In this paper, we present a general machine learning approach to the problem of deciding when to share probabilistic beliefs between agents for distributed monitoring. Our approach can generally be applied to domains that use a probabilistic model for evaluating hypotheses, and have a method for combining beliefs from multiple agents. We demonstrate the effectiveness of our approach in a concrete application in network intrusion detection as an example of a multi-agent monitoring problem. Based on an evaluation using packet trace data from a real network, we demonstrate that our learning approach can reduce both the delay and communication overhead required to detect network intrusions.