Multitarget Polynomial Regression with Constraints

The paper addresses the task of multi-target polynomial regression, i.e., the task of inducing polynomials that can predict the value of more then one numeric variable. As in other learning tasks, we face the problem of finding an optimal trade-off between the complexity of the induced model and its predictive error. We propose a minimal description length scheme for multi-target polynomial regression, which includes coding schemes for polynomials and their predictive errors on training data. The proposed MDL scheme is implemented in an algorithm for polynomial induction that can also take into account language constraints, i.e., constraints on terms to be included in the induced polynomials. We empirically compare the multi-target model with the multiple single target models. The results of the experiments show that there is no loss in predictive performance when using multi-target models as compared to multiple target models and that fewer equation structures are considered in the former case.