I am having some trouble understanding what loss function is being minimized to ensure that we are converging towards the best set of weights in the Genmatch function in R. I was reading the paper on it and if I understand right, it seems to say somewhat contradictory things on the same page.
1) First it says that a generalized version of the mahalanobis distance is minimized. This doesn't make too much sense to be as this distance metric is only for measuring the distance between 2 subjects, and does not look at the overall balance between 2 populations. If it does minimize the average distance between the two populations, that is not stated in the paper, and does not seem to stated anywhere else either. Excerpt:
2) Then on the same page it is stated the overall balance is maximized using the p values from t-tests and KS tests. This one makes more sense to me. But I am not sure how the Mahalanobis distance mentioned earlier plays a part in this. Excerpt:
If anyone knows what loss function is being used please let me know
Link for paper: https://www.mitpressjournals.org/doi/10.1162/REST_a_00318