Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data

TL;DR

This work develops a novel Time-varying Conditional Instrumental Variables (CIV) for Debiasing causal effect estimation, referred to as TDCIV, which is the first to effectively learn time-varying CIV and its associated conditioning set without relying on domain-specific knowledge.

Abstract

Querying causal effects from time-series data is important across various fields, including healthcare, economics, climate science, and epidemiology. However, this task becomes complex in the existence of time-varying latent confounders, which affect both treatment and outcome variables over time and can introduce bias in causal effect estimation. Traditional instrumental variable (IV) methods are limited in addressing such complexities due to the need for predefined IVs or strong assumptions that do not hold in dynamic settings. To tackle these issues, we develop a novel Time-varying Conditional Instrumental Variables (CIV) for Debiasing causal effect estimation, referred to as TDCIV. TDCIV leverages Long Short-Term Memory (LSTM) and Variational Autoencoder (VAE) models to disentangle and learn the representations of time-varying CIV and its conditioning set from proxy variables without prior knowledge. Under the assumptions of the Markov property and availability of proxy variables, we theoretically establish the validity of these learned representations for addressing the biases from time-varying latent confounders, thus enabling accurate causal effect estimation. Our proposed TDCIV is the first to effectively learn time-varying CIV and its associated conditioning set without relying on domain-specific knowledge.

Figures (8)

• Figure 1: An example of the Women’s Interagency HIV Study demonstrating the impact of treatment adherence on HIV-related outcomes over time. Unmeasured variables, such as HIV disease status, mental health, and psychological well-being, serve as latent confounders that affect both the frequency of medication adherence and HIV viral load.
• Figure 2: (a) The full-time causal DAG $\mathcal{G}_{full}$ represents causal relationships over time, where $W_{t}$ and $Y_{t+1}$ denote the treatment and outcome, respectively. The time-varying causal effects of $W_{t}$ on $Y_{t+1}$ are shown in red. $\mathbf{X}_t$ and $U_t$ represent time-varying covariates and latent confounders, influencing both $W_{t}$ and $Y_{t+1}$. Blue dashed arrows indicate $W_1$'s effects on subsequent states of all variables, and similar temporal relationships exist for other variables. (b) The summary DAG $\mathcal{G}$ simplifies these mechanisms, omitting latent confounders between covariates $\mathbf{X}_t$ for clarity.
• Figure 3: We propose a full-time causal DAG $\mathcal{G}_{full}$, over time from $1$ to $t$, to disentangle and learn the representations of time-varying CIV and its conditioning set. Our goal is to query ${ACE}_t(W_t, Y_{t+1})$ over time, as indicated by the red arrow. $S_t$ and $\mathbf{Z}_t$ are the learned representations of time-varying CIV and its conditioning set.
• Figure 4: An overview of the TDCIV's architecture: The LSTM generates the historical data $\mathbf{H}_t$ as a function of the previous historical data $\mathbf{H}_{t-1}$ and the current input. Within the blue rectangle, the 2SLS estimators can be substituted with any CIV-based causal effect estimator. On the right side, the inference and generative networks collaboratively learn the latent representations of the time-varying CIV, $S_t$, and its corresponding conditioning set, $\mathbf{Z}_t$, over time.
• Figure 5: Comparison of absolute errors across all methods, presented with their means and standard deviations calculated over 30 synthetic datasets.

Theorems & Definitions (5)

• Definition 1
• Definition 2: Faithfulness
• Definition 3
• Theorem 1
• proof