Sequential Causal Effect Estimation by Jointly Modeling the Unmeasured Confounders and Instrumental Variables

Sequential causal effect estimation has recently attracted increasing attention from research and industry. While the existing models have achieved many successes, there are still many limitations. Existing models usually assume the causal graphs to be sufficient, i.e., there are no latent factors, such as the unmeasured confounders and instrumental variables. However, in real-world scenarios, it is hard to record all of the factors in the observational data, which makes the causally sufficient assumptions not hold. Moreover, existing models mainly focus on discrete treatments rather than continuous ones. To alleviate the above problems, in this paper, we propose a novel <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b>ontinous <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b>ausal <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</b>odel by explicitly capturing the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</b>atent <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</b>actors (called <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C<inline-formula><tex-math notation="LaTeX">$^{2}$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="sun-ieq1-3510734.gif"/></alternatives></inline-formula>M-LF</b> for short). Specifically, we define a sequential causal graph by simultaneously considering the unmeasured confounders and instrumental variables. Second, we describe the independence that should be satisfied among different variables from the mutual information perspective and further propose our learning objective. Then, we reweight different samples in the continuous treatment space to optimize our model unbiasedly. Beyond the above designs, we also theoretically analyze our model’s causal identifiability and unbiasedness. Finally, we conduct extensive experiments on both simulation and real-world datasets to demonstrate the effectiveness of our proposed model.