Identifiability of Gaussian linear structural equation models with homogeneous and heterogeneous error variances

Park, Gunwoong; Kim, Youngwhan

doi:10.1007/s42952-019-00019-7

Cited by 14 publications

(17 citation statements)

References 7 publications

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“…This is the well-known linear Gaussian structural causal model Y = N + N . Only recently it has been tackled successfully by Chen, Drton, and Wang (2019); Park and Kim (2019). However, we do not consider their approach in this work.…”

Section: Linear Modelsmentioning

confidence: 98%

Causal Identification with Additive Noise Models: Quantifying the Effect of Noise

Kap¹,

Aleksandrova²,

Engel³

2021

Preprint

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In recent years, a lot of research has been conducted within the area of causal inference and causal learning. Many methods have been developed to identify the cause-effect pairs in models and have been successfully applied to observational real-world data to determine the direction of causal relationships. Yet in bivariate situations, causal discovery problems remain challenging. One class of such methods, that also allows tackling the bivariate case, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of these methods has not received much attention until now: what is the impact of different noise levels on the ability of these methods to identify the direction of the causal relationship. This work aims to bridge this gap with the help of an empirical study. We test Regression with Subsequent Independence Test using an exhaustive range of models where the level of additive noise gradually changes from 1% to 10000% of the causes' noise level (the latter remains fixed). Additionally, the experiments in this work consider several different types of distributions as well as linear and non-linear models. The results of the experiments show that ANMs methods can fail to capture the true causal direction for some levels of noise.

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Section: Linear Modelsmentioning

confidence: 98%

Causal Identification with Additive Noise Models: Quantifying the Effect of Noise

Kap¹,

Aleksandrova²,

Engel³

2021

Preprint

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“…However, some identifiability conditions need to be imposed for the identifiability of the DAG structure. Please see Theorem 2.2 of Park and Kim (2020) for a state-of-the-art result on the identifiability of a Gaussian DAG, which essentially says that a Gaussian DAG…”

Section: Supplementary Materialsmentioning

confidence: 99%

Scalable Bayesian High-dimensional Local Dependence Learning

Lee

Lin

2023

Bayesian Anal.

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In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities of spatial locations, and so on, with the natural assumption that variables far apart tend to have weak correlations. Applications of such models abound in a variety of fields such as finance, genome associations analysis and spatial modeling. We adopt a flexible framework under which each variable is dependent on its neighbors or predecessors, and the neighborhood size can vary for each variable. It is of great interest to reveal this local dependence structure by estimating the covariance or precision matrix while yielding a consistent estimate of the varying neighborhood size for each variable. The existing literature on banded covariance matrix estimation, which assumes a fixed bandwidth cannot be adapted for this general setup. We employ the modified Cholesky decomposition for the precision matrix and design a flexible prior for this model through appropriate priors on the neighborhood sizes and Cholesky factors. The posterior contraction rates of the Cholesky factor are derived which are nearly or exactly minimax optimal, and our procedure leads to consistent estimates of the neighborhood size for all the variables. Another appealing feature of our procedure is its scalability to models with large numbers of variables due to efficient posterior inference without resorting to MCMC algorithms. Numerical comparisons are carried out with competitive methods, and applications are considered for some real datasets.

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“…Peters et al (2014) apply Algorithm 1 under an assumption of strictly nonlinear structural equations with additive noise. Meanwhile Ghoshal & Honorio (2017), Park &Kim (2020), andChen et al (2019) apply this sequential sorting procedure under a bounded conditional variance assumption: a ≤ V[X j |X P Aj ] ≤ b for each j ∈ [p] and some unknown positive constants a ≤ b restricted by the signal a parent sends its child node. Park & Kim (2020) can be considered the most general of the three similar approaches as it contains an extended discussion on the case of a node's possibly non-linear relation with its parents.…”

Section: Review Of Lingammentioning

confidence: 99%

Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores

Ruiz¹,

Padilla²,

Zhou³

2022

Preprint

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Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions, it is sometimes possible to identify an exact causal Directed Acyclic Graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is on one such case: a linear structural equation model with non-Gaussian noise, a model known as the Linear Non-Gaussian Acyclic Model (LiNGAM). Given a specified parametric noise model, we develop a novel sequential approach to estimate the causal ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. Under mild assumptions, the population version of our procedure provably identifies a true ordering of the underlying causal DAG. We provide extensive numerical evidence to demonstrate that our sequential procedure is scalable to cases with possibly thousands of nodes and works well for high-dimensional data. We also conduct an application to a single-cell gene expression dataset to demonstrate our estimation procedure.

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Identifiability of Gaussian linear structural equation models with homogeneous and heterogeneous error variances

Cited by 14 publications

References 7 publications

Causal Identification with Additive Noise Models: Quantifying the Effect of Noise

Causal Identification with Additive Noise Models: Quantifying the Effect of Noise

Scalable Bayesian High-dimensional Local Dependence Learning

Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores

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