Latent confounders are a fundamental challenge for inferring causal effects from observational data. The instrumental variable (IV) approach is a practical way to address this challenge. Existing IV based estimators need a known IV or other strong assumptions, such as the existence of two or more IVs in the system, which limits the application of the IV approach. In this paper, we consider a relaxed requirement, which assumes there is an IV proxy in the system without knowing which variable is the proxy. We propose a Variational AutoEncoder (VAE) based disentangled representation learning method to learn an IV representation from a dataset with latent confounders and then utilise the IV representation to obtain an unbiased estimation of the causal effect from the data. Extensive experiments on synthetic and real-world data have demonstrated that the proposed algorithm outperforms the existing IV based estimators and VAE-based estimators.

Instrumental variables (IVs), sources of treatment randomization that are conditionally independent of the outcome, play an important role in causal inference with unobserved confounders. However, the existing IV-based counterfactual prediction methods need well-predefined IVs, while it's an art rather than science to find valid IVs in many real-world scenes. Moreover, the predefined hand-made IVs could be weak or erroneous by violating the conditions of valid IVs. These thorny facts hinder the application of the IV-based counterfactual prediction methods. In this paper, we propose a novel Automatic Instrumental Variable decomposition (AutoIV) algorithm to automatically generate representations serving the role of IVs from observed variables (IV candidates). Specifically, we let the learned IV representations satisfy the relevance condition with the treatment and exclusion condition with the outcome via mutual information maximization and minimization constraints, respectively. We also learn confounder representations by encouraging them to be relevant to both the treatment and the outcome. The IV and confounder representations compete for the information with their constraints in an adversarial game, which allows us to get valid IV representations for IV-based counterfactual prediction. Extensive experiments demonstrate that our method generates valid IV representations for accurate IV-based counterfactual prediction.