161 research outputs found
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
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