Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning

TL;DR

This work tackles long-term individual causal effect estimation in the presence of latent confounding by adopting an identifiability-driven latent representation learning approach. It introduces ICEVAE, a three-module estimator that uses an auxiliary variable $U$ and iVAE to recover latent confounders $Z$ from heterogeneous observational and experimental data, enabling identification of the long-term ITE $\tau(x)$. The authors prove identifiability of $Z$ up to permutation and invertible transformations under standard nonlinear ICA conditions and then show $\tau(x)$ is identifiable given $Z$, providing strong theoretical guarantees. Empirically, ICEVAE outperforms baselines on five synthetic and two semi-synthetic datasets, demonstrating robustness to violations of latent unconfoundedness and confounding strength, and achieving superior heterogeneous long-term effect estimation. These results suggest practical applicability for long-horizon decision-making in domains with data heterogeneity and unobserved confounding.

Abstract

Estimating long-term causal effects by combining long-term observational and short-term experimental data is a crucial but challenging problem in many real-world scenarios. In existing methods, several ideal assumptions, e.g. latent unconfoundedness assumption or additive equi-confounding bias assumption, are proposed to address the latent confounder problem raised by the observational data. However, in real-world applications, these assumptions are typically violated which limits their practical effectiveness. In this paper, we tackle the problem of estimating the long-term individual causal effects without the aforementioned assumptions. Specifically, we propose to utilize the natural heterogeneity of data, such as data from multiple sources, to identify latent confounders, thereby significantly avoiding reliance on idealized assumptions. Practically, we devise a latent representation learning-based estimator of long-term causal effects. Theoretically, we establish the identifiability of latent confounders, with which we further achieve long-term effect identification. Extensive experimental studies, conducted on multiple synthetic and semi-synthetic datasets, demonstrate the effectiveness of our proposed method.

Figures (6)

• Figure 1: Three causal graphs in long-term scenarios with $X$ being the pre-treatment variables, $Y$ being the long-term outcome, $Z$ being the latent confounders, $S$ being short-term outcome, $U$ being the auxiliary variable, and $W$ being the treatment. White nodes denote the observed variables and grey nodes denote the unobserved variables. The dashed edges exist in the observational data but are absent in the experimental data. The dashed node $Y$ means $Y$ can be observed in observational data but not in experimental data. Specifically, Fig. \ref{['figure lat uncon']} shows the causal graph satisfying the latent confoundedness assumption athey2020combining. Fig. \ref{['figure condi uncon']} shows the causal graph satisfying the equi-confounding bias assumption ghassami2022combining, where the blue arrows in Fig. \ref{['figure condi uncon']} indicate the equal confounding bias. Fig. \ref{['figure our model setting graph']} shows the causal graph of our setting.
• Figure 2: Two causal graphs in our setting. The white nodes denote observed variables and the grey denote unobserved variables. Fig. \ref{['figure obs']} is the causal graphs of observational in our setting. Fig. \ref{['figure exp']} is the causal graph of experimental data in our setting.
• Figure 3: Overall architecture of the generative and inference networks for our model. Grey nodes represent MLP, green nodes correspond to the distribution trained on experimental data and blue nodes correspond to the distribution trained on observational data.
• Figure 4: Result on the fifth synthetic dataset. Fig. \ref{['figure MCC1']}-\ref{['figure MCC4']} show the scatterplots between each ground-truth and estimated latent confounder.
• Figure A.1: Two causal graphs in our setting. The white nodes denote observed variables and the grey denote unobserved variables. Fig. \ref{['figure obs']} is causal graphs of experimental in our setting. Fig. \ref{['figure exp']} is causal graph of observational data in our setting.

Theorems & Definitions (5)

• Theorem 1
• Theorem 2
• Definition A.1: Identifiability of Latent Variables $Z$
• proof
• proof