## 4 Effectiveness of Data Imputation
### Observations
* **Noise-insensitive tasks**: Tasks with contour curves above the diagonal (e.g., NLP-SL) are more robust to imputation noise. These observations are summarized in the Figure 8.  
Additional experiments were conducted using other common imputation methods. For NLP-SL, two imputation methods are introduced: \"wordvec\" and \"BERT\". The wordvec imputation uses context word vector embeddings (GloVe) and cosine similarity to impute missing words. The BERT method leverages the pre-trained bert-base-uncased model for imputation. These two imputation methods are examples of \"exact imputation\". The results of these experiments are shown in Figure 9a,b. To speed up preprocessing, a subset ratio of 0.1 was used for BERT imputation. Figure 8: An illustration of the imputation advantage pattern. The \(x\)-axis denotes the data-missing ratio \(p\), and the \(y\)-axis represents the imputation noise level \(q\). “Imputation advantageous corner” and “Imputation disadvantageous edge” are areas where imputation advantage and disadvantage concentrate, respectively. A task with a decision boundary below the diagonal line is called “noise-sensitive” and its decision boundary is fitted by exponential function. A task with a decision boundary above the diagonal line is called “noise-insensitive” and its decision boundary is fitted by logistic function. The model score for the NLP-SL task shows an increasing standard error, rising from 0.0015 to 0.0227 as the data corruption ratio increases from 0.1 to 1.0. Imputation using Word2 Vec leads to a significant performance decline relative to the no-imputation baseline (Figure 9a), indicating that this approach introduces more noise than it mitigates. BERT-based imputation effectively reconstructs informative content for classification while introducing minimal additional noise, resulting in better performance compared to the no-imputation condition (Figure 9b). At a noise-missing ratio of 0.3, the model score difference between BERT-based imputation and the no-imputation baseline is +0.046, with a standard error of 0.0043, yielding a \(z\)-score of 10.65. This difference is statistically significant. An important observation is that common imputation methods do not maintain a fixed accuracy level as the missing data ratio \(p\) varies. Instead, their performance corresponds to curves, rather than horizontal lines, on the advantage heatmap. For Signal-RL tasks, an imputation method called \"context-filling\" is proposed. In this approach, road occupancy cells with a value of zero are imputed as one if sufficient surrounding vehicles are detected, as illustrated in Figure 10. This imputation method is an example of \"general imputation\", where each element of the state vector is evaluated  
Figure 9: The effectiveness of alternative imputation methods. The \(x\)-axis represents the data-missing ratio, and the \(y\)-axis indicates the model score (normalized accuracy). Solid lines denote the no-imputation baseline, while dashed lines represent model performance with imputation. **(a)** Imputation using word vectors (NLP-SL task): This method introduces substantial noise, resulting in a significant performance drop compared to the no-imputation baseline. **(b)** Imputation using BERT (NLP-SL task): BERT-based imputation effectively recovers informative content useful for classification while introducing considerably less noise, leading to improved performance over the no-imputation baseline. At \(p=0.3,\text{model score difference}=+0.046,\text{std error}=0.0043\), \(z\)-score = 10.65; the difference is significant. **(c)** Context-filling imputation (Signal-RL task): This method shows no clear advantage over no imputation. At \(p=0.6,\text{model score difference}=-22,\text{std error}=15,z\)-score = \(-1.48,p\)-value = 0.14; the difference is not significant. for potential correction. Model performance with context-filling imputation, compared to the no-imputation baseline, is presented in Figure 9c.