CV criterions and tuning

[erikcs]

Some "heuristic" covariate imbalance related CV criterions are

• balance loss (Tan, 2020)
• average norm of gradient of balance loss = norm of covariate imbalance (Zhao, 2019)
• mean covariate imbalance, SMD, (Wang & Zubizarreta, 2020; Chattopadhyay, Hase, & Zubizarreta, 2020)

AFAIK these CV criterions are not explicitly theoretically grounded, are some open questions in the literature.

This paper discusses alternative ways of selecting the level of regularization.

(Ensure: do not divide by zero as all these metrics are evaluated out-of-fold)

• For augmentation/debiasing end-use cases, there's the Riesz loss.