Qualitatively faithful quantitative prediction

We describe an approach to machine learning from numerical data that combines both qualitative and numerical learning. This approach is carried out in two stages: (1) induction of a qualitative model from numerical examples of the behaviour of a physical system, and (2) induction of a numerical regression function that both respects the qualitative constraints and fits the training data numerically. We call this approach Q^2 learning, which stands for Qualitatively faithful Quantitative learning. Induced numerical models are “qualitatively faithful” in the sense that they respect qualitative trends in the learning data. Advantages of Q^2 learning are that the induced qualitative model enables a (possibly causal) explanation of relations among the variables in the modelled system, and that numerical predictions are guaranteed to be qualitatively consistent with the qualitative model which alleviates the interpretation of the predictions. Moreover, as we show experimentally the qualitative modelʹs guidance of the quantitative modelling process leads to predictions that may be considerably more accurate than those obtained by state-of-the-art numerical learning methods. The experiments include an application of Q^2 learning to the identification of a car wheel suspension system-a complex, industrially relevant mechanical system.