**3. Results**

According to historical experience, the weekly morbidities of acute gastroenteritis, food poisoning, and other acute gastrointestinal infections are predicted based on food-contamination data one week before. However, the time-lag effects of food contamination on chronic gastroenteritis, gastrointestinal ulcers, and gastrointestinal tumors are unknown. Therefore, we first tested the RMSE of the models for predicting the morbidities of the three types of diseases with a time lag of 1–8 weeks, respectively. Results are given in Figure 1, from which we can observe that:


Consequently, we chose a time lag of three weeks for predicting the morbidities of both chronic gastroenteritis and gastrointestinal ulcers. For gastrointestinal tumors, because we could not determine an appropriate time lag for most models, we determined a different time lag for each model that resulted in the best RMSE for the model (6, 2, 6, 2, 1, 6, 5, and 1 week(s) for MLR, ANN, DBN, EvoDBN, DAE, EvoDAE, DDAE, and EvoDDAE, respectively).

Figure 2a–f presents the prediction accuracies of the models for the six gastrointestinal diseases, respectively. Results show that the traditional MLR exhibits the worst prediction performance on all diseases, the shallow ANN exhibits significantly better performance than MLR, and all deep-learning models exhibited much better performance than the MLR and shallow ANN. Among the six deep models, EvoDDAE exhibited the best performance on five diseases except gastrointestinal tumors. The average prediction accuracy of EvoDDAE was over 80% on acute gastroenteritis and food poisoning, close to 80% on other gastrointestinal infections, and approximately 72%–73% on chronic gastroenteritis and gastrointestinal ulcers. For gastrointestinal tumors, except that EvoDBN obtained an average perdition accuracy of approximately 52%, the accuracies of all other models were less than 50%, which indicates that the gastrointestinal-tumor morbidity is difficult to predict using these models. We also observed that, in most cases, the performance of a deep model could be significantly improved by using evolutionary training to replace traditional gradient-based training.

**Figure 1.** Prediction root mean squared error (RMSE) of the eight models using different time lags. *x*-axis denotes the time lag in weeks, and *y*-axis denotes the RMSE. (**a**) Chronic gastroenteritis; (**b**) gastrointestinal ulcers; (**c**) gastrointestinal tumors. MLR: multiple linear regression; ANN: artificial neural network; DBN: deep belief network; EvoDBN: evolutionary DBN; DAE: deep autoencoder; EvoDAE: evolutionary DAE; DDAE: deep denoising autoencoder; EvoDDAE: evolutionary DDAE.

**Figure 2.** *Cont.*

**Figure 2.** Accuracies of the models for gastrointestinal morbidity prediction. (**a**) Acute gastroenteritis; (**b**) chronic gastroenteritis; (**c**) gastrointestinal ulcers; (**d**) gastrointestinal tumors; (**e**) food poisoning; (**f**) other gastrointestinal infections.
