Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Dynamic Causal Structure Discovery and Causal Effect Estimation

Jianian Wang, Rui Song

TL;DR

This work tackles the problem of learning causal graphs that evolve over time and estimating time-varying causal effects. It introduces a dynamic causal structure discovery framework that marries basis approximation with score-based learning, and extends to time-lagged dependencies via dynamic SVAR models. A variational autoencoder–based approach enforces acyclicity and treatment constraints to recover valid, time-varying graphs, while enabling past and future graph estimation and forecasting of causal effects. The method is validated through simulations and a real-world COVID-19 policy-analysis, showing accurate dynamic graph recovery and time-dependent policy effects. Overall, the paper advances causal discovery in nonstationary settings and provides a practical toolkit for dynamic policy impact assessment.

Abstract

To represent the causal relationships between variables, a directed acyclic graph (DAG) is widely utilized in many areas, such as social sciences, epidemics, and genetics. Many causal structure learning approaches are developed to learn the hidden causal structure utilizing deep-learning approaches. However, these approaches have a hidden assumption that the causal relationship remains unchanged over time, which may not hold in real life. In this paper, we develop a new framework to model the dynamic causal graph where the causal relations are allowed to be time-varying. We incorporate the basis approximation method into the score-based causal discovery approach to capture the dynamic pattern of the causal graphs. Utilizing the autoregressive model structure, we could capture both contemporaneous and time-lagged causal relationships while allowing them to vary with time. We propose an algorithm that could provide both past-time estimates and future-time predictions on the causal graphs, and conduct simulations to demonstrate the usefulness of the proposed method. We also apply the proposed method for the covid-data analysis, and provide causal estimates on how policy restriction's effect changes.

Dynamic Causal Structure Discovery and Causal Effect Estimation

TL;DR

This work tackles the problem of learning causal graphs that evolve over time and estimating time-varying causal effects. It introduces a dynamic causal structure discovery framework that marries basis approximation with score-based learning, and extends to time-lagged dependencies via dynamic SVAR models. A variational autoencoder–based approach enforces acyclicity and treatment constraints to recover valid, time-varying graphs, while enabling past and future graph estimation and forecasting of causal effects. The method is validated through simulations and a real-world COVID-19 policy-analysis, showing accurate dynamic graph recovery and time-dependent policy effects. Overall, the paper advances causal discovery in nonstationary settings and provides a practical toolkit for dynamic policy impact assessment.

Abstract

To represent the causal relationships between variables, a directed acyclic graph (DAG) is widely utilized in many areas, such as social sciences, epidemics, and genetics. Many causal structure learning approaches are developed to learn the hidden causal structure utilizing deep-learning approaches. However, these approaches have a hidden assumption that the causal relationship remains unchanged over time, which may not hold in real life. In this paper, we develop a new framework to model the dynamic causal graph where the causal relations are allowed to be time-varying. We incorporate the basis approximation method into the score-based causal discovery approach to capture the dynamic pattern of the causal graphs. Utilizing the autoregressive model structure, we could capture both contemporaneous and time-lagged causal relationships while allowing them to vary with time. We propose an algorithm that could provide both past-time estimates and future-time predictions on the causal graphs, and conduct simulations to demonstrate the usefulness of the proposed method. We also apply the proposed method for the covid-data analysis, and provide causal estimates on how policy restriction's effect changes.
Paper Structure (33 sections, 2 theorems, 33 equations, 9 figures, 5 tables)

This paper contains 33 sections, 2 theorems, 33 equations, 9 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Dynamic Causal Structure Discovery
  4. Graph terminology
  5. Dynamic linear structural equation model
  6. Identifiability
  7. Basis approximation for varying coefficient modeling
  8. Constrained causal structural learning
  9. Dynamic Causal Structure Discovery with Time-Lagged Dependency
  10. Dynamic structural vector autoregression
  11. Basis approximation and constrained causal structural learning
  12. Dynamic causal effect
  13. Assumptions
  14. Dynamic causal effect
  15. Experimental results
  16. ...and 18 more sections

Key Result

Theorem 3.1

Let $\mathcal{L}(\mathbf{X})$ denotes a function of $\mathbf{X}$ generated from equation dynamic_lsem, and $\mathcal{G}$ denotes the directed acyclic graph described in equation dynamic_lsem. Under assumptions in Section assumption, the graph $\mathcal{G}$ is identifiable from $\mathcal{L}(\mathbf{X

Figures (9)

  • Figure 1: Estimated causal strength for Scenario 1 in the dynamic LSEM setup. The solid line denotes the estimated coefficient in the ten time stamps and the dashed line denotes the one-step ahead prediction.
  • Figure 2: Estimated causal graphs at multiple time-stamps for dynamic LSEM setup, Scenario 2. The horizontal axis denotes the number of timestamps.
  • Figure 3: Estimated causal graph at March and July. Each node represents a variable and the arrows represent the discovered causal relations. Red color represents positive causal relations and blue color represents negative causal relations.
  • Figure 4: Estimated dynamic causal effect of the contact restriction policy on new cases. The shaded region represents the time period when the policy starts to implement.
  • Figure 5: Causal strength estimates with different number of knots under scenario 1 with cosine function in the dynamic LSEM setup using the proposed method.
  • ...and 4 more figures

Theorems & Definitions (2)

  • Theorem 3.1
  • Theorem 5.1