Multi-Tree Genetic Programming-based Transformation for Transfer Learning in Symbolic Regression with Highly Incomplete Data

Baligh Al-Helali, Qi Chen, Bing Xue, Mengjie Zhang

Abstract: Transfer learning has been considered a key solution for the problem of learning when there is a lack of knowledge in some target domains. Its idea is to benefit from the learning on different (but related in some way) domains that have adequate knowledge and transfer what can improve the learning in the target domains. Although incompleteness is one of the main causes of knowledge shortage in many machine learning real-world tasks, it has received a little effort to be addressed by transfer learning. In particular, to the best of our knowledge, there is no single study to utilize transfer learning for the symbolic regression task when the underlying data are incomplete. The current work addresses this point by presenting a transfer learning method for symbolic regression on data with high ratios of missing values. A multi-tree genetic programming algorithm based feature-based transformation is proposed for transferring data from a complete source domain to a different, incomplete target domain. The experimental work has been conducted on real-world data sets considering different transfer learning scenarios each is determined based on three factors: missingness ratio, domain difference, and task similarity. In most cases, the proposed method achieved positive transductive transfer learning in both homogeneous and heterogeneous domains. Moreover, even with less significant success, the obtained results show the applicability of the proposed approach for inductive transfer learning.