Loss Functions for Binary Class Probability Estimation and Classification: Structure and Applications

By Andreas Buja, Werner Stuetzle, Yi Shen. 2005

321 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d6706b6e626c15680688b0774419662f2341caee

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Citations in the corpus

Composite Binary Losses (2009, background): “Buja et al. [9] introduced the notion of a canonical link deﬁned by ψ (cid:48) ( v ) = w ( v ).”
On Symmetric Losses for Learning from Corrupted Labels (2019, background): “This similar property has been observed and well-studied for the hinge loss ‘ hinge ( z ) = max(0 , 1 − z ), where its minimizer is the Bayes-optimal classiﬁer sign( η ( x ) − ), which suggests that the hinge loss is not suitable for class probability estimation [Bartlett & Tewari, 2007; Buja et al.”
Covariate balancing propensity score by tailored loss functions (2016, methodology): “Buja, A., W. Stuetzle, and Y. Shen (2005).”
Information, Divergence and Risk for Binary Experiments (2009, background): “The relationship between risks and Bregman divergences is studied by Grünwald and Dawid (2004); Buja et al. (2005).”
Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings (2015, methodology): “Different choices of the mixing measure yield the standard examples of scoring rules in this case; see Buja et al. (2005) and Table 1 in Gneiting and Raftery (2007).”
Learning in Implicit Generative Models (2016, methodology): “Given this scoring function, we must specify a proper scoring rule (Buja et al., 2005; Gneiting and Raftery, 2007) for binary discrimination to allow for parameter learning, such as those in Table 1.”
Making and Evaluating Point Forecasts (2009, background): “Compare Savage (1971), DeGroot and Fienberg (1983), Schervish (1989), Winkler (1996), Buja, Stuetzle, and Shen (2005), and Gneiting and Raftery (2007), among others.”
Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms (2018, background): “This form of a loss, SΩ(ψ (θ);y), is sometimes called composite (Buja et al., 2005; Reid and Williamson, 2010; Williamson et al., 2016).”
Robust Bi-Tempered Logistic Loss Based on Bregman Divergences (2019, background): “2 Matching losses Next, we recall the notion of a matching loss [11, 12, 4, 17].”
Under Review as a Conference Paper at Iclr 2017 Learning in Implicit Generative Models (2017, methodology): “Given this scoring function, we must specify a proper scoring rule (Gneiting and Raftery, 2007; Buja et al., 2005) for binary discrimination to allow for parameter learning, such as those in Table 1.”
Strictly Proper Scoring Rules, Prediction, and Estimation (2007, methodology): “If the expected score function, G, is smooth, then ν(dc) has Lebesgue density G′′(c) (Buja et al. 2005).”
Composite Multiclass Losses (2011, methodology): “Our results suggest that in order to design losses for multiclass prediction problems it is helpful to use the composite representation, and design the proper part via the Bayes risk as suggested for the binary case in [1].”
On the Consistency of Ordinal Regression Methods (2014, background): “, 2003; Ramaswamy and Agarwal, 2012), infinite sample consistency (Zhang, 2004b) and proper surrogates (Buja et al., 2005; Gneiting and Raftery, 2007).”
Predicting accurate probabilities with a ranking loss (2012, methodology): “In such cases, we call the corresponding probabilistic loss P a proper (or Fisher-consistent ) loss (Buja et al., 2005), and say that (cid:96) corresponds to a proper loss.”
An experimental comparison of performance measures for classification (2009, background): “Buja et al. (2005) studies several metrics (LogLoss, squared error, and others) checking whether these are proper scoring rules, defining proper score rules as, ‘‘functions that score probability estimates in view of data in a Fisher-consistent manner”.”