569 research outputs found
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
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
Fault-Tolerant Aggregation: Flow-Updating Meets Mass-Distribution
Flow-Updating (FU) is a fault-tolerant technique that has proved to be
efficient in practice for the distributed computation of aggregate functions in
communication networks where individual processors do not have access to global
information. Previous distributed aggregation protocols, based on repeated
sharing of input values (or mass) among processors, sometimes called
Mass-Distribution (MD) protocols, are not resilient to communication failures
(or message loss) because such failures yield a loss of mass. In this paper, we
present a protocol which we call Mass-Distribution with Flow-Updating (MDFU).
We obtain MDFU by applying FU techniques to classic MD. We analyze the
convergence time of MDFU showing that stochastic message loss produces low
overhead. This is the first convergence proof of an FU-based algorithm. We
evaluate MDFU experimentally, comparing it with previous MD and FU protocols,
and verifying the behavior predicted by the analysis. Finally, given that MDFU
incurs a fixed deviation proportional to the message-loss rate, we adjust the
accuracy of MDFU heuristically in a new protocol called MDFU with Linear
Prediction (MDFU-LP). The evaluation shows that both MDFU and MDFU-LP behave
very well in practice, even under high rates of message loss and even changing
the input values dynamically.Comment: 18 pages, 5 figures, To appear in OPODIS 201
Distributed Inference and Learning with Byzantine Data
We are living in an increasingly networked world with sensing networks of varying shapes and sizes: the network often comprises of several tiny devices (or nodes) communicating with each other via different topologies. To make the problem even more complicated, the nodes in the network can be unreliable due to a variety of reasons: noise, faults and attacks, thus, providing
corrupted data. Although the area of statistical inference has been an active area of research in the
past, distributed learning and inference in a networked setup with potentially unreliable components
has only gained attention recently. The emergence of big and dirty data era demands new
distributed learning and inference solutions to tackle the problem of inference with corrupted data.
Distributed inference networks (DINs) consist of a group of networked entities which acquire
observations regarding a phenomenon of interest (POI), collaborate with other entities in the network
by sharing their inference via different topologies to make a global inference. The central
goal of this thesis is to analyze the effect of corrupted (or falsified) data on the inference performance
of DINs and design robust strategies to ensure reliable overall performance for several
practical network architectures. Specifically, the inference (or learning) process can be that of detection
or estimation or classification, and the topology of the system can be parallel, hierarchical
or fully decentralized (peer to peer).
Note that, the corrupted data model may seem similar to the scenario where local decisions
are transmitted over a Binary Symmetric Channel (BSC) with a certain cross over probability,
however, there are fundamental differences. Over the last three decades, research community
has extensively studied the impact of transmission channels or faults on the distributed detection
system and related problems due to its importance in several applications. However, corrupted
(Byzantine) data models considered in this thesis, are philosophically different from the BSC or
the faulty sensor cases. Byzantines are intentional and intelligent, therefore, they can optimize
over the data corruption parameters. Thus, in contrast to channel aware detection, both the FC and
the Byzantines can optimize their utility by choosing their actions based on the knowledge of their
opponentâs behavior. Study of these practically motivated scenarios in the presence of Byzantines
is of utmost importance, and is missing from the channel aware detection and fault tolerant detection
literature. This thesis advances the distributed inference literature by providing fundamental
limits of distributed inference with Byzantine data and provides optimal counter-measures (using
the insights provided by these fundamental limits) from a network designerâs perspective. Note
that, the analysis of problems related to strategical interaction between Byzantines and network
designed is very challenging (NP-hard is many cases). However, we show that by utilizing the
properties of the network architecture, efficient solutions can be obtained. Specifically, we found
that several problems related to the design of optimal counter-measures in the inference context
are, in fact, special cases of these NP-hard problems which can be solved in polynomial time.
First, we consider the problem of distributed Bayesian detection in the presence of data falsification
(or Byzantine) attacks in the parallel topology. Byzantines considered in this thesis are those
nodes that are compromised and reprogrammed by an adversary to transmit false information to
a centralized fusion center (FC) to degrade detection performance. We show that above a certain
fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable
(or blind) of utilizing the sensor data for detection. When the fraction of Byzantines is not
sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies
for the Byzantines that most degrade the detection performance. Optimal attacking strategies
in certain cases have the minimax property and, therefore, the knowledge of these strategies has
practical significance and can be used to implement a robust detector at the FC.
In several practical situations, parallel topology cannot be implemented due to limiting factors,
such as, the FC being outside the communication range of the nodes and limited energy budget of
the nodes. In such scenarios, a multi-hop network is employed, where nodes are organized hierarchically
into multiple levels (tree networks). Next, we study the problem of distributed inference
in tree topologies in the presence of Byzantines under several practical scenarios. We analytically
characterize the effect of Byzantines on the inference performance of the system. We also look at
the possible counter-measures from the FCâs perspective to protect the network from these Byzantines.
These counter-measures are of two kinds: Byzantine identification schemes and Byzantine
tolerant schemes. Using learning based techniques, Byzantine identification schemes are designed
that learn the identity of Byzantines in the network and use this information to improve system
performance. For scenarios where this is not possible, Byzantine tolerant schemes, which use
game theory and error-correcting codes, are developed that tolerate the effect of Byzantines while
maintaining a reasonably good inference performance in the network.
Going a step further, we also consider scenarios where a centralized FC is not available. In
such scenarios, a solution is to employ detection approaches which are based on fully distributed
consensus algorithms, where all of the nodes exchange information only with their neighbors. For
such networks, we analytically characterize the negative effect of Byzantines on the steady-state
and transient detection performance of conventional consensus-based detection schemes. To avoid
performance deterioration, we propose a distributed weighted average consensus algorithm that is
robust to Byzantine attacks. Next, we exploit the statistical distribution of the nodesâ data to devise
techniques for mitigating the influence of data falsifying Byzantines on the distributed detection
system. Since some parameters of the statistical distribution of the nodesâ data might not be known
a priori, we propose learning based techniques to enable an adaptive design of the local fusion or
update rules.
The above considerations highlight the negative effect of the corrupted data on the inference
performance. However, it is possible for a system designer to utilize the corrupted data for networkâs
benefit. Finally, we consider the problem of detecting a high dimensional signal based on
compressed measurements with secrecy guarantees. We consider a scenario where the network
operates in the presence of an eavesdropper who wants to discover the state of the nature being
monitored by the system. To keep the data secret from the eavesdropper, we propose to use cooperating
trustworthy nodes that assist the FC by injecting corrupted data in the system to deceive the
eavesdropper. We also design the system by determining the optimal values of parameters which
maximize the detection performance at the FC while ensuring perfect secrecy at the eavesdropper
Distributed Detection over Noisy Networks: Large Deviations Analysis
We study the large deviations performance of consensus+innovations
distributed detection over noisy networks, where sensors at a time step k
cooperate with immediate neighbors (consensus) and assimilate their new
observations (innovation.) We show that, even under noisy communication,
\emph{all sensors} can achieve exponential decay e^{-k C_{\mathrm{dis}}} of the
detection error probability, even when certain (or most) sensors cannot detect
the event of interest in isolation. We achieve this by designing a single time
scale stochastic approximation type distributed detector with the optimal
weight sequence {\alpha_k}, by which sensors weigh their neighbors' messages.
The optimal design of {\alpha_k} balances the opposing effects of communication
noise and information flow from neighbors: larger, slowly decaying \alpha_k
improves information flow but injects more communication noise. Further, we
quantify the best achievable C_{\mathrm{dis}} as a function of the sensing
signal and noise, communication noise, and network connectivity. Finally, we
find a threshold on the communication noise power below which a sensor that can
detect the event in isolation still improves its detection by cooperation
through noisy links.Comment: 30 pages, journal, submitted August 2nd, 201
Quantized Consensus by the Alternating Direction Method of Multipliers: Algorithms and Applications
Collaborative in-network processing is a major tenet in the fields of control, signal processing, information theory, and computer science. Agents operating in a coordinated fashion can gain greater efficiency and operational capability than those perform solo missions. In many such applications the central task is to compute the global average of agents\u27 data in a distributed manner. Much recent attention has been devoted to quantized consensus, where, due to practical constraints, only quantized communications are allowed between neighboring nodes in order to achieve the average consensus. This dissertation aims to develop efficient quantized consensus algorithms based on the alternating direction method of multipliers (ADMM) for networked applications, and in particular, consensus based detection in large scale sensor networks.
We study the effects of two commonly used uniform quantization schemes, dithered and deterministic quantizations, on an ADMM based distributed averaging algorithm. With dithered quantization, this algorithm yields linear convergence to the desired average in the mean sense with a bounded variance. When deterministic quantization is employed, the distributed ADMM either converges to a consensus or cycles with a finite period after a finite-time iteration. In the cyclic case, local quantized variables have the same sample mean over one period and hence each node can also reach a consensus. We then obtain an upper bound on the consensus error, which depends only on the quantization resolution and the average degree of the network. This is preferred in large scale networks where the range of agents\u27 data and the size of network may be large.
Noticing that existing quantized consensus algorithms, including the above two, adopt infinite-bit quantizers unless a bound on agents\u27 data is known a priori, we further develop an ADMM based quantized consensus algorithm using finite-bit bounded quantizers for possibly unbounded agents\u27 data. By picking a small enough ADMM step size, this algorithm can obtain the same consensus result as using the unbounded deterministic quantizer. We then apply this algorithm to distributed detection in connected sensor networks where each node can only exchange information with its direct neighbors. We establish that, with each node employing an identical one-bit quantizer for local information exchange, our approach achieves the optimal asymptotic performance of centralized detection. The statement is true under three different detection frameworks: the Bayesian criterion where the maximum a posteriori detector is optimal, the Neyman-Pearson criterion with a constant type-I error constraint, and the Neyman-Pearson criterion with an exponential type-I error constraint. The key to achieving optimal asymptotic performance is the use of a one-bit deterministic quantizer with controllable threshold that results in desired consensus error bounds
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