In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation pro- cedure. This connection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the sug- gested mapping is interval-valued, providing a set of posterior probabil- ities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classifica- tion, when decisions result in unequal (asymmetric) losses.

The composition of the training dataset has key implications for machine learning models' behavior [Fel19; CLK+19; KL17; GZ19; IPE+22], especially as the training environments often deviate from deployment conditions [RGL19; KSM+20; HBM+20]. For example, a model might struggle on specific subpopulations in the data if that subpopulation was mislabeled [NAM21; SC18; BHK+20; VCG+22], underrepresented [SKH+20; STM21], or corrupted [HD19; HBM+20]. More broadly, the training dataset might contain spurious correlations, encouraging the model to depend on prediction rules that do not generalize to deployment [XEI+20; GJM+20; DJL21]. Moreover, identifying meaningful subpopulations within data allows for dataset refinement (such as filtering or relabeling) [YQF+19; SC18], and training more fair [KGZ19; DYZ+21] or accurate [JFK+20; SHL20] models. However, dominant approaches to such identification of biases and difficult subpopulations within datasets often require human intervention, which is typically labor intensive and thus not conducive to routine usage.

In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation procedure. This connection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the suggested mapping is interval-valued, providing a set of posterior probabilities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classification, when decisions result in unequal (asymmetric) losses. Experiments show improvements over state-of-the-art procedures.

In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation procedure. This connection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the suggested mapping is interval-valued, providing a set of posterior probabilities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classification, when decisions result in unequal (asymmetric) losses. Experiments show improvements over state-of-the-art procedures.

In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation procedure. Thisconnection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the suggested mappingis interval-valued, providing a set of posterior probabilities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classification, whendecisions result in unequal (asymmetric) losses. Experiments show improvements over state-of-the-art procedures.