Learning monotone nonlinear models using the choquet integral

  • Authors:

  • Ali Fallah Tehrani;Weiwei Cheng;Krzysztof Dembczynski;Eyke Hüllermeier

  • Affiliations:

  • Mathematics and Computer Science, University of Marburg, Germany;Mathematics and Computer Science, University of Marburg, Germany;Mathematics and Computer Science, University of Marburg, Germany and Institute of Computing Science, Poznan University of Technology, Poland;Mathematics and Computer Science, University of Marburg, Germany

  • Venue:
  • ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
  • Year:
  • 2011

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Abstract

The learning of predictive models that guarantee monotonicity in the input variables has received increasing attention in machine learning in recent years. While the incorporation of monotonicity constraints is rather simple for certain types of models, it may become a more intricate problem for others. By trend, the difficulty of ensuring monotonicity increases with the flexibility or, say, nonlinearity of a model. In this paper, we advocate the so-called Choquet integral as a tool for learning monotone nonlinear models. While being widely used as a flexible aggregation operator in different fields, such as multiple criteria decision making, the Choquet integral is much less known in machine learning so far. Apart from combining monotonicity and flexibility in a mathematically sound and elegant manner, the Choquet integral has additional features making it attractive from a machine learning point of view. Notably, it offers measures for quantifying the importance of individual predictor variables and the interaction between groups of variables. As a concrete application of the Choquet integral, we propose a generalization of logistic regression. The basic idea of our approach, referred to as choquistic regression, is to replace the linear function of predictor variables, which is commonly used in logistic regression to model the log odds of the positive class, by the Choquet integral.