**4. Discussion**

This study constructed and compared eight models for predicting the morbidities of six main gastrointestinal diseases from food contamination. Results demonstrate that some deep-learning models can achieve relatively high prediction accuracy. However, this does not mean that gastrointestinal diseases are mainly caused by food contamination, or that gastrointestinal morbidities in a region are mainly determined by the levels of food contamination. In fact, the relationships between food contamination and gastrointestinal morbidities can be highly complex and probabilistic, and morbidities are also affected by many other factors, such as the dietary habits and working pressures of inhabitants, and the levels of health services of that society. Our study reveals that, given a large number of historical data of food contamination and gastrointestinal morbidities in a region, we could use deep neural networks to learn such highly complex and probabilistic relationships. After sufficient training, we could obtain models that embed other influencing factors into model parameters, and thus output relatively accurate morbidities from food-contamination inputs. Consequently, the prediction results would be very useful to improve healthcare services.

In general, the traditional MLR model is incapable of learning complex relationships for morbidity prediction. According to our results, its average prediction accuracy is below 20% on most diseases. For food poisoning, MLR achieves the highest prediction accuracy of 41.5%, which is also significantly less than the seven other models. The low performance of MLR indicates that relationships between food contamination and gastrointestinal morbidities are highly nonlinear and probabilistic, which is beyond the capability of the linear model.

The shallow ANN model performs much better in approximating nonlinear relationships. However, its average prediction accuracy is only between 30% and 40% in most cases, which is still too low for medical management. This is mainly because the number of food-contamination indicators is large, and the generalization ability of the classical three-layer structure of ANN decreases dramatically with increasing dimension.

DNN models can effectively overcome the limitations of the MLR and shallow ANN models, as they can learn complex probabilistic distributions over a large number of influence factors by automatically discovering intermediate abstractions layer by layer. Comparing DBN and DAE, two of the most widely used DNNs, DAE achieved higher accuracies than DBN on five gastrointestinal diseases, while DBN only achieved higher accuracy on gastrointestinal tumors. This indicates that the energy-based probabilistic model of DBN is less effective than the reconstruction-error minimization model of DAE in morbidity prediction. By introducing the denoising learning mechanism into DAE, DDAE achieved significantly higher accuracies than DBN and DAE on all gastrointestinal diseases. This is because the food-contamination data inevitably contain much noise, which can often mislead the learning process of DAE, while DDAE is much more robust in handling noisy inputs.

It was also observed that the prediction performance of all three DDNs could be significantly improved by equipping them with evolutionary training algorithms, because gradient-based training algorithms are easily trapped in local optima. An evolutionary algorithm uses a population of candidate solutions to simultaneously explore the search space; if some solutions are trapped in local optima, others can still explore other regions and help the trapped solutions jump out of local optima. Consequently, evolutionary DNNs can effectively suppress premature convergence and exhibit high learning abilities. Among the eight models, EvoDDAE that combines DDAE with evolutionary learning exhibited the best performance for morbidity prediction.

Among the six main types of gastrointestinal diseases, the prediction accuracies on three types of acute diseases are generally higher than other diseases, because the pathogenic mechanisms of acute diseases are relatively simpler, and their time-lag effects are easier to determine. That is why all models achieved the highest prediction accuracies on food poisoning, which is considered as "the most acute" disease. Among the diseases, each DNN model achieved the lowest prediction accuracy on gastrointestinal tumors, mainly because the pathogenic mechanisms of tumors are more complex than other diseases, and thus their correlation with food contamination is much weaker or is much difficult to learn.
