Yet Another Method for Combining Classifiers Outputs: A Maximum Entropy Approach Marco Saerens and Fran¸cois Fouss Information Systems Research Unit (ISYS – IAG) Universit´ e catholique de Louvain Place des Doyens 1 B-1348 Louvain-la-Neuve, Belgium {saerens, fouss}@isys.ucl.ac.be Abstract. In this paper, we present a maximum entropy (maxent) approach to the fusion of experts opinions, or classifiers outputs, problem. The maxent approach is quite versatile and allows us to express in a clear, rigorous, way the a priori knowledge that is available on the problem. For instance, our knowl- edge about the reliability of the experts and the correlations between these experts can be easily integrated: Each piece of knowledge is expressed in the form of a linear constraint. An iterative scaling algorithm is used in order to compute the maxent solution of the problem. The maximum entropy method seeks the joint probability density of a set of random variables that has maxi- mum entropy while satisfying the constraints. It is therefore the “most honest” characterization of our knowledge given the available facts (constraints). In the case of conflicting constraints, we propose to minimise the “lack of constraints satisfaction” or to relax some constraints and recompute the maximum entropy solution. The maxent fusion rule is illustrated by some simulations. 1. Introduction The fusion of various sources of knowledge has been an active subject of research since more than three decades (for some review references, see [2], [6], [8]). It has recently been successfully applied to the problem of classifiers combination or fusion (see for instance [13]). Many different approaches have been developped for experts opinions fusion, in- cluding weighted average (see for instance [2], [8]), Bayesian fusion (see for instance [2], [8]), majority vote (see for instance [1], [12], [16]), models coming from incertainty rea- soning: fuzzy logic, possibility theory [14] (see for instance [3]), standard multivariate statistical analysis techniques such as correpondence analysis [18], etc. One of these approaches is based on maximum entropy modeling (see [17], [19]). Maximum entropy is a versatile modeling technique allowing to easily integrate various constraints, such as correlation between experts, reliability of these experts, etc. In this work, we propose a new model of experts opinions integration, based on a maximum entropy model (for a review of maximum entropy theory and applications, see for instance [7], [9], [10] or [11]). In this paper, we use the term “experts opinions”,