The Effect of Distinct Geometric Semantic Crossover Operators in Regression Problems

This paper investigates the impact of geometric semantic crossover operators in a wide range of symbolic regression problems. First, it analyses the impact of using Manhattan and Euclidean distance geometric semantic crossovers in the learning process. Then, it proposes two strategies to numerically optimize the crossover mask based on mathematical properties of these operators, instead of simply generating them randomly. An experimental analysis comparing geometric semantic crossovers using Euclidean and Manhattan distances and the proposed strategies is performed in a test bed of twenty datasets. The results show that the use of different distance functions in the semantic geometric crossover has little impact on the test error, and that our optimized crossover masks yield slightly better results. For SGP practitioners, we suggest the use of the semantic crossover based on the Euclidean distance, as it achieved similar results to those obtained by more complex operators

On explaining machine learning models by evolving crucial and compact features

Feature construction can substantially improve the accuracy of Machine Learning (ML) algorithms. Genetic Programming (GP) has been proven to be effective at this task by evolving non-linear combinations of input features. GP additionally has the potential to improve ML explainability since explicit expressions are evolved. Yet, in most GP works the complexity of evolved features is not explicitly bound or minimized though this is arguably key for explainability. In this article, we assess to what extent GP still performs favorably at feature construction when constructing features that are (1) Of small-enough number, to enable visualization of the behavior of the ML model; (2) Of small-enough size, to enable interpretability of the features themselves; (3) Of sufficient informative power, to retain or even improve the performance of the ML algorithm. We consider a simple feature construction scheme using three different GP algorithms, as well as random search, to evolve features for five ML algorithms, including support vector machines and random forest. Our results on 21 datasets pertaining to classification and regression problems show that constructing only two compact features can be sufficient to rival the use of the entire original feature set. We further find that a modern GP algorithm, GP-GOMEA, performs best overall. These results, combined with examples that we provide of readable constructed features and of 2D visualizations of ML behavior, lead us to positively conclude that GP-based feature construction still works well when explicitly searching for compact features, making it extremely helpful to explain ML models