Research map / Learning theory and algorithms / Prediction and decision losses
H-Consistency Bounds for Surrogate Loss Minimizers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Restrict hypothesis set from all measurable functions (H_all) to linear hypotheses with bounded weights (H_lin) when deriving 0/1-loss bounds from surrogate excess error | Hinge surrogate, 0/1 loss · Theoretical (H-consistency bounds, linear hypotheses) | H-estimation error transformation / bound tightness | No clear effect |
| Add Massart's noise condition (|Δη(x)| ≥ β) to distribution-dependent bounds for quadratic, logistic, exponential surrogates with H_all | Quadratic, logistic, exponential surrogates with 0/1 loss · Theory under Massart's noise | bound exponent (square-root vs linear dependence) | Helped |
| Add Massart's noise condition to adversarial bounds for supremum-based hinge and sigmoid losses | Supremum-based hinge and sigmoid surrogates, adversarial 0/1 loss · Theory under Massart's noise | existence of non-trivial H-consistency bound | Helped |
| Use supremum-based sigmoid or hinge (no noise assumption) as adversarial surrogate with symmetric/convex losses, for regular hypothesis sets containing 0 | Supremum-based convex and symmetric surrogates, adversarial 0/1 loss · Theory, distribution-independent | best achievable function f in H-consistency bound | Hurt |
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