  Modern health care systems are conducting continuous, automated surveillance
of the electronic medical record (EMR) to identify adverse events with
increasing frequency; however, many events such as sepsis do not have
elucidated prodromes (i.e., event chains) that can be used to identify and
intercept the adverse event early in its course. Clinically relevant and
interpretable results require a framework that can (i) infer temporal
interactions across multiple patient features found in EMR data (e.g., Labs,
vital signs, etc.) and (ii) identify patterns that precede and are specific to
an impending adverse event (e.g., sepsis). In this work, we propose a linear
multivariate Hawkes process model, coupled with ReLU link function, to recover
a Granger Causal (GC) graph with both exciting and inhibiting effects. We
develop a scalable two-phase gradient-based method to obtain a maximum
surrogate-likelihood estimator, which is shown to be effective via extensive
numerical simulation. Our method is subsequently extended to a data set of
patients admitted to Grady hospital system in Atlanta, GA, USA, where the
estimated GC graph identifies several highly interpretable GC chains that
precede sepsis. The code is available at
\url{https://github.com/SongWei-GT/two-phase-MHP}.
