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Regression with Multi-Expert Deferral
In this work, we introduce a novel framework of regression with deferral, which involves deferring the prediction to multiple experts.
$H$-Consistency Guarantees for Regression
Next, we prove a series of novel $H$-consistency bounds for surrogate loss functions of the squared loss, under the assumption of a symmetric distribution and a bounded hypothesis set.
Top-$k$ Classification and Cardinality-Aware Prediction
For these functions, we derive cost-sensitive comp-sum and constrained surrogate losses, establishing their $H$-consistency bounds and Bayes-consistency.
Principled Approaches for Learning to Defer with Multiple Experts
We present a study of surrogate losses and algorithms for the general problem of learning to defer with multiple experts.
Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms
We study the key framework of learning with abstention in the multi-class classification setting.
Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention
We introduce new families of surrogate losses for the abstention loss function, which include the state-of-the-art surrogate losses in the single-stage setting and a novel family of loss functions in the two-stage setting.
Ranking with Abstention
We introduce a novel framework of ranking with abstention, where the learner can abstain from making prediction at some limited cost $c$.
Cross-Entropy Loss Functions: Theoretical Analysis and Applications
These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set $H$ used.
$\mathscr{H}$-Consistency Estimation Error of Surrogate Loss Minimizers
We also show that previous excess error bounds can be recovered as special cases of our general results.
A Finer Calibration Analysis for Adversarial Robustness
Moreover, our calibration results, combined with the previous study of consistency by Awasthi et al. (2021), also lead to more general $H$-consistency results covering common hypothesis sets.
Calibration and Consistency of Adversarial Surrogate Losses
We then give a characterization of H-calibration and prove that some surrogate losses are indeed H-calibrated for the adversarial loss, with these hypothesis sets.
