High throughput and high content screening involve determination of the effect of many compounds on a given target. As currently practiced, screening for each new target typically makes little use of information from screens of prior targets. Further, choices of compounds to advance to drug development are made without significant screening against off-target effects. The overall drug development process could be made more effective, as well as less expensive and time consuming, if potential effects of all compounds on all possible targets could be considered, yet the cost of such full experimentation would be prohibitive. In this paper, we describe a potential solution: probabilistic models that can be used to predict results for unmeasured combinations, and active learning algorithms for efficiently selecting which experiments to perform in order to build those models and determining when to stop. Using simulated and experimental data, we show that our approaches can produce powerful predictive models without exhaustive experimentation and can learn them much faster than by selecting experiments at random.