Entity Resolution and Federated Learning get a Federated Resolution

Consider two data providers, each maintaining records of different feature sets about common entities. They aim to learn a linear model over the whole set of features. This problem of federated learning over vertically partitioned data includes a crucial upstream issue: entity resolution, i.e. finding the correspondence between the rows of the datasets. It is well known that entity resolution, just like learning, is mistake-prone in the real world. Despite the importance of the problem, there has been no formal assessment of how errors in entity resolution impact learning. In this paper, we provide a thorough answer to this question, answering how optimal classifiers, empirical losses, margins and generalisation abilities are affected. While our answer spans a wide set of losses --- going beyond proper, convex, or classification calibrated ---, it brings simple practical arguments to upgrade entity resolution as a preprocessing step to learning. One of these suggests that entity resolution should be aimed at controlling or minimizing the number of matching errors between examples of distinct classes. In our experiments, we modify a simple token-based entity resolution algorithm so that it indeed aims at avoiding matching rows belonging to different classes, and perform experiments in the setting where entity resolution relies on noisy data, which is very relevant to real world domains. Notably, our approach covers the case where one peer \textit{does not} have classes, or a noisy record of classes. Experiments display that using the class information during entity resolution can buy significant uplift for learning at little expense from the complexity standpoint.