## 4 Experimental Results
### Results of Structural Performance  
As shown in Figure 2a (see Table S1 in the Supplementary Materials for details), the precision values of the networks inferred based on the original data (dashed line) and the  
Figure 3: Results of precision, recall, and structural accuracy on the Boolean discretization dataset. (**a–c**) Results for the network with \(|V|=50\). (**d–f**) Results for the network with \(|V|=100\). The Y-axis denotes the performance metrics, and the X-axis indicates the number of observed time steps in the original gene expression data. For the synthesized dataset, gene expression data are generated for \((100-K)\) time steps. Solid and dashed lines represent the results based on the synthesized and the original dataset, respectively. Each point and error bar indicates the average value and the standard deviation, respectively, over 10 random networks. The bar charts show the performance improvement of the synthesized dataset over the original dataset. Figure 2: Results of precision, recall, and structural accuracy on the multi-level discretization dataset. (**a–c**). Results for the network with \(|V|=50\). (**d–f**). Results for the network with \(|V|=100\). The Y-axis denotes the performance metrics, and the X-axis indicates the number of observed time steps in the original gene expression data. For the synthesized dataset, gene expression data are generated for \((100-K)\) time steps. Solid and dashed lines represent the results based on the synthesized and the original dataset, respectively. Each point and error bar indicates the average value and the standard deviation, respectively, over 10 random networks. The bar charts show the performance improvement of the synthesized dataset over the original dataset. synthetic data (solid line) continuously increase as the observed time steps (\(K\)) increase in the networks with \(|V|=50\). This is because the more expression data used for the inference algorithm, the higher the inference performance. The precision improvement by the use of the synthetic data was observed in all \(K\) values except for \(K=60\) and \(90\). In addition, we can observe a similar trend with respect to the recall performance (Figure 2b). In particular, the degree of the performance improvement at \(K=10\) was significantly larger. These observations indicate that the precision improvement by the synthetic data is not by reducing the number of positive predictions of interactions but by predicting the true positive interactions more accurately. Although the synthetic data also improved the structural accuracy, the improvement was not significant (Figure 2c). This is because the number of true negatives is much larger than that of true positives. We note that these findings were consistently observed in the networks with a larger network size (\(|V|=100\)) (Figure 2d-f). Taken together, our synthetic approach can be considerably useful when the observation time of the gene expression is limited in the real experimental environment. We also investigated our method with respect to the Boolean networks, as shown in Figure 3 (see Table S2 in the Supplementary Materials for details). As in the ternary network results, we can observe the performance improvement of precision, recall, and structural accuracy in most cases. This means that our method is also effective in the Boolean network models. It is interesting that the recall improvement by our method was relatively larger on average than the precision improvement in the case of \(|V|=50\), whereas the latter was relatively larger than the first in the case of \(|V|=100\). This is because the MIDNI algorithm cannot control the number of positive predictions. However, we note that there is no negative influence on any performance measure. It is also interesting that the performance improvement does not increase as the observation time step \(K\) increases.