# Adaptive Imputation of Irregular Truncated Signals with Machine Learning
## 5 Discussion  
From the results shown in Table 5, we can see that for most features and under all missing data mechanisms, the MAE and RMSE increase as the level of missingness increases. This is expected behavior as the more missing data there is, the harder it is to achieve accurate imputation as there is less data to base predictions off of. Between the two error metrics, the RMSE values are consistently higher than the MAE values for the same conditions, reflecting the sensitivity of RMSE to larger errors due to its squaring of error terms. When data was missing in an MCAR scheme, the temperature feature showed a relatively stable performance up to 50%, after which a significant uptick in the error percentage was observed in both metrics. A continuous increase in error rates as the level of missingness increases is observed for the pressure feature, indicating greater difficulty in imputing the values in this feature accurately under MCAR. For the values in the vibration feature, the error rate actually improved marginally for higher levels of missingness up to 50%, which is an interesting characteristic that warrants further examination. For MAR, there was an irregular pattern in MAE and RMSE but generally worse performance with very high missingness for the temperature feature, while the vibration feature showcased a slightly more controlled increase in error rates as missingness increased, especially when compared to MCAR. For the pressure feature under an MNAR scheme, the error rates remained somewhat stable across varying levels of missingness, suggesting that the imputation method may be somewhat robust to the MNAR mechanism for this particular feature. The vibration feature showed a gradual increase in error with missingness but starts from a higher baseline at lower missingness levels. Overall, across all of the levels of missingness, the different imputation techniques, and the type of missing data, the pressure feature generally shows the highest rates of errors, suggesting that it may be inherently more difficult to impute accurately compared to temperature and vibration. Table 6 shows that when no data is missing from the simulated dataset, the RF classifier is extremely accurate at identifying both the operational condition of the machine, as well as the type of fault that is occurring if one is. From Table 7, it is apparent that imputed data where the missing data mechanism was MCAR has the most detrimental effect on the performance of the RF classifier, especially as the percentage of data that was imputed rises. The results show that for missing data percentages of 11%, classifying machine condition and fault type performs relatively well, but at 30% missing data, there is a drastic drop off in terms of classification accuracy, which, despite a mild uptick at 31%, continues as the missing data percentage increases. This accuracy drop off is especially apparent when trying to diagnose the specific type of fault that is occurring, with the lowest accuracy score for values in the \"Error_Code\" feature being 20.69% compared to 58.55% for the \"Status\" feature. Of the three missing data mechanisms, MAR appears to lead to the most consistent results with the least negative impact on classification accuracy. The results show that up until the percentage of missing data gets to 90%, the accuracy of the model does not drop below 90%, and even with the accuracy does drop off at 90% missing data, the model still returns the correct machine condition 83.26% of the time and the correct fault type 82.89% of the time, which is still a reasonable accuracy. As with the classification accuracy under MCAR, the accuracy for the \"Error_Code\" class is slightly lower than the \"Status\" class. The performance of the RF classifier on imputed MNAR data is slightly worse than on MAR data, but is still relatively consistent and accurate, especially compared to MCAR data. The accuracy drops more frequently and at lower percentages of missing data compared to MAR, but it is still reasonable.