Discovering Cyclic Causal Models by Independent Components Analysis

By Gustavo Lacerda, Peter Spirtes, J. Ramsey, Patrik O. Hoyer. 2008

208 citations recorded by the source corpus.

We generalize Shimizu et al's (2006) ICA-based approach for discovering linear non-Gaussian acyclic (LiNGAM) Structural Equation Models (SEMs) from causally sufficient, continuous-valued observational data. By relaxing the assumption that the generating SEM's graph is acyclic, we solve the more general problem of linear non-Gaussian (LiNG) SEM discovery. LiNG discovery algorithms output the distribution equivalence class of SEMs which, in the large sample limit, represents the population distribution. We apply a LiNG discovery algorithm to simulated data. Finally, we give sufficient conditions under which only one of the SEMs in the output class is 'stable'.

Subfields: Analytical Chemistry, Artificial Intelligence, Signal Processing

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Citations in the corpus

Causal Discovery from Temporally Aggregated Time Series (2017, background): “When the error terms are non-Gaussian, it has the same form as the Linear, Non-Gaussian Model (LiNG) (Lacerda et al., 2008); when the causal relations are further assumed to be acyclic, it follows the form of the Linear, Non-Gaussian Acyclic Model (LiNGAM) (Shimizu et al., 2006).”
Causal Structure Learning (2017, methodology): “(d) A cycle in the graph again has a detrimental eﬀect on LINGAM (which is likely diﬀerent in the version of LINGAM that allows for cycles (Lacerda et al., 2008)).”
From Dependence to Causation (2016, background): “, 2010), cyclic graphs (Mooij et al., 2011; Lacerda et al., 2012), and postnonlinear equations xi = gi(fi(Pa(xi)) + ni), where gi : R→ R is an additional monotone function (Zhang and Hyvärinen, 2009).”
Learning Optimal Causal Graphs with Exact Search (2018, background): “We consider both allowing cycles (assuming absence of self-loops as they are unidentifiable from (in)dependence constraints (Lacerda et al., 2008; Hyttinen et al., 2012)) and assuming acyclicity; in the latter case the causal graphs are semi-Markovian graphs (Pearl, 2000).”
Independent component analysis: recent advances (2013, background): “As already mentioned, cyclic models can be estimated, replacing the acyclicity assumption by a weaker one [14,17].”
Structure learning in causal cyclic networks (2008, background): “Based on these, (Richardson, 1996) established an algorithm for discovering a partial structure on DCGs. Recently, (Lacerda et al., 2008) provided an alternative algorithm.”
Causal modelling combining instantaneous and lagged effects: an identifiable model based on non-Gaussianity (2008, methodology): “Here, we can justify the procedure by using the theory of cyclic model estimation proposed by (Lacerda et al., 2008); the estimation here gives the only“stable” model according to that theory.”
Review of Causal Discovery Methods Based on Graphical Models (2019, background): “Furthermore, when the underlying causal model has cycles or feedbacks, which violates the acyclicity assumption, one may still be able to reveal the causal knowledge under certain assumptions (Lacerda et al., 2008; Sanchez-Romero et al., 2019).”
Specific and Shared Causal Relation Modeling and Mechanism-Based Clustering (2019, background): “In addition, if there are cycles in the instantaneous causal structure, the identiﬁability requires two more conditions [23]: (1) the cycles are disjoint, and (2) the causal model is stable, i.e., lim k →∞ B k = 0 .”
Cyclic Causal Discovery from Continuous Equilibrium Data (2013, background): “Similar ideas have also been studied in the cyclic case (Lacerda et al., 2008; Mooij et al., 2011).”
Modeling Discrete Interventional Data using Directed Cyclic Graphical Models (2009, methodology): “Lacerda et al. (2008) recently proposed a new method of learning cyclic SEMs for certain types of (non-interventional) continuous data.”
From Random Differential Equations to Structural Causal Models: the stochastic case (2018, background): “They can be derived from an underlying discrete-time or continuous-time dynamical system (Fisher, 1970; Iwasaki and Simon, 1994; Dash, 2005; Lacerda et al., 2008; Mooij et al., 2013).”
Algebraic problems in structural equation modeling (2016, background): “These spectral conditions are also needed to give cyclic models an interpretation of representing observation of an equilibrium [31, 45].”
Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity (2010, methodology): “The starting point is the likelihood of the ICA model which is well-known, see, for example, Pham and Garrat (1997) and Hyvärinen et al.”
Causal feature learning: an overview (2017, unknown): “Like the majority of work in causal inference and discovery—notable exceptions being (Richardson 1996; Mooij et al. 2011; Lacerda et al. 2012; Hyttinen et al. 2012, 2014)—CFL assumes that the microvariable system is acyclic: in our toy example, hue has causal influence on eda, but we assumed (quite…”