Unifying lower bounds on prediction dimension of convex surrogates

The convex consistency dimension of a supervised learning task is the lowest prediction dimension $d$ such that there exists a convex surrogate $L: \mathbb{R}^d \times \mathcal Y \to \mathbb R$ that is consistent for the given task. We present a new tool based on property elicitation, $d$-flats, for lower-bounding convex consistency dimension.