Data association is a fundamental component of effective multi-object tracking. Current approaches to data-association tend to frame this as an assignment problem relying on gating and distance-based cost matrices, or offset the challenge of data association to a problem of tracking by detection. The latter is typically formulated as a supervised learning problem, and requires labelling information about tracked object identities to train a model for object recognition. This paper introduces an expectation maximisation approach to train neural models for data association, which does not require labelling information. Here, a Sinkhorn network is trained to predict assignment matrices that maximise the marginal likelihood of trajectory observations. Importantly, networks trained using the proposed approach can be re-used in downstream tracking applications.