Convex Calibrated Surrogates for Low-Rank Loss Matrices with Applications to Subset Ranking Losses

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Quantifying Learning Guarantees for Convex but Inconsistent Surrogates (2018, methodology): “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].”
Cross-Entropy Loss Functions: Theoretical Analysis and Applications (2023, background): “…learning with rejection (Cortes et al., 2016b;a; Ramaswamy et al., 2015; Cao et al., 2022), ranking (Duchi et 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 &…”
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.”
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).”