I have a question on imputation of missing values. A support vector machine does not work with missing values, and in practice i thus hence na.omit the rows / cases with missing values on any of the parameters (e.g. X1 to X10). From a theoretical perspective, can one improve the overall classification performance if one imputes the missing values for the values of one missing parameter (lets say X1) through predicting the missing values of this parameter based on e.g. a multiple regression, SVM on the remaining parameters (e.g. X2-X10)? Asking the question, because the performance in practice is often disappointing, and hence wondering whether there is a theoretical reason why my approach per above might be nonsense / not useful.

In a similar vein - as a decision tree does work with missing values, and hence should use the full information of the existing dataset, am i right to assume that in this case from a theoretical perspective there is definitely no value-add / benefit in imputing missing values by using the other input parameters?