## 3 Results
### Gene Association Predictions Using Differential Gene Expression and Gene Embedding Profiles  
In order to acquire a differential gene expression profile for ASD, we extracted gene expression data from the GEO database [14] for the GSE6575 and GSE28521 datasets. The GSE6575 dataset encompassed 22,237 genes, whereas the GSE28521 dataset comprised 8363 genes. By comparing these datasets, we identified 8268 genes that were common to both. Subsequently, we narrowed down our selection to only include genes present in the STRING database [41], and this resulted in a final set of 5330 genes. For each gene, we calculated the differential gene expression values, resulting in 2088 features. Additionally, we performed gene embeddings on the ASD-associated gene network and obtained 128 features. By combining 2088 differential expression features, we obtained a total of 2216 features for each gene. These differential gene expression profiles and gene embedding profiles were concatenated for all 5330 genes. After this, these profiles were used to calculate association features for gene pairs, and this resulted in a total of 14,201,785 gene pairs with 2216 association features. Among these pairs, 3611 pairs were recognized in the AutDB database [42,44] and thus defined as the positive set for gene association prediction. To train and test the classification models, we employed a balanced binary classification approach in which the number of positive instances and the number of negative instances were equal in order to ensure unbiased predictions for both classes. To achieve this task, we employed the undersampling technique, randomly selecting positive and negative samples in the same quantity, which amounted to 3611 instances. During the training  
Figure 1: Overview of gene association analysis framework. processes, we applied the RFE algorithm to find the optimal features for each classifier. In this study, the naive Bayes classifier, neural network classifier, random forest classifier, and the XGBoost algorithm were tested for their classification performance. The XGBoost algorithm proved to be the best classifier. The comparisons of the performances of these classification methods and the investigation of the top relevant features recognized by the RFE algorithm will be analyzed and discussed in this section. The promising associations detected by the algorithm are reported in the next section. Using the complete association features generated from the differential expression profiles and the gene embedding profiles, the XGBoost classifier yielded the best performance, with an average area under the curve (AUC) of 0.8249 and an average accuracy of 0.7532. Furthermore, we also investigated the impact of different feature sets on classification performance. Therefore, we discarded some of the association features generated from the gene embedding profile and used the same procedures for the classifications. The performance slightly decreased, with an average AUC of 0.8074 and an average accuracy of 0.7368. Moreover, we excluded the differential expression profile from the association features and performed the same classification procedures. The performance further decreased, with an average AUC of 0.7805 and an average accuracy of 0.7106. These results indicate that both the differential gene expression profile and the gene embedding profile are essential for the association classifications. Furthermore, we explored other classifiers, i.e., the naive Bayes, neural network, and random forest classifiers, using the complete set of association features. The results showed that the XGBoost classifier outperformed the other classifiers, while the random forest classifier presented good performances, with an average AUC of 0.7779. However, in our experiments, its performance was still inferior to the classification performances of the XGBoost classifier. Moreover, we observed the classification performances obtained from the naive Bayes and neural network classifiers.