Sample Representing a Different Population I have two sets of populations: containing 1.5 million and 5.5 million units. I need to select a sample out of 5.5 million population so that the sample represents the 1.5 million population based on one or more variables. 
Is there any technique available in order to achieve this?
 A: Your problem is a bit similar to domain adaptation.
You can use the following idea.
Create a unified dataset of both populations and use the source of the sample as the concept.
Lest call the 1.5M dataset source and the 5.5M dataset target.
Build a classifier to distinguish between the samples.
If your classifier is prefect than the populations are different and you have a proof of that. Hence, you cannot sample from the target population samples similar to the source population. Don't worry about this scenario to much, perfect classifiers are very rare.
If your classifier performs well, than you find a way to identify the samples from the source. Now take samples from the target that your classifier predicts that they belong to the source. Note that these are actually errors of the classifier but it errors on them since they are similar to samples from the source.
In case that your classifier doesn't perform well, we would have want to conclude that the datasets are indistinguishable so you can just sample however you want from the target source. Unfortunately, this is not true. There are plenty of reasons why your classifier can miss identify existing difference (e.g. , not the proper classifier).  
In such case you should still go and sample from the target, at least knowing that there was no difference that you have found, meaning that they are similar from your point of view.
