Machine learning for imputation? I am currrently working on a paper where we have two datasets, where I wish to impute variables from one dataset onto the other. The way that I have been currently thinking about this is to use machine learning. The case is as follows: 
Dataset 1: Linkable, randomly drawn and representative survey data (firm level)
Dataset 2: Linkable, high dimension, administrative total population data (firm level)
Within Dataset 1, we have a binary variable of interest (Collaborative innovation) which we wish to impute for the entire population in Dataset 2. The strategy that I have applied for this so far is to use LASSO, where a wide array of variables from Dataset 2 have been used to create a predictive model. 
The problem, however, is that the outcome, "Collaborative innovation" is too rare for the LASSO to stick, despite rich data. My question is hence:
Are there other contending techniques (machine learning or otherwise) that could be used to impute these outcomes? Could perhaps Generative Adverserial Networks be applied? (i.e., create a "fake" outcome based on supplementary data). 
I hope I have expressed myself sufficiently clear. 
Thank you for your time.
 A: Judging by the data that you present, it does not look like an inputation problem, but rather a prediction one. If I am not mistaken, you have a first representative dataset containing your target variable, and a second dataset where you want to insert it. This can be seen as a supervised learning problem (and indeed, LASSO is a supervised learning algorithm). 
You can use any algorithm for supervised classification, I suggest Random Forests given the balance between performance on structured data and ease of use, but anything you are comfortable with will do it. 
Also, you mention that you target variable is very "rare", which in a classification setting means you have unbalanced classes. Some algorithm implementations allow to take this into account by setting up a ratio between the classes, other approaches can be oversampling of the minority class or undersampling of the majority one (I don't suggest the last one unless you have a lot of data). Finally, try to score your model using a metric that is more sensitive to unbalanced data, such as pAUC. 
if you are interested, I suggest this paper on the use of Random Forests for unbalanced data. Reading the beginning can give you an idea of the approaches to deal with the unbalance.
