Genetic Programming-based Feature Selection for Symbolic Regression on Incomplete Data.

High-dimensionality is one of the serious real-world data challenges in symbolic regression and it is more challenging if the data are incomplete. Genetic programming has been successfully utilised for high-dimensional tasks due to its natural feature selection ability, but it is not directly applicable to incomplete data. Commonly, it needs to impute the missing values first and then perform genetic programming on the imputed complete data. However, in the case of having many irrelevant features being incomplete, intuitively, it is not necessary to perform costly imputations on such features. For this purpose, this work proposes a genetic programming-based approach to select features directly from incomplete high-dimensional data to improve symbolic regression performance. We extend the concept of identity/neutral elements from mathematics into the function operators of genetic programming, thus they can handle the missing values in incomplete data. Experiments have been conducted on a number of data sets considering different missingness ratios in high-dimensional symbolic regression tasks. The results show that the proposed method leads to better symbolic regression results when compared with state-of-the-art methods that can select features directly from incomplete data. Further results show that our approach not only leads to better symbolic regression accuracy but also selects a smaller number of relevant features, and consequently improves both the effectiveness and the efficiency of the learning process.