Data-driven functions for operation and management often require measurements collected through monitoring for model training and prediction. The number of data sources can be very large, which requires a significant communication and computing overhead to continuously extract and collect this data, as well as to train and update the machine-learning models. We present an online algorithm, called OSFS, that selects a small feature set from a large number of available data sources, which allows for rapid, low-overhead, and effective learning and prediction. OSFS is instantiated with a feature ranking algorithm and applies the concept of a stable feature set, which we introduce in the paper. We perform extensive, experimental evaluation of our method on data from an in-house testbed. We find that OSFS requires several hundreds measurements to reduce the number of data sources by two orders of magnitude, from which models are trained with acceptable prediction accuracy. While our method is heuristic and can be improved in many ways, the results clearly suggests that many learning tasks do not require a lengthy monitoring phase and expensive offline training.