Research map / Optimization / Implicit bias and generalization
On Structured Prediction Theory with Calibrated Convex Surrogate Losses
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Constrain scores to contain the loss matrix column space | Quadratic surrogate · Structured prediction, arbitrary task loss | calibration function lower bound: ε^2/(2k max_{i≠j}||proj_S Δ_{ij}||_2^2) ≥ ε^2/(4k) | Helped |
| Use unconstrained scores instead of loss-structured constraints | Quadratic surrogate · Structured prediction, pseudometric task loss | calibration function: ε^2/(2k), 0 ≤ ε ≤ L_max | Hurt |
| Restrict scores to the smallest consistent score subspace | Quadratic surrogate · 0-1 loss | calibration function: ε^2/(4k) | Helped |
| Constrain scores to be equal within blocks | Quadratic surrogate · Block 0-1 loss | calibration function: ε^2/(4m), 0 ≤ ε ≤ 1 | Helped |
| Constrain scores to be separable | Quadratic surrogate · Hamming loss | calibration function: ε^2/(8h), 0 ≤ ε ≤ 1 | Helped |
| Use block-equal score constraints | Quadratic surrogate · Mixed 0-1 and block 0-1 loss | calibration function: 0 for ε ≤ η/2; for ε > η/2, of the order (1/m)(ε-η/2)^2 | Mixed |
| Use a structured loss rather than 0-1 loss | Quadratic surrogate with ASGD · Structured prediction | DM optimization constant: O(k) vs O(m) and O(log_2^3 k) | Helped |
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