Deep Learning for Causal Inference
Momiao Xiong · 2022
The problems for causal discovery can be divided into two classes: bivariate causal discovery and causal network discovery. There are many methods for inferring causal relationships. A popular method that can be used for both bivariate causal discovery and causal network discovery is properly constrained functional structural causal models, including linear and nonlinear functions. The functional structural causal models can be used to model the observational variables and latent variables. Neural network is a universal approximation to any function. In this chapter, we will introduce deep learning as a general framework for causal inference. Two types of generative models: generative adversarial networks(GANs) and variational autoencoders(VAEs) will be explored as major tools for both bivariate causal discovery and large causal network reconstruction with discrete and continuous variables. Mediation analysis is to study how independent variables (causes, interventions) influence the outcomes (effects, outcomes) through intermediate variables (mediators). Univariate, multivariate, cascade unobserved mediation, and application of VAE to cascade unobserved mediation will be discussed. Confounders that affect both an intervention and its outcome obscure the real effect of the cases. Confounders will cause bias. It is a major obstacle to making valid causal inferences from observational data. This chapter introduces VAE with latent variable models and linear and nonlinear instrumental variables for causal inference with unobserved confounders.