PAC-Bayesian Generalization Bound on Confusion Matrix for Multi-Class Classification

Emilie Morvant (1) , Sokol Koço (1) , Liva Ralaivola (1)

1 QARMA - éQuipe AppRentissage et MultimediA [Marseille]

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error measure; this puts our contribution in the line of work aiming at dealing with performance measure that are richer than mere scalar criterion such as the misclassification rate. Thanks to very recent and beautiful results on matrix concentration inequalities, we derive two bounds showing that the true confusion risk of the Gibbs classifier is upper-bounded by its empirical risk plus a term depending on the number of training examples in each class. To the best of our knowledge, this is the first PAC-Bayes bounds based on confusion matrices.

Mots clés: PAC-Bayes generalization bounds; Confusion Matrix; Concentration Inequality; Multi-Class Classification

Domaines: Machine Learning [stat.ML]

Emilie Morvant, Sokol Koço, Liva Ralaivola. PAC-Bayesian Generalization Bound on Confusion Matrix for Multi-Class Classification. International Conference on Machine Learning 2012, Jun 2012, Edinburgh, United Kingdom. ⟨hal-00674847v4⟩