A note on margin-based loss functions in classification

By Yi Lin. 2004

244 citations recorded by the source corpus.

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In Statistical Learning Theory

Citations in the corpus

On Structured Prediction Theory with Calibrated Convex Surrogate Losses (2017, methodology): “Deﬁnition 3 with η = 0 through Theorem 2 implies Fisher consistency as formulated, e.g., by Pedregosa et al. [34] for general losses and Lin [24] for binary classiﬁcation.”
How to Compare Different Loss Functions and Their Risks (2007, background): “[18, 19, 37, 27, 1]), and for margin-based loss functions L2, i.”
Composite Binary Losses (2009, methodology): “The condition CC 12 is equivalent to what is called “classiﬁcation calibrated” by Bartlett et al. [7] and “Fisher consistent for classiﬁcation problems” by Lin [30] although their deﬁnitions were only for margin losses.”
Long-tail learning via logit adjustment (2020, background): “However, when doing so, it is important to ensure Fisher consistency [Lin, 2004] (or classiﬁcation calibration [Bartlett et al., 2006]) of the resulting loss for the balanced error.”
Multicategory Support Vector Machines, Theory, and Application to the Classiﬁcation of Microarray Data and Satellite Radiance Data (2002, methodology): “The second kind of explanation was provided by Lin (2002). He identified the asymptotic target function of the SVM formulation, and associated it with the Bayes decision rule. With the class label Y either 1 or -1, one can verify that the Bayes decision rule in (2) is φB(x) = sign(p1(x) − 1/2). It w”
Convexity, Classification, and Risk Bounds (2006, background): “Thus we consider the weakest possible condition on φ : that it is “classiﬁcation-calibrated,” which is essentially a pointwise form of Fisher consistency for classiﬁcation (Lin 2004).”
Alternating Decision Forests (2013, unknown): “Lin [23] showed that minimizing so called Fisher-consistent marginbased loss functions automatically leads to good approximations of the unknown Bayes decision rule.”
Support Vector Machines with Applications (2006, background): “[61] PLATT, J. C. (1999). Fast training of support vector machines”
On the Consistency of Ordinal Regression Methods (2014, background): “Fisher consistency is a desirable property for surrogate loss functions [14].”
Theory of classification : a survey of some recent advances (2005, methodology): “Properties of convex loss functions were investigated by Lin [139], Steinwart [206], and Zhang [244].”