Fully distributed data mining algorithms build global models over large amounts of data distributed over a large number of peers in a network, without moving the data itself. In the area of peer-to-peer (P2P) networks, such algorithms have various applications in P2P social networking, and also in trackerless BitTorrent communities. The difficulty of the problem involves realizing good quality models with an affordable communication complexity, while assuming as little as possible about the communication model. Here we describe a conceptually simple, yet powerful generic approach for designing efficient, fully distributed, asynchronous, local algorithms for learning models of fully distributed data. The key idea is that many models perform a random walk over the network while being gradually adjusted to fit the data they encounter, using a stochastic gradient descent search. We demonstrate our approach by implementing the support vector machine (SVM) method and by experimentally evaluating its performance in various failure scenarios over different benchmark datasets. Our algorithm scheme can implement a wide range of machine learning methods in an extremely robust manner.