Author

Mingyuan Zhang

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Preprint Aug 2026

Exponential Convex Calibration Dimension for the Multi-Label Jaccard Measure

The per-instance Jaccard score, or intersection over union (IoU), is standard in multi-label classification and binary segmentation. With $s$ labels, its loss matrix has $2^s$ outcomes and reports. Under the convention $\mathrm{Jac}(\varnothing,\varnothing)=1$, we prove that the Jaccard score, shifted-loss, and ordinar...

Mingyuan Zhang · 1 citation

Preprint Aug 2026

Exact Rank and Convex Calibration Dimension Lower Bounds for the Multi-Label F1 Loss

A distribution for which precisely all supersets of a fixed core label set are Bayes optimal, and it is shown that the corresponding active loss columns have affine dimension $hn$.

Mingyuan Zhang · 3 citations