Learning Monotone Nonlinear Models using the Choquet Integral

author: Weiwei Cheng, Mathematik und Informatik, Philipps-Universität Marburg
published: Oct. 3, 2011,   recorded: September 2011,   views: 4818


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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.

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Reviews and comments:

Comment1 Amani RHM, May 27, 2019 at 10:49 p.m.:

Hi sir ,
I have projet of the determinants of the orientation choice , i would like to use predictive model to do this
i would like also to use the choquistic regression with the MATLAB , I find a package of you and yours collegues named "ordinal choquistic regression" i can't implement it into MATLAB to show interction between variables and the importance of every varible .I have a data set of factors of university orientation , i want to practise it with the choquistic and have experiment results. Can you Help me PLEASE
Thanks a lot

Comment2 milesmsith Smith, July 17, 2019 at 12:31 a.m.:

Thank you so much for this. I was into this issue and tired to tinker around to check if its possible but couldnt get it done. Now https://filezilla.software/ that i have seen the way you did it, thanks guys

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