Partially Monotone Networks Applied to Breast Cancer Detection on Mammograms

In many prediction problems it is known that the response variable depends monotonically on most of the explanatory variables but not on all. Often such partially monotone problems cannot be accurately solved by unconstrained methods such as standard neural networks. In this paper we propose so-called MIN-MAX networks that are partially monotone by construction. We prove that this type of networks have the uniform approximation property, which is a generalization of the result by Sill on totally monotone networks. In a case study on breast cancer detection on mammograms we show that enforcing partial monotonicity constraints in MIN-MAX networks leads to models that not only comply with the domain knowledge but also outperform in terms of accuracy standard neural networks especially if the data set is relative small.