Cost-sensitive Multiclass Classification Risk Bounds

By B. '. Pires, Csaba Szepesvari, Mohammad Ghavamzadeh. 2013

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Quantifying Learning Guarantees for Convex but Inconsistent Surrogates (2018, background): “Consistency of convex surrogates has been the central question of many studies for such problems as binary classification [2, 24, 19], multi-class classification [23, 21, 1, 17], ranking [11, 4, 5, 18, 15] and, more recently, structured prediction [7, 14].”
On Structured Prediction Theory with Calibrated Convex Surrogate Losses (2017, methodology): “We now formalize the connection between the actual risk R L and the surrogate Φ -risk R Φ via the so-called calibration function , see Deﬁnition 1 [4, 45, 39, 16, 2].”
On the Consistency of Ordinal Regression Methods (2014, background): “particular, Bartlett et al. (2003) provide a characterization of the Fisher consistency for convex margin-based surrogates that we extend to the all threshold (AT) and immediate threshold (IT) family of surrogate loss functions.”
Precision Medicine. (2019, background): “…Y d X < 0 π A; X , hence, it can be seen that d𝒟 opt minimizes a cost-sensitive classification problem (Elkan 2001; Zadrozny et al 2003; Zhou and Liu 2006; Pires et al 2013) with cost function |Y|/π(A; X), class label A sign(Y), and inputX ∈ 𝒳, over the set of classifiers 𝒟 (see Zhao et al…”
Cross-Entropy Loss Functions: Theoretical Analysis and Applications (2023, unknown): “…al., 2010; Ravikumar et al., 2011; Ramaswamy et al., 2013; Gao & Zhou, 2015; Uematsu & Lee, 2017; Mao et al., 2023), cost-sensitive classification (Pires et al., 2013; Pires & Szepesvári, 2016), structured prediction (Ciliberto et al., 2016; Osokin et al., 2017; Blondel, 2019), top-k…”
Parametric Adversarial Divergences are Good Task Losses for Generative Modeling (2017, background): “…because it makes traditional multi-class classification methods unusable in general.3 Standard practice in structured prediction (Taskar et al., 2003; Collins, 2002; Pires et al., 2013) is to consider predictors based on 1We focus in this paper on the divergence minimization perspective of GANs.”
Consistent Multiclass Algorithms for Complex Performance Measures (2015, background): “, 2012), and some work on general multiclass losses (Steinwart, 2007; Ramaswamy & Agarwal, 2012; Pires et al., 2013; Ramaswamy et al., 2013).”
Convex Calibration Dimension for Multiclass Loss Matrices (2014, background): “More recently, Pires et al. [20] used Steinwart’s techniques to obtain surrogate regret bounds for certain surrogates w.r.t. general multiclass losses, and Ramaswamy et al. [22] showed how to design explicit convex calibrated surrogates for any low-rank loss matrix.”