ICML 2025

Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants
Daniele Tramontano 1 Yaroslav Kivva 2 Saber Salehkaleybar 3 Negar Kiyavash 2 Mathias Drton 1 4
Abstract
This paper investigates causal effect identification
in latent variable Linear Non-Gaussian Acyclic
Models (lvLiNGAM) using higher-order cumu-
lants, addressing two prominent setups that are
challenging in the presence of latent confound-
ing: (1) a single proxy variable that may causally
influence the treatment and (2) underspecified in-
strumental variable cases where fewer instruments
exist than treatments. We prove that causal effects
are identifiable with a single proxy or instrument
and provide corresponding estimation methods.
Experimental results demonstrate the accuracy
and robustness of our approaches compared to
existing methods, advancing the theoretical and
practical understanding of causal inference in lin-
ear systems with latent confounders.
1. Introduction
Predicting the impact of an unseen intervention in a sys-
tem is a crucial challenge in many fields, such as medicine
(Sanchez et al., 2022; Michoel & Zhang, 2023), policy evalu-
ation (Athey & Imbens, 2017), fair decision-making (Kilber-
tus et al., 2017), and finance (de Prado, 2023). Randomized
experiments/interventional studies are the gold standard for
addressing this challenge but are often infeasible due to a
variety of reasons, such as ethical concerns or prohibitively
high costs. Thus, when merely observational data is avail-
able, additional assumptions on the underlying causal sys-
tem are needed to compensate for the lack of interventional
data. The field of causal inference seeks to formalize such
assumptions. One notable approach in causal inference is
modeling causal relationships through structural causal mod-
els (SCM) (Pearl, 2009). In this framework, a random vector
1Technical University of Munich, Munich, Germany 2Ecole
Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland
3Leiden Institute of Advanced...