Common Geodesics Do Not Guarantee Fisher Consistency of the Structured SVM: Minimal Counterexamples and a Tree-Metric Classification

A known necessary condition for Fisher consistency of the structured support vector machine requires the task loss to be a metric for which every output triple has a common geodesic point.

A known necessary condition for Fisher consistency of the structured support vector machine requires the task loss to be a metric for which every output triple has a common geodesic point. We show that this condition is not sufficient for the canonical coordinate-wise argmax…