Instrumental Variable Estimation for Causal Inference in Longitudinal
  Data with Time-Dependent Latent Confounders
Debo Cheng Ziqi Xu Jiuyong Li Lin Liu Jixue Liu Wentao Gao Thuc Duy Le
Causal inference from longitudinal observational data is a challenging
problem due to the difficulty in correctly identifying the time-dependent
confounders, especially in the presence of latent time-dependent confounders.
Instrumental variable (IV) is a powerful tool for addressing the latent
confounders issue, but the traditional IV technique cannot deal with latent
time-dependent confounders in longitudinal studies. In this work, we propose a
novel Time-dependent Instrumental Factor Model (TIFM) for time-varying causal
effect estimation from data with latent time-dependent confounders. At each
time-step, the proposed TIFM method employs the Recurrent Neural Network (RNN)
architecture to infer latent IV, and then uses the inferred latent IV factor
for addressing the confounding bias caused by the latent time-dependent
confounders. We provide a theoretical analysis for the proposed TIFM method
regarding causal effect estimation in longitudinal data. Extensive evaluation
with synthetic datasets demonstrates the effectiveness of TIFM in addressing
causal effect estimation over time. We further apply TIFM to a climate dataset
to showcase the potential of the proposed method in tackling real-world
problems.