Ranking the best instances

We formulate the local ranking problem in the framework of bipartite ranking where the goal is to focus on the best instances. We propose a methodology based on the construction of real-valued scoring functions. We study empirical risk minimization of dedicated statistics which involve empirical quantiles of the scores. We first state the problem of finding the best instances which can be cast as a classification problem with mass constraint. Next, we develop special performance measures for the local ranking problem which extend the Area Under an ROC Curve (AUC/AROC) criterion and describe the optimal elements of these new criteria. We also highlight the fact that the goal of ranking the best instances cannot be achieved in a stage-wise manner where first, the best instances would be tentatively identified and then a standard AUC criterion could be applied. Eventually, we state preliminary statistical results for the local ranking problem.Comment: 29 page

What Makes a Good Plan? An Efficient Planning Approach to Control Diffusion Processes in Networks

In this paper, we analyze the quality of a large class of simple dynamic resource allocation (DRA) strategies which we name priority planning. Their aim is to control an undesired diffusion process by distributing resources to the contagious nodes of the network according to a predefined priority-order. In our analysis, we reduce the DRA problem to the linear arrangement of the nodes of the network. Under this perspective, we shed light on the role of a fundamental characteristic of this arrangement, the maximum cutwidth, for assessing the quality of any priority planning strategy. Our theoretical analysis validates the role of the maximum cutwidth by deriving bounds for the extinction time of the diffusion process. Finally, using the results of our analysis, we propose a novel and efficient DRA strategy, called Maximum Cutwidth Minimization, that outperforms other competing strategies in our simulations.Comment: 18 pages, 3 figure

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]Comment: Published at http://dx.doi.org/10.1214/009053606000001046 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org