In many real-world networks, nodes have class labels, attributes, or variables that affect the network's topology. If the topology of the network is known but the labels of the nodes are hidden, we would like to select a small subset of nodes such that, if we knew their labels, we could accurately predict the labels of all the other nodes. We develop an active learning algorithm for this problem which uses information-theoretic techniques to choose which nodes to explore. We test our algorithm on networks from three different domains: a social network, a network of English words that appear adjacently in a novel, and a marine food web. Our algorithm makes no initial assumptions about how the groups connect, and performs well even when faced with quite general types of network structure. In particular, we do not assume that nodes of the same class are more likely to be connected to each other---only that they connect to the rest of the network in similar ways.
Learning can be made more efficient if we can actively select particularly salient data points. Within a Bayesian learning framework, objective functions are discussed that measure the expected informativeness of candidate measurements. Three alternative specifications of what we want to gain information about lead to three different criteria for data selection. All these criteria depend on the assumption that the hypothesis space is correct, which may prove to be their main weakness.  An "active learning system" will sequentially decide which unlabeled instance to label, with the goal of efficiently gathering the information necessary to produce a good classifier. Some such systems greedily select the next instance based only on properties of that instance and the few currently labeled points -- e.g., selecting the one closest to the current classification boundary. Unfortunately, these approaches ignore the valuable information contained in the other unlabeled instances, which can help identify a good classifier much faster. For the previous approaches that do exploit this unlabeled data, this information is mostly used in a conservative way. One common property of the approaches in the literature is that the active learner sticks to one single query selection criterion in the whole process. We propose a system, MM+M, that selects the query instance that is able to provide the maximum conditional mutual information about the labels of the unlabeled instances, given the labeled data, in an optimistic way. This approach implicitly exploits the discriminative partition information contained in the unlabeled data. Instead of using one selection criterion, MM+M also employs a simple on-line method that changes its selection rule when it encounters an "unexpected label". Our empirical results demonstrate that this new approach works effectively.