I have a basic question as I am new to Data Science. I have a typical problem where I need to estimate the effect of an intervention between experimental and control groups. I read propensity matching is the way to go to compare 'like' candidates and people use Logistic regression (LR) to calculate propensity scores. My basic question is, isn't LR a supervised machine learning technique? What will be my training data for LR? In other words, how can LR predict the probability of being assigned to either groups just based on some properties about the candidates?
The test data is the training data. Logistic regression uses the observed relationships between the predictors the observed treatment assignment to estimate numerical relationships between those predictors and the probability (actually the odds) of treatment assignment. Then once you have those numerical relationships, you apply them to the same data set used to estimate the relationships to generate the predicted probabilities.
Overfitting is not really a problem here because the goal or propensity score analysis is not good prediction but rather covariate balance (where each covariate has the same distribution across treatment groups). There actually are machine learning methods to estimate propensity scores: generalized boosted modeling is the most popular. Again, because the test data is the training data, you must impose a stopping condition other than good prediction to arrive at valid propensity scores; that stopping condition is usually a numerical summary of covariate balance.