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Algebraic Dimensional Reduction for the Fellegi-Sunter Model in Record Linkage and General Parameter Input Specification for BigMatch

Written by:
RRS2025-04

Abstract

The Fellegi-Sunter model for record linkage can be framed as a latent class model. As such, it is vulnerable to convergence to boundary estimates when attempting to maximize the likelihood. Boundary estimates are the result of attempting to maximize a likelihood that is not strictly convex. In the context of identifiable log-linear models, Fienberg and Rinaldo propose a theory for extending classic exponential models to allow the estimation of dimensionally-collapsed parameter spaces. We recast the ideas of Fienberg and Rinaldo in the context of the Fellegi-Sunter model and we suggest a related approach based on computing dimensionally-reduced toric varieties in the associated linear algebra. This approach leads to fully parameterized applications of the Fellegi-Sunter model in record-linkage situations where parameters are not nominally estimable.

Page Last Revised - September 10, 2025