Extracting qualitative relations from categorical data

Qualitative modeling is traditionally concerned with the abstraction of numerical data. In numerical domains, partial derivatives describe the relation between the independent and dependent variable; qualitatively, they tell us the trend of the dependent variable. In this paper, we address the problem of extracting qualitative relations in categorical domains. We generalize the notion of partial derivative by defining the probabilistic discrete qualitative partial derivative (PDQ PD). PDQ PD is a qualitative relation between the target class c and the discrete attribute; the derivative corresponds to ordering the attribute's values, ai, by P(c|ai) in a local neighborhood of the reference point, respecting the ceteris paribus principle. We present an algorithm for computation of PDQ PD from labeled attribute-based training data. Machine learning algorithms can then be used to induce models that explain the influence of the attribute's values on the target class in different subspaces of the attribute space.