A Practical Approach to Proper Inference with Linked Data

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.

💡 Research Summary

This paper addresses a critical but often overlooked step in data‑integration pipelines: the selection of a single representative record from each cluster of linked records produced by an entity‑resolution (ER) process. While ER merges duplicate records across noisy databases, downstream statistical or machine learning tasks (e.g., regression, classification) typically require a deduplicated data set. The authors formalize the notion of a “canonical record” as a function ψθ that maps a cluster and its raw fields to a single record, and a “canonical data set” as the collection of such records across all clusters.

Five unsupervised canonicalization methods are proposed. 1) Random selection draws a record from each cluster according to a user‑specified probability vector. 2) Composite aggregation constructs a synthetic record by field‑wise summarization (means for continuous variables, modes for categorical, medians for ordinal). 3) Frequency‑based selection picks the most common record (or most frequent combination of field values) within the cluster. 4) Weighted selection uses posterior linkage probabilities from a Bayesian ER model as weights to choose the record with the highest expected utility. 5) Bayesian canonicalization treats the canonicalization stage itself as a Bayesian inference problem: it propagates the posterior samples of the linkage structure directly into the selection of canonical records, thereby fully transmitting ER uncertainty to downstream analyses.

All methods scale linearly with the number of records; the Bayesian approach adds only a factor proportional to the number of posterior samples, making it feasible for datasets with hundreds of thousands of rows.

The authors evaluate the methods on three simulated scenarios and on a real‑world application: North Carolina voter registration data (NCVD) consisting of five yearly snapshots that contain multiple duplicate entries for the same voter. After performing Bayesian ER using the scalable model of Marchant et al. (2021), they apply each canonicalization technique and fit both linear and logistic regression models to study the relationship between demographic variables (race, sex, age) and party affiliation.

Simulation results show that Bayesian canonicalization yields the smallest bias in regression coefficients, the lowest mean‑squared error, and coverage of 95 % confidence intervals that are closest to the nominal level, outperforming the other four methods. In the NCVD analysis, Bayesian canonicalization achieves the highest predictive accuracy (AUC) and the narrowest credible intervals for the effect estimates, especially for minority groups where data are sparse. The composite and frequency methods perform reasonably well but do not capture ER uncertainty, leading to slightly over‑confident inference.

The paper argues that canonicalization is indispensable whenever downstream tasks require a single record per entity, and that propagating ER uncertainty through a Bayesian canonicalization stage markedly improves inferential validity. It also highlights the practical advantage of a two‑stage workflow: ER can be performed once, and the resulting posterior linkage structure can be reused for any number of downstream tasks without re‑running the computationally intensive ER model.

In conclusion, the authors contribute (i) a clear formal definition of canonical records and data sets, (ii) a suite of scalable unsupervised canonicalization algorithms, and (iii) empirical evidence that Bayesian canonicalization provides superior downstream inference by faithfully transmitting linkage uncertainty. They suggest future work on joint modeling of canonicalization and downstream tasks, and extensions to non‑tabular data such as text or images.