# Age Estimation from fMRI Data Using Recurrent Neural Network
## 4 Experiments
### Results  
Table 3 shows the performance of the proposed model and other baseline models on the test dataset (155 data points). It provides the correlation between estimated age and the actual age. In addition to \(MSE\), we compute the mean absolute error (\(MAE\)) to measure the accuracy of age estimation  
\[MAE=\frac{1}{n}\sum_{i=1}^{n}|f_{NN}(X^{(i)}-y^{(i)}|\]  
We also provide the intraclass correlation coefficient (ICC) to evaluate the model's performance. The ICC evaluates the consistency of the same number of measurement results measured by multiple observers. Here, we take the actual age and the predicted age as two measurement results and judge the prediction model's performance by the degree of consistency. The GRU model shows the best performance while the Transformer model has comparable results. Figure 4a shows the performance of the GRU model where the \(x\)-axis shows the age of the subject and the \(y\)-axis represents the estimated age by the proposed model. The gender of the subjects are indicated where blue dots represent male subjects, and red triangles represent female subjects. It can be seen that more than 80% of the estimations are \begin{table}
\begin{tabular}{c c} \hline
**Training/Validation** & **Test** \\ \hline
640 & 155 \\ \hline \end{tabular}
\end{table} 
Table 2: Data volume distribution of training, validation, and test datasets. within the \(\pm 12\) range of the actual age. The correlation coefficient between the estimation and the actual age is \(r=0.905\). The training results using the Transformer model are shown in Figure 4b. These results will be discussed in Section 4.5. Since most previous works [37; 39; 40; 42] focus on structural MRI input and codes are not available online, we compare our results with [PERSON] et al. [46], which computes a correlation between entropy and actual age based on fMRI data samples. Figure 4c shows the relation between entropy and age. The correlation coefficient between the entropy and the age is \(r=0.292\), which is weaker than the proposed estimation model. In addition, we provide Bland-Altman plots to visualize the results. The Bland-Altman plot shows the consistency between two different measurements. Here, we use the actual age of the test data sets as a known measurement and the predicted age as another measurement value. Figure 4d,e show Bland-Altman plots of the GRU model and Transformer model. What needs attention here is the processing of the entropy results. Since the entropy value is not an age estimation, we first find a linear regression model that  
Figure 4: The first line of figures are age estimation results of the proposed GRU model and Transformer model, and the relation between entropy and age. The \(x\)-axis represents the actual age of the subject whereas the \(y\)-axis represents the estimated age. (**a**) MSE loss function with dropout; (**b**) use Transformer encoder model; (**c**) relation between entropy and age. The solid line is the best diagonal when the actual age matches the estimated age. The dotted line refers to the deviation line 12 years away from the actual age. The second line of figures are the Bland–Altman (B&A) plot corresponding to the above. (**d**) Bland–Altman plot of GRU; (**e**) Bland–Altman plot of Transformer encoder model; (**f**) Bland–Altman plot of entropy. The \(x\)-axis is the average of each sample’s actual and predicted age, and the \(y\)-axis is the difference between the exact age and the predicted age of the sample. The solid line is the average of the difference. The dashed line is the upper and lower limits of 95% agreement, i.e., \(\pm 1.96\) standard deviations.