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The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…

Artificial Intelligence · Computer Science 2007-05-23 Patrik O. Hoyer , Shohei Shimizu , Antti J. Kerminen

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…

Machine Learning · Computer Science 2024-12-02 Yuhang Liu , Zhen Zhang , Dong Gong , Mingming Gong , Biwei Huang , Anton van den Hengel , Kun Zhang , Javen Qinfeng Shi

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…

Methodology · Statistics 2018-06-19 Dominik Rothenhäusler , Peter Bühlmann , Nicolai Meinshausen

This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure…

Machine Learning · Statistics 2026-02-03 Seunghyun Lee , Yuqi Gu

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…

Machine Learning · Computer Science 2023-11-01 Lingjing Kong , Biwei Huang , Feng Xie , Eric Xing , Yuejie Chi , Kun Zhang

We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from…

Artificial Intelligence · Computer Science 2025-06-16 Yaroslav Kivva , Sina Akbari , Saber Salehkaleybar , Negar Kiyavash

This paper investigates causal effect identification in latent variable Linear Non-Gaussian Acyclic Models (lvLiNGAM) using higher-order cumulants, addressing two prominent setups that are challenging in the presence of latent confounding:…

Machine Learning · Statistics 2025-06-09 Daniele Tramontano , Yaroslav Kivva , Saber Salehkaleybar , Mathias Drton , Negar Kiyavash

Causal disentanglement aims to learn about latent causal factors behind data, holding the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability…

Machine Learning · Computer Science 2024-12-25 Ryan Welch , Jiaqi Zhang , Caroline Uhler

We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…

Methodology · Statistics 2026-05-28 Tom Hochsprung , Nils Sturma , Jakob Runge , Mathias Drton , Andreas Gerhardus

We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional mixtures of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and…

We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal…

Machine Learning · Computer Science 2019-08-13 Saber Salehkaleybar , AmirEmad Ghassami , Negar Kiyavash , Kun Zhang

Unobserved confounding presents a major threat to causal inference from observational studies. Recently, several authors suggest that this problem may be overcome in a shared confounding setting where multiple treatments are independent…

Methodology · Statistics 2020-11-25 Dehan Kong , Shu Yang , Linbo Wang

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…

Machine Learning · Statistics 2023-12-07 Simon Bing , Jonas Wahl , Urmi Ninad , Jakob Runge

Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In…

Machine Learning · Computer Science 2025-10-28 Wei Chen , Linjun Peng , Zhiyi Huang , Haoyue Dai , Zhifeng Hao , Ruichu Cai , Kun Zhang

Causal representation learning (CRL) offers the promise of uncovering the underlying causal model by which observed data was generated, but the practical applicability of existing methods remains limited by the strong assumptions required…

Machine Learning · Computer Science 2026-01-30 Yuhang Liu , Zhen Zhang , Dong Gong , Erdun Gao , Biwei Huang , Mingming Gong , Anton van den Hengel , Kun Zhang , Javen Qinfeng Shi

Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…

Methodology · Statistics 2026-03-05 Daniele Tramontano , Mathias Drton , Jalal Etesami

Inferring causal relationships from observed data is an important task, yet it becomes challenging when the data is subject to various external interferences. Most of these interferences are the additional effects of external factors on…

Machine Learning · Computer Science 2025-11-14 Ruichu Cai , Xiaokai Huang , Wei Chen , Zijian Li , Zhifeng Hao

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the…

Machine Learning · Statistics 2024-10-31 Yuanyuan Wang , Biwei Huang , Wei Huang , Xi Geng , Mingming Gong

We propose a method for inferring the existence of a latent common cause ('confounder') of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus…

Machine Learning · Statistics 2012-05-14 Dominik Janzing , Jonas Peters , Joris Mooij , Bernhard Schoelkopf

The task of inferring high-level causal variables from low-level observations, commonly referred to as causal representation learning, is fundamentally underconstrained. As such, recent works to address this problem focus on various…

Machine Learning · Statistics 2024-03-26 Simon Bing , Urmi Ninad , Jonas Wahl , Jakob Runge
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