Kailkhura, Bhavya, Ph.D., Syracuse University, “Distributed inference and learning with Byzantine data” (2017)

Kailkhura, Bhavya, Ph.D., SYRACUSE UNIVERSITY, “Distributed inference and learning with Byzantine data” (2017) Advisor: Varshney, Pramod K.

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).

First, the authors 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. The authors 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, the authors 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, the authors study the problem of distributed inference in tree topologies in the presence of Byzantines under several practical scenarios. The authors analytically characterize the effect of Byzantines on the inference performance of the system. The authors also look at the possible counter-measures from the FC’s 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, the authors 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.

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 network’s benefit. Finally, the authors consider the problem of detecting a high dimensional signal based on compressed measurements with secrecy guarantees. The authors 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, the authors propose to use cooperating trustworthy nodes that assist the FC by injecting corrupted data in the system to deceive the eavesdropper. The authors 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.