A Mathematical Framework for E-Commerce Sales Prediction Using Attention-Enhanced BiLSTM and Bayesian Optimization

Accurate sales prediction is crucial for inventory and marketing in e-commerce. Cross-border sales involve complex patterns that traditional models cannot capture. To address this, we propose an improved Bidirectional Long Short-Term Memory (BiLSTM) model, enhanced with an attention mechanism and Bayesian hyperparameter optimization. The attention mechanism focuses on key temporal features, improving trend identification. The BiLSTM captures both forward and backward dependencies, offering deeper insights into sales patterns. Bayesian optimization fine-tunes hyperparameters such as learning rate, hidden-layer size, and dropout rate to achieve optimal performance. These innovations together improve forecasting accuracy, making the model more adaptable and efficient for cross-border e-commerce sales. Experimental results show that the model achieves an Root Mean Square Error (RMSE) of 13.2, Mean Absolute Error (MAE) of 10.2, Mean Absolute Percentage Error (MAPE) of 8.7 percent, and a Coefficient of Determination (R²) of 0.92. It outperforms baseline models, including BiLSTM (RMSE 16.5, MAPE 10.9 percent), BiLSTM with Attention (RMSE 15.2, MAPE 10.1 percent), Temporal Convolutional Network (RMSE 15.0, MAPE 9.8 percent), and Transformer for Time Series (RMSE 14.8, MAPE 9.5 percent). These results highlight the model’s superior performance in forecasting cross-border e-commerce sales, making it a valuable tool for inventory management and demand planning.