A comparative study of 11 non-linear regression models highlighting autoencoder, DBN, and SVR, enhanced by SHAP importance analysis in soybean branching prediction

Abstract To explore a robust tool for advancing digital breeding practices through an artificial intelligence-driven phenotype prediction expert system, we undertook a thorough analysis of 11 non-linear regression models. Our investigation specifically emphasized the significance of Support Vector Regression (SVR) and SHapley Additive exPlanations (SHAP) in predicting soybean branching. By using branching data (phenotype) of 1918 soybean accessions and 42 k SNP (Single Nucleotide Polymorphism) polymorphic data (genotype), this study systematically compared 11 non-linear regression AI models, including four deep learning models (DBN (deep belief network) regression, ANN (artificial neural network) regression, Autoencoders regression, and MLP (multilayer perceptron) regression) and seven machine learning models (e.g., SVR (support vector regression), XGBoost (eXtreme Gradient Boosting) regression, Random Forest regression, LightGBM regression, GPs (Gaussian processes) regression, Decision Tree regression, and Polynomial regression). After being evaluated by four valuation metrics: R 2 (R-squared), MAE (Mean Absolute Error), MSE (Mean Squared Error), and MAPE (Mean Absolute Percentage Error), it was found that the SVR, Polynomial Regression, DBN, and Autoencoder outperformed other models and could obtain a better prediction accuracy when they were used for phenotype prediction. In the assessment of deep learning approaches, we exemplified the SVR model, conducting analyses on feature importance and gene ontology (GO) enrichment to provide comprehensive support. After comprehensively comparing four feature importance algorithms, no notable distinction was observed in the feature importance ranking scores across the four algorithms, namely Variable Ranking, Permutation, SHAP, and Correlation Matrix, but the SHAP value could provide rich information on genes with negative contributions, and SHAP importance was chosen for feature selection. The results of this study offer valuable insights into AI-mediated plant breeding, addressing challenges faced by traditional breeding programs. The method developed has broad applicability in phenotype prediction, minor QTL (quantitative trait loci) mining, and plant smart-breeding systems, contributing significantly to the advancement of AI-based breeding practices and transitioning from experience-based to data-based breeding.