  We propose temporal Poisson square root graphical models (TPSQRs), a
generalization of Poisson square root graphical models (PSQRs) specifically
designed for modeling longitudinal event data. By estimating the temporal
relationships for all possible pairs of event types, TPSQRs can offer a
holistic perspective about whether the occurrences of any given event type
could excite or inhibit any other type. A TPSQR is learned by estimating a
collection of interrelated PSQRs that share the same template parameterization.
These PSQRs are estimated jointly in a pseudo-likelihood fashion, where Poisson
pseudo-likelihood is used to approximate the original more
computationally-intensive pseudo-likelihood problem stemming from PSQRs.
Theoretically, we demonstrate that under mild assumptions, the Poisson
pseudo-likelihood approximation is sparsistent for recovering the underlying
PSQR. Empirically, we learn TPSQRs from Marshfield Clinic electronic health
records (EHRs) with millions of drug prescription and condition diagnosis
events, for adverse drug reaction (ADR) detection. Experimental results
demonstrate that the learned TPSQRs can recover ADR signals from the EHR
effectively and efficiently.
