Hypergraph effects in event streams are difficult to estimate because a group-level burst can often be explained either by direct higher-order excitation or by a collection of ordinary pairwise Hawkes interactions. This paper studies maximum-likelihood estimation for a hyperedge-triggered Hawkes process, in which the conditional intensity is excited both by individual past events and by the completion of a multi-node firing pattern within a short temporal window. We derive a closed-form EM algorithm based on latent branching responsibilities and a piecewise compensator for the most-recent-anchor hyperedge mechanism. The compensator corrects the naive integral that overcounts superseded pattern completions. For independently parameterised candidate hyperedges, the EM updates are closed form; when a low-rank CP parameterisation is imposed, the hyperedge factors are updated by block-coordinate ascent on the same expected complete-data objective, yielding a generalised EM implementation. Synthetic experiments show near-unbiased recovery under a time-rescaling-validated simulator, stable EM convergence, identifiable trigger-window structure, and the expected O(n^2) event-count scaling of the prototype implementation. The main statistical limitation is not numerical optimisation but identifiability: when pairwise and hyperedge components are supported on the same co-firing events, likelihood gains can be hard to attribute. Held-out analyses on retina and primary visual-cortex spike-train datasets show stable positive candidate-count BIC differences for the two cortical datasets and more fragile evidence for the retina dataset as the candidate set expands. Code and reproducibility scripts are available at https://github.com/Hanii0210/hypergraph-hawkes.

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