Qualitatively Faithful Quantitative Prediction

Abstract

In this paper we describe a case study in which we applied an approach to qualitative machine learning to induce, from system's behaviour data, a qualitative model of a complex, industrially relevant mechanical system (a car wheel suspension system). The induced qualitative model enables nice causal interpretation of the relations in the modelled system. Moreover, we also show that the qualitative model can be used to guide the quantitative modelling process leading to numerical predictions that may be considerably more accurate than those obtained by state-of-the-art numerical modelling methods. This idea of combining qualitative and quantitative machine learning for system identification is in this paper carried out in two stages: (1) induction of qualitative constraints from system's behaviour data, and (2) induction of a numerical regression function that both respects the qualitative constraints and fits the training data numerically. We call this approach Q2 learning, which stands for Qualitatively faithful Quantitative learning.