Title: Bayesian Network Regularized Regression for Modeling Urban Crime Occurrences,
Abstract: This paper considers the problem of statistical inference and prediction for
processes defined on networks. We assume that the network is known and measures
similarity, and our goal is to learn about an attribute associated with its
vertices. Classical regression methods are not immediately applicable to this
setting, as we would like our model to incorporate information from both
network structure and pertinent covariates. Our proposed model consists of a
generalized linear model with vertex indexed predictors and a basis expansion
of their coefficients, allowing the coefficients to vary over the network. We
employ a regularization procedure, cast as a prior distribution on the
regression coefficients under a Bayesian setup, so that the predicted responses
vary smoothly according to the topology of the network. We motivate the need
for this model by examining occurrences of residential burglary in Boston,
Massachusetts. Noting that crime rates are not spatially homogeneous, and that
the rates appear to vary sharply across regions in the city, we construct a
hierarchical model that addresses these issues and gives insight into spatial
patterns of crime occurrences. Furthermore, we examine efficient
expectation-maximization fitting algorithms and provide
computationally-friendly methods for eliciting hyper-prior parameters.