Exponential Convex Calibration Dimension for the Multi-Label Jaccard Measure
Exact Jaccard calibration in multi-label prediction is shown to need exponentially many surrogate coordinates.
Zhang proves the Jaccard loss matrices are nonsingular and have affine dimension `2^s - 1` for `s` labels. The paper bounds the convex calibration dimension between `2^(s-1)` and `2^s - 1`, making exact zero-regret calibration exponentially large. It also gives polynomial-size approximation routes, including an `F1`-to-Jaccard transfer and MinHash square-loss constructions with explicit regret floors. Source: ArXiv · AI/CL/LG's note
Zhang proves the Jaccard loss matrices are nonsingular and have affine dimension `2^s - 1` for `s` labels. The paper bounds the convex calibration dimension between `2^(s-1)` and `2^s - 1`, making exact zero-regret calibration exponentially large. It also gives polynomial-size approximation routes, including an `F1`-to-Jaccard transfer and MinHash square-loss constructions with explicit regret floors. Source: ArXiv · AI/CL/LG's note
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