Monotonicity maintenance in information-theoretic machine learning algorithms

Abstract

Abstract. Decision trees that are based on information-theory are useful paradigms for learning from examples. However, in some real-world applications, known information-theoretic methods frequently generate nonmonotonic decision trees, in which objects with bettet attribute values are sometimes classified to lower classes than objects with inferior values. This property is undesirable for problem solving in many application domains, such as credit scoring and insurance premium determination, Where monotonicity of subsequent classifications is important. An attribute-selection metric is proposed here that takes both the error as weil as monotonicity into account while building decision trees. The metric is empirically shown capable of significantly reducing the degree of non-monotonicity of decision-trees without sacrificing their inductive accuracy.

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…in machine learning [12,28,90] and fuzzy modelling [128,155,161]. However, real-life data is often imperfect and does not fully comply with the monotonicity hypothesis.…”

“…(6.11). In terms of the variables of the ILP problem, this cost is given by 12) where the values o i represent the corresponding values of the votrix induced by the given profile of rankings.…”

Efficient Learning of Classifiers Based on the 2-Additive Choquet Integral

“…Most notably, it combines three features in a non-trivial way, namely monotonicity, nonlinearity and interpretability. As for the first, a monotone dependence between the input and output attributes is often desirable in a classification setting and sometimes even requested by the application [11,12,13]. At the same time, the Choquet integral also allows for modeling interactions between different attributes in a flexible, nonlinear way.…”

Isotonic Classification Trees

“…In this paper we present a new algorithm, called ICT, for learning monotone classification trees for problems with ordered class labels. Our approach differs from earlier monotone tree algorithms such as [5,18,11] in that we adjust the probability estimates in the leaf nodes in case of a violation. This is done in such a way that, subject to the monotonicity constraint, the sum of absolute prediction errors on the training sample is minimized.…”