Minimax Optimality in Causal Inference

EDWARD KENNEDY – CARNEGIE MELLON UNIVERSITY 

ABSTRACT

In this talk I will survey some recent work on minimax optimality in causal inference problems. We consider minimax optimality in smooth, structure-agnostic, and combined models, for both average and heterogeneous/conditional causal effects. In smooth models, higher-order influence function-based methods can yield optimal rates, which roughly resemble optimal rates for simpler quadratic functionals in smooth models (depending on assumptions about the covariate distribution). In structure-agnostic models, simpler doubly robust estimators are optimal. For particular combined models, the optimal rate is in between, and requires non-trivial bias correction involving regressions on estimated nuisance functions. For heterogeneous causal effects, minimax optimal rates interpolate between rates for functional estimation and nonparametric regression / density estimation, illustrating how these effects behave as a regression/functional hybrid.

Related Papers:

• https://arxiv.org/abs/2305.04116
• https://arxiv.org/abs/2203.00837
• https://arxiv.org/abs/2405.08525
• https://arxiv.org/abs/2403.15175