Bipartite Ranking through Minimization of Univariate Loss

Minimization of the rank loss or, equivalently, maximization of the AUC in bipartite ranking calls for minimizing the number of disagreements between pairs of instances. Since the complexity of this problem is inherently quadratic in the number of training examples, it is tempting to ask how much is actually lost by minimizing a simple univariate loss function, as done by standard classification methods, as a surrogate. In this paper, we first note that minimization of 0/1 loss is not an option, as it may yield an arbitrarily high rank loss. We show, however, that better results can be achieved by means of a weighted (cost-sensitive) version of 0/1 loss. Yet, the real gain is obtained through margin-based loss functions, for which we are able to derive proper bounds, not only for rank risk but, more importantly, also for rank regret. The paper is completed with an experimental study in which we address specific questions raised by our theoretical analysis

Bipartite Ranking through Minimization of Univariate Loss

Minimization of the rank loss or, equivalently, maximization of the AUC in bipartite ranking calls for minimizing the number of disagreements between pairs of instances. Since the complexity of this problem is inherently quadratic in the number of training examples, it is tempting to ask how much is actually lost by minimizing a simple univariate loss function, as done by standard classification methods, as a surrogate. In this paper, we first note that minimization of 0/1 loss is not an option, as it may yield an arbitrarily high rank loss. We show, however, that better results can be achieved by means of a weighted (cost-sensitive) version of 0/1 loss. Yet, the real gain is obtained through margin-based loss functions, for which we are able to derive proper bounds, not only for rank risk but, more importantly, also for rank regret. The paper is completed with an experimental study in which we address specific questions raised by our theoretical analysis

Approximating cost functions in resource-based configuration

In this paper, we propose a method for approximating cost functions arising in connection with configuration problems within the formal framework of resource-based configuration. Knowledge about cost functions is important since these functions can be used for guiding the heuristical search for (approximations of) optimal solutions to configuration problems. Not only is the approximation method motivated by theoretical considerations, but also validated by means of empirical results. Moreover, approximating functions can be computed very efficiently. (orig.)SIGLEAvailable from TIB Hannover: RR 6673(60) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A two-phase search method for solving configuration problems

We consider the problem of finding solutions to resource-based configuration problems under real-time conditions. The objective of finding the best solutions possible, given the time restrictions, is formalized within a decision theoretic framework. The utility of a configuration returned by a search algorithm depends on the cost of this configuration as well as on the time required to find it. We propose a heuristic search strategy as an approximation of a (computationally intractable) search algorithm which is optimal in the sense that it maximizes the (expected) value of computation. This search strategy consists of two phases. In connection with the heuristic principles underlying both search phases, the decision whether to continue or break off the search along a certain path of the search tree has to be made. We propose a formalization of as well as a soolution to this termination problem. Experimental studies show very promising results for the search algorithm. (orig.)SIGLEAvailable from TIB Hannover: RR 6673(62) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A note on interactions-driven business cycles

Socioeconomic interactions, Business cycles, Keynesian multiplier model, D11, E12, E32,

Possibility Theory and its applications: a retrospective and prospective view.

International audienceThis paper provides an overview of possibility theory, emphasising its historical roots and its recent developments; Possibility theory lies at the crossroads between fuzzy sets, probability and non-monotonic reasoning. Possibility theory can be cast either in an ordinal or in a numerical setting. Qualitative possibility theory is closely related to belief revision theory, and common-sense reasoning with exception-tainted knowledge in Artificial Intelligence. It has been axiomatically justified in a decision-theoretic framework in the style of Savage, thus providing a foundation for qualitative decision theory. Quantitative possibility theory is the simplest framework for statiscal reasoning with imprecise probabilities. As such it has close connections with random set theory and confidence intervals, and can provide a tool for uncertainty propagation with limited statistical or subjective information