## 4 Experiment
### Result
#### 4.4.2 Missing Factor in VS-GRU  
In order to further discuss the missing factor impact on classification problems, we implement two experiments: replacing the missing factor with missing rate (VS-GRU-\(\mu\) and VS-GRU-i-\(\mu\)) and removing the missing factor from the update functions (VS-GRU w/o \(\beta\) and VS-GRU-i w/o \(\beta\)). To be specific, we replace the missing factor \(\beta\) with missing rate \(\mu\) in the first layer of VS-GRU-i-\(\mu\) and replace the missing factor \(\beta\) with \(1-\mu\) in penalized mechanism in the second layer. Thus, the variables with a higher missing rate get more punishment. The experimental results are shown in Tables 4 and 5. We can see from the results that missing factor is beneficial to model performances. In single-task problems, VS-GRU-\(\mu\) outperforms VS-GRU w/o \(\beta\). However, the situation is quite the opposite in multi-task problems. We suggest that the reason is that the missing factor is not only used in the update functions in the first layer but also used as penalized mechanism in the second layer of VS-GRU-i. Given the massive missing values in the datasets, the missing rate of many variables is close to 1. The missing factor can learn the slight differences between missing rates and provide more learnable features to the models. In addition, instead of calculating the missing rate using all the records, we calculate the missing rate within the first and last 24 h, which are called VS-GRU-update and VS-GRU-i-update. Then we test the models if we can update the missing rate every 24 h without significant changes in model performance. We execute the two tasks experiments on MIMIC-III using the update models and original models we propose without the dynamic imputation mechanism. We can see from Table 6 that the performances of VS-GRU and VS-GRU-i stay stable in the case of updating the missing rate.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Mortality Task (PhysioNet)** & **Mortality Task (MIMIC-III)** \\ \hline VS-GRU & **0.8502 \(\pm\) 0.010** & **0.8576 \(\pm\) 0.007** \\ VS-GRU-\(\mu\) & 0.8479 \(\pm\) 0.006 & 0.8554 \(\pm\) 0.007 \\ VS-GRU w/o \(\beta\) & 0.8469 \(\pm\) 0.014 & 0.8549 \(\pm\) 0.008 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison on the missing factor in a single task.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **All 4 Tasks (PhysioNet)** & **ICD-9 Code Tasks (MIMIC-III)** \\ \hline VS-GRU-i 1  & **0.8534 \(\pm\) 0.018** & **0.7196 \(\pm\) 0.003** \\ VS-GRU-i-\(\mu\) & 0.8451 \(\pm\) 0.008 & 0.7103 \(\pm\) 0.002 \\ VS-GRU-i w/o \(\beta\) & 0.8455 \(\pm\) 0.015 & 0.7174 \(\pm\) 0.003 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison on the missing factor in multi-task.  
Figure 9: The Pearson correlation coefficient between labels in ICD-9 Code tasks on MIMIC-III. \(x\)-axis, the label pair id in ICD-9 Code tasks; \(y\)-axis, Pearson correlation coefficient between labels.  
Figure 10 plots the learned missing factor of 33 variables in PhysioNet. More than half of the variables have an unchanged missing factor during the changing missing rate, which means that the missing rate of these variables may have little impact on this classification task. In other situations, the missing factor decreases as the missing rate increases, which fit the common sense that we should pay more attention to the variables with a low missing rate. This indicates that the characteristics of these variables are related to their observation frequency. However, two variables behave in the opposite way: TropT (missing rate 0.9983) and Urine (missing rate 0.9917). We suggest that variables with relatively high missing rates lack training examples for missing factors to learn the pattern at a low missing rate, resulting in different trends from other variables. In addition, in the test set, the examples of these variables in the low missing rate are rare. It is safe to say that it causes little impact on classification performance.