This paper provides the first --to the best of our knowledge-- analysis of online learning algorithms for multiclass problems when the 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.

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 algorithm and show how the theoretical study motivate 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, thus allowing the user from having to recours to any optimization package to implement it.

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 algorithm and show how the theoretical study motivate 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, thus allowing the user from having to recours to any optimization package to implement it. Papers published at the Neural Information Processing Systems Conference.

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 algorithm and show how the theoretical study motivate 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, thus allowing the user from having to recours to any optimization package to implement it.