Machine Learning of Choquet Integral Regression with Respect to a Bounded Capacity (or Non-monotonic Fuzzy Measure)

Regression is the process of learning the relationship between sets of variables, enabling predictions of continuous output variables. Many approaches have been proposed to learn parameterized models with respect to numerous error metrics. In this paper, we propose a regression model based on the Choquet integral with respect to a bounded capacity (of which fuzzy measures are a subset). Our model has a generalized bias that enables capability beyond previously proposed Choquet integral regression approaches. We also develop an approach for learning the parameters of the Choquet integral regression from training data. Simulated and real-world benchmark data are used to demonstrate the performance of our regression approach compared with several competing regression methods. Results show that our approach has superior performance and is computationally very fast. An additional benefit of our Choquet integral regression is that it enables interpretability of the learned model, which we will explore in later works.