a
distributed algorithm. In a follow up work, Fraigniaud et al. (2016) have shown
how to detect 4-cycles in a constant number of rounds as well. However, the
techniques in these latter works were shown not to generalize to larger cycles
with . In this paper, we completely settle the problem of cycle
detection, by establishing the following result. For every , there
exists a distributed property testing algorithm for -freeness, performing
in a constant number of rounds. All these results hold in the classical CONGEST
model for distributed network computing. Our algorithm is 1-sided error. Its
round-complexity is where is the property
testing parameter measuring the gap between legal and illegal instances
Distributed Detection over Random Networks: Large Deviations Performance Analysis
We study the large deviations performance, i.e., the exponential decay rate
of the error probability, of distributed detection algorithms over random
networks. At each time step each sensor: 1) averages its decision variable
with the neighbors' decision variables; and 2) accounts on-the-fly for its new
observation. We show that distributed detection exhibits a "phase change"
behavior. When the rate of network information flow (the speed of averaging) is
above a threshold, then distributed detection is asymptotically equivalent to
the optimal centralized detection, i.e., the exponential decay rate of the
error probability for distributed detection equals the Chernoff information.
When the rate of information flow is below a threshold, distributed detection
achieves only a fraction of the Chernoff information rate; we quantify this
achievable rate as a function of the network rate of information flow.
Simulation examples demonstrate our theoretical findings on the behavior of
distributed detection over random networks.Comment: 30 pages, journal, submitted on December 3rd, 201
Fusing Censored Dependent Data for Distributed Detection
In this paper, we consider a distributed detection problem for a censoring
sensor network where each sensor's communication rate is significantly reduced
by transmitting only "informative" observations to the Fusion Center (FC), and
censoring those deemed "uninformative". While the independence of data from
censoring sensors is often assumed in previous research, we explore spatial
dependence among observations. Our focus is on designing the fusion rule under
the Neyman-Pearson (NP) framework that takes into account the spatial
dependence among observations. Two transmission scenarios are considered, one
where uncensored observations are transmitted directly to the FC and second
where they are first quantized and then transmitted to further improve
transmission efficiency. Copula-based Generalized Likelihood Ratio Test (GLRT)
for censored data is proposed with both continuous and discrete messages
received at the FC corresponding to different transmission strategies. We
address the computational issues of the copula-based GLRTs involving
multidimensional integrals by presenting more efficient fusion rules, based on
the key idea of injecting controlled noise at the FC before fusion. Although,
the signal-to-noise ratio (SNR) is reduced by introducing controlled noise at
the receiver, simulation results demonstrate that the resulting noise-aided
fusion approach based on adding artificial noise performs very closely to the
exact copula-based GLRTs. Copula-based GLRTs and their noise-aided counterparts
by exploiting the spatial dependence greatly improve detection performance
compared with the fusion rule under independence assumption
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations
We establish the large deviations asymptotic performance (error exponent) of
consensus+innovations distributed detection over random networks with generic
(non-Gaussian) sensor observations. At each time instant, sensors 1) combine
theirs with the decision variables of their neighbors (consensus) and 2)
assimilate their new observations (innovations). This paper shows for general
non-Gaussian distributions that consensus+innovations distributed detection
exhibits a phase transition behavior with respect to the network degree of
connectivity. Above a threshold, distributed is as good as centralized, with
the same optimal asymptotic detection performance, but, below the threshold,
distributed detection is suboptimal with respect to centralized detection. We
determine this threshold and quantify the performance loss below threshold.
Finally, we show the dependence of the threshold and performance on the
distribution of the observations: distributed detectors over the same random
network, but with different observations' distributions, for example, Gaussian,
Laplace, or quantized, may have different asymptotic performance, even when the
corresponding centralized detectors have the same asymptotic performance.Comment: 30 pages, journal, submitted Nov 17, 2011; revised Apr 3, 201
Distributed Detection in Sensor Networks with Limited Range Sensors
We consider a multi-object detection problem over a sensor network (SNET)
with limited range sensors. This problem complements the widely considered
decentralized detection problem where all sensors observe the same object.
While the necessity for global collaboration is clear in the decentralized
detection problem, the benefits of collaboration with limited range sensors is
unclear and has not been widely explored. In this paper we develop a
distributed detection approach based on recent development of the false
discovery rate (FDR). We first extend the FDR procedure and develop a
transformation that exploits complete or partial knowledge of either the
observed distributions at each sensor or the ensemble (mixture) distribution
across all sensors. We then show that this transformation applies to
multi-dimensional observations, thus extending FDR to multi-dimensional
settings. We also extend FDR theory to cases where distributions under both
null and positive hypotheses are uncertain. We then propose a robust
distributed algorithm to perform detection. We further demonstrate scalability
to large SNETs by showing that the upper bound on the communication complexity
scales linearly with the number of sensors that are in the vicinity of objects
and is independent of the total number of sensors. Finally, we deal with
situations where the sensing model may be uncertain and establish robustness of
our techniques to such uncertainties.Comment: Submitted to IEEE Transactions on Signal Processin
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