Find the best interpolation method for missing observations
The most basic method that springs to mind is split of a test set:
Take the data where you have recorded all variables which you might need to extrapolate in another set, and split of a percentage of that and &quot;mask&quot; or hide the variable you wish to interpolate in this split (maybe using the data from the other part of the split if you're using some sort of trained interpolation).
Compare the results of the different interpolation methods you are using with the actual values (that you've taken out) on a metric that suits your purpose for the data best (e.g. mean squared error, mean absolute error, logistic loss, or maybe even the outcome of some machine learning method trained on the dataset).
That way, you'll find the interpolation method that best suits your data + problem.
One thing to keep in mind is that your masking should follow the same (if any) patterns that your actual missing data has: e.g. if it only happens on certain time periods, your masking method should try to follow that pattern if possible.