We infer local relations of influence between networked entities from data on outcomes and assess the value of temporally richer data by characterizing the speed of learning when knowing the set of entities who take a particular action, versus when knowing the order that the entities take an action. We propose a parametric model of influence which captures directed pairwise interactions, formulate different variations of the learning problem, and provide theoretical guarantees for correct learning based on sets and sequences. The asymptotic gain of having access to richer temporal data for the speed of learning is thus quantified in terms of the gap between the derived asymptotic requirements under different data modes. Experiments on real data on mobile app installations quantify the improvement due to the availability of richer temporal data, and show that our maximum likelihood methodology recovers the underlying network well.