  The problems of selecting partial correlation and causality graphs for count
data are considered. A parameter driven generalized linear model is used to
describe the observed multivariate time series of counts. Partial correlation
and causality graphs corresponding to this model explain the dependencies
between each time series of the multivariate count data. In order to estimate
these graphs with tunable sparsity, an appropriate likelihood function
maximization is regularized with an l1-type constraint. A novel MCEM algorithm
is proposed to iteratively solve this regularized MLE. Asymptotic convergence
results are proved for the sequence generated by the proposed MCEM algorithm
with l1-type regularization. The algorithm is first successfully tested on
simulated data. Thereafter, it is applied to observed weekly dengue disease
counts from each ward of Greater Mumbai city. The interdependence of various
wards in the proliferation of the disease is characterized by the edges of the
inferred partial correlation graph. On the other hand, the relative roles of
various wards as sources and sinks of dengue spread is quantified by the number
and weights of the directed edges originating from and incident upon each ward.
From these estimated graphs, it is observed that some special wards act as
epicentres of dengue spread even though their disease counts are relatively
low.
