Systems and methods establish groups among numerous indications of failure in order to infer a cause of failure common to each group. In one implementation, a system computes the groups such that each group has the maximum likelihood of resulting from a common failure. Indications of failure are grouped by probability, even when a group's inferred cause of failure is not directly observable in the system. In one implementation, related matrices provide a system for receiving numerous health indications from each of numerous autonomous systems connected with the Internet. A correlational matrix links input (failure symptoms) and output (known or unknown root causes) through probability-based hypothetical groupings of the failure indications. The matrices are iteratively refined according to self-consistency and parsimony metrics to provide most likely groupings of indicators and most likely causes of failure.