Enhanced $H$-Consistency Bounds
Recent research has introduced a key notion of $H$-consistency bounds for surrogate losses. These bounds offer finite-sample guarantees, quantifying the relationship between the zero-one estimation error (or other target loss) and the surrogate loss estimation error for a specific hypothesis set. However, previous bounds were derived under the condition that a lower bound of the surrogate loss conditional regret is given as a convex function of the target conditional regret, without non-constant factors depending on the predictor or input instance. Can we derive finer and more favorable $H$-consistency bounds? In this work, we relax this condition and present a general framework for establishing enhanced $H$-consistency bounds based on more general inequalities relating conditional regrets. Our theorems not only subsume existing results as special cases but also enable the derivation of more favorable bounds in various scenarios. These include standard multi-class classification, binary and multi-class classification under Tsybakov noise conditions, and bipartite ranking.
Code (0)
등록된 구현이 없습니다.
Tasks
Multi-class ClassificationSimilar Papers 제목 키워드 기반
Beyond Tsybakov: Model Margin Noise and $\mathcal{H}$-Consistency Bounds
We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise c…
Multi-class ClassificationMastering Multiple-Expert Routing: Realizable $H$-Consistency and Strong Guarantees for Learning to Defer
The problem of learning to defer with multiple experts consists of optimally assigning input instances to experts, balancing the trade-off between their accuracy and computational cost. This is a critical challenge in na…
Text GenerationConsistency of Extreme Learning Machines and Regression under Non-Stationarity and Dependence for ML-Enhanced Moving Objects
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object…
regressionFundamental Novel Consistency Theory: $H$-Consistency Bounds
In machine learning, the loss functions optimized during training often differ from the target loss that defines task performance due to computational intractability or lack of differentiability. We present an in-depth s…
Multi-class ClassificationBinary ClassificationBounds Arc Consistency for Weighted CSPs
The Weighted Constraint Satisfaction Problem (WCSP) framework allows representing and solving problems involving both hard constraints and cost functions. It has been applied to various problems, including resource alloc…
ARCScheduling