A flexible class of dependence-aware multi-label loss functions

The idea to exploit label dependencies for better prediction is at the core of methods for multi-label classification (MLC), and performance improvements are normally explained in this way. Surprisingly, however, there is no established methodology that allows to analyze the dependence-awareness of MLC algorithms. With that goal in mind, we introduce a class of loss functions that are able to capture the important aspect of label dependence. To this end, we leverage the mathematical framework of non-additive measures and integrals. Roughly speaking, a non-additive measure allows for modeling the importance of correct predictions of label subsets (instead of single labels), and thereby their impact on the overall evaluation, in a flexible way. The well-known Hamming and subset 0/1 losses are rather extreme special cases of this function class, which give full importance to single label sets or the entire label set, respectively. We present concrete instantiations of this class, which appear to be especially appealing from a modeling perspective. The assessment of multi-label classifiers in terms of these losses is illustrated in an empirical study, clearly showing their aptness at capturing label dependencies. Finally, while not being the main goal of this study, we also show some preliminary results on the minimization of this parametrized family of losses.

Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

Kinetic ballooning modes in magnetically confined toroidal plasmas are investigated putting emphasis on specific stellarator features. In particular, we propose a Mercier criterion which is purposely designed to allow for direct comparison with local flux-tube gyrokinetics simulations. We investigate the influence on the marginal frequency of the mode of a magnetic curvature which is inhomogeneous on the magnetic flux surface due to the fieldline-label dependence. This is a typical (surface) global effect present in non-axisymmetry. Finally, we propose an artificial equilibrium model that explicitly retains the fieldline-label dependence in the magnetic drift, and analyse the stability of the system by introducing a representation of the perturbations similar to the flux-bundle model of Sugamaet al. (Plasma Fusion Res., vol. 7, 2012, 2403094). The coupling of flux bundles is shown to have a stabilising effect on the most unstable local flux-tube mode.