I want to classify customers who at risk to churn (unsubscribe). The typical path would be to have a training set of historical data that includes observations of customers who churned so that we have a binary target variable. In such a case, there are many straightforward options.
Now, assume we have the same objective of predicting a customer who is at risk of churning, but our data has exclusively customers that have not churned. For example, say the company providing the data doesn't understand statistics, and they automatically delete all records of customers who churned such that we only have the "survivors." Assume that this data on churned observations is 100% gone and unrecoverable, we can only work with the data on survivors.
In this case, we do not have the desired target variable, but we still want to predict churn. What we do have are several variables that we know tend to be highly correlated to churn based on other data sets and literature.
I've thought of fitting a model to a similar population then using that model on my data (requires the strong assumption that the populations are the same). I've considered predicting something that is known to be correlated to churn instead, and hoping that the company can provided expert opinion based on their experience to infer churn risk from that (not data-driven). I can't think of any way to make this into a supervised learning problem that results in a model that can be validated properly. Am I doomed to educated guesses, or can I pull some magic model out of a hat?