  Entity resolution (ER), comprising record linkage and de-duplication, is the
process of merging noisy databases in the absence of unique identifiers to
remove duplicate entities. One major challenge of analysis with linked data is
identifying a representative record among determined matches to pass to an
inferential or predictive task, referred to as the \emph{downstream task}.
Additionally, incorporating uncertainty from ER in the downstream task is
critical to ensure proper inference. To bridge the gap between ER and the
downstream task in an analysis pipeline, we propose five methods to choose a
representative (or canonical) record from linked data, referred to as
canonicalization. Our methods are scalable in the number of records,
appropriate in general data scenarios, and provide natural error propagation
via a Bayesian canonicalization stage. The proposed methodology is evaluated on
three simulated data sets and one application -- determining the relationship
between demographic information and party affiliation in voter registration
data from the North Carolina State Board of Elections. We first perform
Bayesian ER and evaluate our proposed methods for canonicalization before
considering the downstream tasks of linear and logistic regression. Bayesian
canonicalization methods are empirically shown to improve downstream inference
in both settings through prediction and coverage.
