  Machine learning over fully distributed data poses an important problem in
peer-to-peer (P2P) applications. In this model we have one data record at each
network node, but without the possibility to move raw data due to privacy
considerations. For example, user profiles, ratings, history, or sensor
readings can represent this case. This problem is difficult, because there is
no possibility to learn local models, the system model offers almost no
guarantees for reliability, yet the communication cost needs to be kept low.
Here we propose gossip learning, a generic approach that is based on multiple
models taking random walks over the network in parallel, while applying an
online learning algorithm to improve themselves, and getting combined via
ensemble learning methods. We present an instantiation of this approach for the
case of classification with linear models. Our main contribution is an ensemble
learning method which---through the continuous combination of the models in the
network---implements a virtual weighted voting mechanism over an exponential
number of models at practically no extra cost as compared to independent random
walks. We prove the convergence of the method theoretically, and perform
extensive experiments on benchmark datasets. Our experimental analysis
demonstrates the performance and robustness of the proposed approach.
