Symbolic Regression Driven by Training Data and Prior Knowledge
This addresses the issue of inaccurate models in symbolic regression for researchers when data coverage is poor, though it is an incremental improvement over existing methods.
The paper tackles the problem of symbolic regression when training data is insufficient, by incorporating prior knowledge as formal constraints during the search process. It shows that this approach outperforms standard symbolic regression by several orders of magnitude in mean squared deviation from a reference model.
In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error does not provide sufficient guidance toward desired models. Standard symbolic regression techniques then yield models that are partially incorrect, for instance, in terms of their steady-state characteristics or local behavior. If these properties were considered already during the search process, more accurate and relevant models could be produced. We propose a multi-objective symbolic regression approach that is driven by both the training data and the prior knowledge of the properties the desired model should manifest. The properties given in the form of formal constraints are internally represented by a set of discrete data samples on which candidate models are exactly checked. The proposed approach was experimentally evaluated on three test problems with results clearly demonstrating its capability to evolve realistic models that fit the training data well while complying with the prior knowledge of the desired model characteristics at the same time. It outperforms standard symbolic regression by several orders of magnitude in terms of the mean squared deviation from a reference model.