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Causal Effect Identification in LiNGAM Models with Latent Confounders

Daniele Tramontano, Yaroslav Kivva, Saber Salehkaleybar, Mathias Drton, Negar Kiyavash

TL;DR

This work advances causal inference in LiNGAM models with latent confounders by establishing complete graphical criteria for the generic identifiability of direct and total effects among observed variables, in settings with known and unknown graphs. It provides polynomial-time certifying algorithms and introduces Graphical RICA (GRICA) to estimate causal effects from observational data using the graph structure to reduce dimensionality. The results encompass scenarios with proxies, longitudinal data, and underspecified instruments, and are complemented by extensive experiments showing practical estimation improvements over prior methods. By focusing on generic identifiability and graph-aware estimation, the paper offers scalable, actionable tools for causal effect determination in complex linear non-Gaussian models with latent confounders.

Abstract

We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and when it is unknown. In both settings, we provide a complete graphical characterization of the identifiable direct or total causal effects among observed variables. Moreover, we propose efficient algorithms to certify the graphical conditions. Finally, we propose an adaptation of the reconstruction independent component analysis (RICA) algorithm that estimates the causal effects from the observational data given the causal graph. Experimental results show the effectiveness of the proposed method in estimating the causal effects.

Causal Effect Identification in LiNGAM Models with Latent Confounders

TL;DR

This work advances causal inference in LiNGAM models with latent confounders by establishing complete graphical criteria for the generic identifiability of direct and total effects among observed variables, in settings with known and unknown graphs. It provides polynomial-time certifying algorithms and introduces Graphical RICA (GRICA) to estimate causal effects from observational data using the graph structure to reduce dimensionality. The results encompass scenarios with proxies, longitudinal data, and underspecified instruments, and are complemented by extensive experiments showing practical estimation improvements over prior methods. By focusing on generic identifiability and graph-aware estimation, the paper offers scalable, actionable tools for causal effect determination in complex linear non-Gaussian models with latent confounders.

Abstract

We study the generic identifiability of causal effects in linear non-Gaussian acyclic models (LiNGAM) with latent variables. We consider the problem in two main settings: When the causal graph is known a priori, and when it is unknown. In both settings, we provide a complete graphical characterization of the identifiable direct or total causal effects among observed variables. Moreover, we propose efficient algorithms to certify the graphical conditions. Finally, we propose an adaptation of the reconstruction independent component analysis (RICA) algorithm that estimates the causal effects from the observational data given the causal graph. Experimental results show the effectiveness of the proposed method in estimating the causal effects.
Paper Structure (32 sections, 16 theorems, 58 equations, 18 figures, 4 tables, 6 algorithms)

This paper contains 32 sections, 16 theorems, 58 equations, 18 figures, 4 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Contribution
  3. Problem Definition
  4. Notation
  5. Model
  6. Identifiability
  7. Main Results on Causal Effect Identification
  8. Identification with an Unknown Graph
  9. Identification with a Known Graph
  10. Examples
  11. Certifying Identifiability
  12. Estimation Algorithms
  13. Related Work
  14. Experimental Results
  15. Identification
  16. ...and 17 more sections

Key Result

Theorem 3.1

salehkaleybar:2020 For $\mathbf{B}'\in\mathbb{R}^\mathcal{G}$, matrix $\mathbf{B}_{o}$ is generically identifiable without knowing the causal graph if and only if there are no pairs $j\neq i\in\mathcal{V}$ such that $\mathop{\rm de}\nolimits_o(j)=\mathop{\rm de}\nolimits_o(i)$.

Figures (18)

  • Figure 1: Instrumental variable graph. The parameters in blue are identifiable without knowledge of the graph, while the parameters in red are not identifiable.
  • Figure 5: On the $x$-axis, the probability of acceptance of an edge. On the $y$-axis, the percentage of identifiable parameters.
  • Figure 6: On the $x$-axis, the size of the graph. On the $y$-axis, the average running time in seconds. $p_o/p$ is fixed to 0.5.
  • Figure 7: The causal graphs considered in the experiments.
  • Figure 8: Relative error vs sample size
  • ...and 13 more figures

Theorems & Definitions (38)

  • Remark 2.1
  • Theorem 3.1
  • Remark 3.2: The scaling matrix
  • Theorem 3.3: Total causal effect
  • Theorem 3.4: Direct causal effect
  • Example 3.5: Identification with instrumental variables
  • Theorem 3.6
  • Example 3.7: \ref{['ex:iv:unknown:graph']} continued
  • Theorem 3.8: Total Causal Effect
  • Theorem 3.9: Direct Causal Effect
  • ...and 28 more