Confusion-Based Online Learning and a Passive-Aggressive Scheme

Liva Ralaivola (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

This paper provides the first ---to the best of our knowledge--- analysis of online learning algorithms for multiclass problems when the {\em confusion} matrix is taken as a performance measure. The work builds upon recent and elegant results on noncommutative concentration inequalities, i.e. concentration inequalities that apply to matrices, and, more precisely, to matrix martingales. We do establish generalization bounds for online learning algorithms and show how the theoretical study motivates the proposition of a new confusion-friendly learning procedure. This learning algorithm, called \copa (for COnfusion Passive-Aggressive) is a passive-aggressive learning algorithm; it is shown that the update equations for \copa can be computed analytically and, henceforth, there is no need to recourse to any optimization package to implement it.

Mots clés: online learning; noncommutative inequalities

Domaines: Apprentissage [cs.LG]

Liva Ralaivola. Confusion-Based Online Learning and a Passive-Aggressive Scheme. Neural Information Processing Systems, NIPS 2012, Dec 2012, Lake Tahoe, United States. pp.3293-3301. ⟨hal-00819045⟩