Aditya Vempaty

Distributed Inference with Byzantine Data: State-of-the-Art Review on Data Falsification Attacks

In 1982, Lamport et al. presented the so-called Byzantine generals problem as follows: a group of generals of the Byzantine army camped with their troops around an enemy city. Communicating only by messenger, the generals must agree upon a common battle plan. However, one or more of them may be traitors who will try to confuse the others. The problem is to find an algorithm to ensure that the loyal generals will reach agreement. The authors gave a sharp characterization of the power of the Byzantine generals. It was shown that if the fraction of Byzantine generals is less than 1/3, there is a way for the loyal generals to reach a consensus agreement, regardless of what the Byzantine generals do. If the fraction is above 1/3, consensus can no longer be guaranteed. This article examines the Byzantine generals problem in the context of distributed inference, where data collected from remote locations are sent to a fusion center (FC) for processing and inference. The assumption is that the data are potentially tampered or falsified by some internal adversary who has the knowledge about the algorithm used at the FC. We refer to the problem considered as distributed inference with Byzantine data.

Adaptive learning of Byzantines' behavior in cooperative spectrum sensing

This paper considers the problem of Byzantine attacks on cooperative spectrum sensing in cognitive radio networks. Our major contribution is a technique to learn about the cognitive radio (CR) potential malicious behavior over time and thereby identifies the Byzantines and then estimates their probabilities of false alarm (Pfa) and detection (Pd). We show that for a given set of data over time, the Byzantines can be identified for any a (percentage of Byzantines). It has also been shown that these estimates of Pfa and Pn of the Byzantines are asymptotically unbiased and converge to their true values at the rate of 0(T–1/2). We then use these probabilities to adaptively design the fusion rule. We calculate the Probability of error (Qe) and compare it with the minimum probability of error possible.

Reliable Crowdsourcing for Multi-Class Labeling Using Coding Theory

Crowdsourcing systems often have crowd workers that perform unreliable work on the task they are assigned. In this paper, we propose the use of error-control codes and decoding algorithms to design crowdsourcing systems for reliable classification despite unreliable crowd workers. Coding theory based techniques also allow us to pose easy-to-answer binary questions to the crowd workers. We consider three different crowdsourcing models: systems with independent crowd workers, systems with peer-dependent reward schemes, and systems where workers have common sources of information. For each of these models, we analyze classification performance with the proposed coding-based scheme. We develop an ordering principle for the quality of crowds and describe how system performance changes with the quality of the crowd. We also show that pairing among workers and diversification of the questions help in improving system performance. We demonstrate the effectiveness of the proposed coding-based scheme using both simulated data and real datasets from Amazon Mechanical Turk, a crowdsourcing microtask platform. Results suggest that use of good codes may improve the performance of the crowdsourcing task over typical majority-voting approaches.

Target Localization in Wireless Sensor Networks Using Error Correcting Codes

In this paper, we consider the task of target localization using quantized data in wireless sensor networks. We propose a computationally efficient localization scheme by modeling it as an iterative classification problem. We design coding theory based iterative approaches for target localization where at every iteration, the fusion center (FC) solves an M-ary hypothesis testing problem and decides the region of interest for the next iteration. The coding theory based iterative approach works well even in the presence of Byzantine (malicious) sensors in the network. We further consider the effect of non-ideal channels. We suggest the use of soft-decision decoding to compensate for the loss due to the presence of fading channels between the local sensors and FC. We evaluate the performance of the proposed schemes in terms of the Byzantine fault tolerance capability and probability of detection of the target region. We also present performance bounds, which help us in designing the system. We provide asymptotic analysis of the proposed schemes and show that the schemes achieve perfect region detection irrespective of the noise variance when the number of sensors tends to infinity. Our numerical results show that the proposed schemes provide a similar performance in terms of mean square error as compared with the traditional maximum likelihood estimation but are computationally much more efficient and are resilient to errors due to Byzantines and non-ideal channels.

Energy-Aware Sensor Selection in Field Reconstruction

In this letter, a new sparsity-promoting penalty function is introduced for sensor selection problems in field reconstruction, which has the property of avoiding scenarios where the same sensors are successively selected. Using a reweighted ℓ1 relaxation of the ℓ0 norm, the sensor selection problem is reformulated as a convex quadratic program. In order to handle large-scale problems, we also present two fast algorithms: accelerated proximal gradient method and alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approaches.

On noise-enhanced distributed inference in the presence of Byzantines

The problem of Byzantine (malicious sensors) threats in a distributed detection framework for inference networks is addressed. Impact of Byzantines is mitigated by suitably adding Stochastic Resonance (SR) noise. Previously, Independent Malicious Byzantine Attack (IMBA), where each Byzantine decides to attack the network independently relying on its own observation was considered. In this paper, we present further results for Cooperative Malicious Byzantine Attack (CMBA), where Byzantines collaborate to make the decision and use this information for the attack. In order to analyze the network performance, we consider KL-Divergence (KLD) to quantify detection performance and minimum fraction of Byzantines needed to blind the network (αblind) as a security metric. We show that both KLD and αblind increase when SR noise is added at the honest sensors. When SR noise is added to the fusion center, we analytically show that there is no gain in terms of αblind or the network-wide performance measured in terms of the deflection coefficient. We also model a game between the network and the Byzantines and present a necessary condition for a strategy (SR noise) to be a saddle-point equilibrium.

Assuring privacy and reliability in crowdsourcing with coding

Crowd workers are often unreliable and anonymous. Hence there is a need to ensure reliable work delivery while preserving some level of privacy to the requesters data. For this purpose, we use a combination of random perturbation to mask the sensitive data and error-correcting codes for quality assurance. We also consider the possibility of collusion attacks by malicious crowd workers. We develop mathematical models to study the precise tradeoffs between task performance quality, level of privacy against collusion attacks, and cost of invoking a large crowd. Such a study provides design strategies and principles for crowd work. The use of classification codes may improve efficiency considerably. We also comment on the applicability of these techniques for scalable assessment in education via peer grading, e.g. for massive open online courses (MOOCs).

On Quantizer Design for Distributed Bayesian Estimation in Sensor Networks

We consider the problem of distributed estimation under the Bayesian criterion and explore the design of optimal quantizers in such a system. We show that, for a conditionally unbiased and efficient estimator at the fusion center and when local observations have identical distributions, it is optimal to partition the local sensors into groups, with all sensors within a group using the same quantization rule. When all the sensors use identical number of decision regions, use of identical quantizers at the sensors is optimal. When the network is constrained by the capacity of the wireless multiple access channel over which the sensors transmit their quantized observations, we show that binary quantizers at the local sensors are optimal under certain conditions. Based on these observations, we address the location parameter estimation problem and present our optimal quantizer design approach. We also derive the performance limit for distributed location parameter estimation under the Bayesian criterion and find the conditions when the widely used threshold quantizer achieves this limit. We corroborate this result using simulations. We then relax the assumption of conditionally independent observations and derive the optimality conditions of quantizers for conditionally dependent observations. Using counter-examples, we also show that the previous results do not hold in this setting of dependent observations and, therefore, identical quantizers are not optimal.

Reliable classification by unreliable crowds

We consider the use of error-control codes and decoding algorithms to perform reliable classification using unreliable and anonymous human crowd workers by adapting coding-theoretic techniques for the specific crowdsourcing application. We develop an ordering principle for the quality of crowds and describe how system performance changes with the quality of the crowd. We demonstrate the effectiveness of the proposed coding scheme using both simulated data and real datasets from Amazon Mechanical Turk, a crowdsourcing microtask platform. Results suggest that good codes may improve the performance of the crowdsourcing task over typical majority-vote approaches.

Target localization in Wireless Sensor Networks with quantized data in the presence of Byzantine attacks

Wireless Sensor Networks (WSNs) are vulnerable to Byzantine attacks in which malicious sensors send wrong data to the fusion center leading to an increase in the probability of incorrect inference. This paper considers Byzantine attacks for the location estimation task in wireless sensor networks where each sensor uses a binary quantization scheme to send binary data to the fusion center. Posterior Cramer-Rao lower Bound (PCRLB) metric and Fisher Information Matrix (FIM) are used to analyze the performance of the network in the presence of Byzantine attacks. We have considered two kinds of attack strategies, independent attacks (all the malicious sensors attack a WSN independently of each other) and collaborative attacks (all the malicious sensors communicate with each other and attack the WSN in a coordinated manner). We determine the fraction of Byzantine attackers in the network above which the fusion center becomes incapable of finding the location of the target. Optimal attacking strategy for given attacking resources is also proposed.