Influence network reconstruction from discrete time-series of count data modelled by multidimensional Hawkes processes

The paper develops (i) an MM scheme for the discrete-time Hawkes count model by Jensen majorization of −∑k ΔN_k log λ_k, yielding decoupled, closed-form parameter updates (with a small-γ approximation in the denominator), and (ii) an ExPKF whose information-form update has a diagonal-plus-rank-1 structure enabling efficient and parallel per-node filtering. These are stated in their equations (3.1)–(3.6), (3.7)–(3.12) for MM and (4.1)–(4.6) for ExPKF, together with the known-decay assumption for ExPKF and per-row independence for MM. The candidate solution re-derives the same MM idea using explicit responsibilities and yields closed-form μ and α updates with exact ∑k s_{j,k} denominators, and it plugs the correct gradient/Hessian of log λ into the ExPKF. The only mismatch is computational: the paper shows the information update can be expressed as a diagonal term plus a rank-1 outer product without dropping the Hessian, while the candidate suggests dropping the residual-Hessian (OPG/Fisher) or a degenerate case to achieve rank-1. Both treat ‘structure recovery’ operationally/empirically rather than proving consistency. Overall, the approaches are substantially the same and correct, with minor differences in approximation/implementation details (paper: small-γ approximation in MM; model: optional OPG in ExPKF) .