Abstract:
An accurate prediction of the garlic price can be one of the most important tasks in modern agriculture. However, the conventional single forecasting models are often limited to the high volatility of the garlic price data due to the complex and intertwined influencing factors. In this study, a high-precision ensemble prediction framework was proposed using deep learning fusion. Three modules were the two-stage feature selection, adaptive sub-model construction, and nonlinear optimization. Firstly, the two-stage feature selection was implemented to integrate the maximum relevance and minimum redundancy (mRMR) algorithm with the least absolute shrinkage and selection operator (LASSO) regression. The mRMR algorithm selected the features to maximize their correlation with the target variable. While the redundancy of the features was minimized to filter out the irrelevant and overlapping variables, in order to reduce the computational complexity and noise interference. The LASSO was used to further refine the subset. The L1 regularization was applied to promote the sparsity in the coefficients and the robustness to suppress the multicollinearity. The resulting feature subset contained the most informative variables that highly correlated with the garlic prices, providing a reliable input for the subsequent modeling. Secondly, two complementary sub-models were designed to solve the multi-scale variability in the garlic prices. The influencing factors and historical garlic prices were input into a bidirectional long short-term memory (BiLSTM) network. Temporal dependencies were captured in both forward and backward directions using BiLSTM. Nonlinear relationships were simulated for a stable prediction sequence. The original series of the garlic price was decomposed by variational mode decomposition (VMD) into several intrinsic mode functions (IMFs) with frequency components. Each IMF was modeled using a deep hybrid kernel extreme learning machine (DHKELM). The global and local kernel advantages were integrated to effectively learn the nonlinear patterns within each component. The prediction of the IMFs was reconstructed to form the final forecast sequence, thereby enhancing the interpretability of the low-frequency trends and high-frequency fluctuations. Thirdly, the advanced optimization was introduced to further enhance the model performance and convergence efficiency. The black-winged kite algorithm (BKA) was employed to optimize the kernel parameters and hidden-layer nodes of the DHKELM. The global search was improved to avoid the local optima. Meanwhile, Bayesian optimization (BYS) was used to fine-tune the BiLSTM hyperparameters, such as the learning rate, number of neurons, and batch size, indicating the high convergence and better generalization. Finally, the outputs of the sub-models were fused using a nonlinear ensemble structure with a convolutional neural network, bidirectional gated recurrent unit, and attention mechanism (CNN–BiGRU–Attention), instead of conventional linear averaging. The CNN was used to extract the local nonlinear interactions among the sub-model outputs. While the BiGRU was adopted to capture the long-term temporal dependencies and cross-period correlations. The attention layer dynamically assigned the adaptive weights to the important time steps and high-performing sub-models. Meanwhile, the end-to-end nonlinear prediction was fused to effectively reduce the accumulated errors for the complementary information. Experimental results demonstrate that the ensemble model achieved a mean absolute percentage error (MAPE) of 1.61%, a root mean square error (RMSE) of 0.078, and a coefficient of determination (
R²) of 0.976. The R² value was improved by approximately 2%–7%, compared with the individual sub-models. The ensemble model also outperformed the conventional linear combination in terms of stability and accuracy. The forecasting precision of the garlic price was significantly enhanced after optimization. The framework can also provide a quantitative decision-making reference for the garlic market regulation. The finding can also serve as a reusable foundation for the price prediction of the agricultural commodities that are characterized by high volatility, complex interactions, and nonlinear dynamics.