Discovering knowledge about which types of events influence others, using datasets of event sequences without time stamps, has several practical applications. While neural sequence models are able to capture complex and potentially long-range historical dependencies, they often lack the interpretability of simpler models for event sequence dynamics. We provide a novel neural framework in such a setting – a probabilistic attention-to-influence neural model – which not only captures complex instance-wise interactions between events but also learns influencers for each event type of interest. Given event sequence data and a prior distribution on type-wise influence, we efficiently learn an approximate posterior for type-wise influence by an attention-to-influence transformation using variational inference. Our method subsequently models the conditional likelihood of sequences by sampling the above posterior to focus attention on influencing event types. We motivate our general framework and show improved performance in experiments compared to existing baselines on synthetic data as well as real-world benchmarks, for tasks involving prediction and influencing set identification.