Unsupervised robust nonparametric learning of hidden community properties

We consider learning of fundamental properties of communities in large noisy networks, in the prototypical situation where the nodes or users are split into two classes according to a binary property, e.g., according to their opinions or preferences on a topic. For learning these properties, we propose a nonparametric, unsupervised, and scalable graph scan procedure that is, in addition, robust against a class of powerful adversaries. In our setup, one of the communities can fall under the influence of a knowledgeable adversarial leader, who knows the full network structure, has unlimited computational resources and can completely foresee our planned actions on the network. We prove strong consistency of our results in this setup with minimal assumptions. In particular, the learning procedure estimates the baseline activity of normal users asymptotically correctly with probability 1; the only assumption being the existence of a single implicit community of asymptotically negligible logarithmic size. We provide experiments on real and synthetic data to illustrate the performance of our method, including examples with adversaries.Comment: Experiments with new types of adversaries adde

Secure State Estimation in the Presence of False Information Injection Attacks

In this dissertation, we first investigate the problem of source location estimation in wireless sensor networks (WSNs) based on quantized data in the presence of false information attacks. Using a Gaussian mixture to model the possible attacks, we develop a maximum likelihood estimator (MLE) to estimate the source location. The Cramer-Rao lower bound (CRLB) for this estimation problem is also derived. Then, the assumption that the fusion center does not have the knowledge of the attack probability and the attack noise power investigated. We assume that the attack probability and power are random variables which follow certain uniform distributions. We derive the MLE for the localization problem. The CRLB for this estimation problem is also derived. It is shown that the proposed estimator is robust in various cases with different attack probabilities and parameter mismatch. The linear state estimation problem subjected to False Information Injection is also considered. The relationship between the attacker and the defender is modeled from a minimax perspective, in which the attacker tries to maximize the cost function. On the other hand, the defender tries to optimize the detection threshold selection to minimize the cost function. We consider that the attacker will attack with deterministic bias, then we also considered the random bias. In both cases, we derive the probabilities of detection and miss, and the probability of false alarm is derived based on the Chi squared distribution. We solve the minimax optimization problem numerically for both the cases