Choosing models from a well-fitted evolved population that generalizes beyond training data is difficult. We introduce a pragmatic method to estimate model complexity using Hessian rank for post-processing selection. Complexity is approximated by averaging the model output Hessian rank across a few points (N=3), offering efficient and accurate rank estimates. This method aligns model selection with input data complexity, calculated using intrinsic dimensionality (ID) estimators. Using the StackGP system, we develop symbolic regression models for the Penn Machine Learning Benchmark and employ twelve scikit-dimension library methods to estimate ID, aligning model expressiveness with dataset ID. Our data-informed complexity metric finds the ideal complexity window, balancing model expressiveness and accuracy, enhancing generalizability without bias common in methods reliant on user-defined parameters, such as parsimony pressure in weight selection.
Random forest (RF) is a type of ensemble-based machine learning method that has been applied to a variety of machine learning tasks in recent years. This article proposes an evolutionary approach to generate an oblique RF for regression problems. More specifically, our method induces an oblique RF by transforming the original feature space to a new feature space through the evolutionary feature construction method. To speed up the searching process, the proposed method evaluates each set of features based on a decision tree (DT) rather than an RF. In order to obtain an RF, we archive top-performing features and corresponding trees during the search. In this way, both the features and the forest can be constructed simultaneously in a single run. The proposed evolutionary forest is applied to 117 benchmark problems with different characteristics and compared with some state-of-the-art regression methods, including several variants of the RF and gradient boosted DTs (GBDTs). The experimental results suggest that the proposed method outperforms the existing RF and GBDT methods.
Ensemble learning methods have been widely used in machine learning in recent years due to their high predictive performance. With the development of genetic programming-based symbolic regression methods, many papers begin to choose a popular ensemble learning method, random forests, as the baseline competitor. Instead of considering them as competitors, an alternative idea might be to consider symbolic regression as an enhancement technique for random forest. Genetic programming-based symbolic regression methods which fit a smooth function are complementary to the piecewise nature of decision trees, as the smooth variation is common in regression problems. In this article, we propose to form an ensemble model with symbolic regression-based decision trees to address this issue. Furthermore, we design a guided mutation operator to speed up the search on high-dimensional problems, a multi-fidelity evaluation strategy to reduce the computational cost and an ensemble selection mechanism to improve predictive performance. Finally, experimental results on a regression benchmark with 120 datasets show that the proposed ensemble model outperforms 25 existing symbolic regression and ensemble learning methods. Moreover, the proposed method can provide notable insights on an XGBoost hyperparameter performance prediction task, which is an important application area of ensemble learning methods.