ADR: An Adversarial Approach to Learn Decomposed Representations for Causal Inference

Estimating the individual treatment effect (ITE) from observational data is an important issue both theoretically and practically. While including all the pre-treatment covariates is the common practice for the inclusion of all possible confounders, it may aggravate the issue of data imbalance. In this paper, we theoretically show that including extra information would increase the variance lower bound. Based on the causal graph, we decompose the covariates into three components, namely instrumental variables (I), confounders (C), and adjustment variables (A). Both C and A should be included for the ITE estimation, while I should be avoided since it would aggravate the imbalance issue and contains no extra information for the ITE estimation. To facilitate the decomposed representation learning, we derive the probabilistic conditions for {I, C, A} from the graphical definitions, and theoretically show that such decomposition can be learned in an adversarial manner. Under the guidance of such theoretical justification, we propose the ADR algorithm, an adversarial learning approach to learn the decomposed representations and simultaneously estimate the treatment effect. The proposed algorithm can be applied to both categorical and numerical treatments and the effectiveness is assured by both theoretical analyses and empirical results. Experimental results on both synthetic and real data show that the ADR Algorithm is advantageous compared to the state-of-the-art methods. The theoretical analyses also provide a path to further explore the issue of decomposed representation learning for causal inference.