Schema-Free Truth Discovery via Wasserstein Barycenters

Truth discovery methods aim to recover reliable values from
multiple conflicting sources, but most existing approaches assume that
observations can be aligned through shared keys or aggregated onto
a common grid before fusion. This assumption breaks down in multi
granular settings, where sources report over different spatial or tem
poral resolutions and direct key matching is unavailable or lossy. We
propose GeoTD, a schema-free truth discovery framework that mod
els each source as a probability measure and estimates consensus truth
as a reliability-weighted Wasserstein barycenter. In this formulation,
disagreement between sources is measured through optimal transport,
which captures both value differences and displacement across supports
without requiring prior alignment. We derive a joint objective that cou
ples barycenter estimation with source reliability learning and solve it
using an entropically regularized Sinkhorn-based algorithm. Experiments
on a synthetic misalignment benchmark and on an open Mediterranean
SST bundle show that transport-based fusion improves substantially over
common-grid aggregation, while adaptive reliability weighting provides
additional gains when source quality differs across inputs.