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Combining experiments to discover linear cyclic models with latent variables
 In AISTATS 2010
, 2010
"... We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure conta ..."
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Cited by 5 (2 self)
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We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure contains feedback loops and latent variables, while the experiments can involve surgical or ‘soft ’ interventions on one or multiple variables at a time. The algorithm is ‘online’ in the sense that it combines the results from any set of available experiments, can incorporate background knowledge and resolves conflicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that (i) determines when the algorithm can uniquely return the true graph, and (ii) can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al (2005). 1
Causal discovery for linear cyclic models with latent variables
"... We consider the problem of identifying the causal relationships among a set of variables in the presence of both feedback loops and unmeasured confounders. This is a challenging task which, for full identification, typically requires the use of randomized experiments. For linear systems, Eberhardt e ..."
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Cited by 3 (2 self)
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We consider the problem of identifying the causal relationships among a set of variables in the presence of both feedback loops and unmeasured confounders. This is a challenging task which, for full identification, typically requires the use of randomized experiments. For linear systems, Eberhardt et al (2010) recently provided a procedure for integrating data from several experiments, and gave a corresponding, but demanding, identifiability condition. In this paper we (i) characterize the underdetermination of the model when the identifiability condition is not fully satisfied, (ii) show that their algorithm is complete with regard to the search space and the assumptions, and (iii) extend the procedure to incorporate the common assumption of faithfulness, and any prior knowledge. The resulting method typically resolves much additional structure and often yields full identification with many fewer experiments. We demonstrate our procedure using simulated data, and apply it to the protein signaling dataset of Sachs et al (2005). 1
Learning linear cyclic causal models with latent variables. Submitted. Available online from the authors’ homepages
, 2012
"... Identifying causeeffect relationships between variables of interest is a central problem in science. Given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables. We provide a detailed description of the model family, full proofs of t ..."
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Cited by 1 (1 self)
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Identifying causeeffect relationships between variables of interest is a central problem in science. Given a set of experiments we describe a procedure that identifies linear models that may contain cycles and latent variables. We provide a detailed description of the model family, full proofs of the necessary and sufficient conditions for identifiability, a search algorithm that is complete, and a discussion of what can be done when the identifiability conditions are not satisfied. The algorithm is comprehensively tested in simulations, comparing it to competing algorithms in the literature. Furthermore, we adapt the procedure to the problem of cellular network inference, applying it to the biologically realistic data of the DREAM challenges. The paper provides a full theoretical foundation for the causal discovery procedure first presented by Eberhardt et al. (2010) and Hyttinen et al. (2010).
On Causal Discovery with Cyclic Additive Noise Models
"... We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussiannoise case. We also propose a method to learn such model ..."
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We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussiannoise case. We also propose a method to learn such models from observational data. In the acyclic case, the method reduces to ordinary regression, but in the more challenging cyclic case, an additional term arises in the loss function, which makes it a special case of nonlinear independent component analysis. We illustrate the proposed method on synthetic data. 1
Discovering Cyclic Causal Models with Latent Variables: A General SATBased Procedure
"... We present a very general approach to learning the structure of causal models based on dseparation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent varia ..."
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We present a very general approach to learning the structure of causal models based on dseparation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent variables. Our approach is based on a logical representation of causal pathways, which permits the integration of quite general background knowledge, and inference is performed using a Boolean satisfiability (SAT) solver. The procedure is complete in that it exhausts the available information on whether any given edge can be determined to be present or absent, and returns “unknown ” otherwise. Many existing constraintbased causal discovery algorithms can be seen as special cases, tailored to circumstances in which one or more restricting assumptions apply. Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales. 1
. Combining Experiments to Discover Linear Cyclic Models with Latent Variables
"... We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure conta ..."
Abstract
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We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure contains feedback loops and latent variables, while the experiments can involve surgical or ‘soft ’ interventions on one or multiple variables at a time. The algorithm is ‘online’ in the sense that it combines the results from any set of available experiments, can incorporate background knowledge and resolves conflicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that (i) determines when the algorithm can uniquely return the true graph, and (ii) can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al (2005). 1
Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering
"... We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; e ..."
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We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; even in the simplest case, cyclic structural equation models imply constraints on the noise. We give a formalization of an alternative Markov chain equilibrium semantics which requires not only the causal graph, but also a sample order. We show how the resulting equilibrium is a function of the sample ordering, both theoretically and empirically. 1
Learning the Structure and Parameters of LargePopulation Graphical Games from Behavioral Data
"... We formalize and study the problem of learning the structure and parameters of graphical games from strictly behavioral data. We cast the problem as a maximum likelihood estimation (MLE) based on a generative model defined by the purestrategy Nash equilibria (PSNE) of the game. The formulation brin ..."
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We formalize and study the problem of learning the structure and parameters of graphical games from strictly behavioral data. We cast the problem as a maximum likelihood estimation (MLE) based on a generative model defined by the purestrategy Nash equilibria (PSNE) of the game. The formulation brings out the interplay between goodnessoffit and model complexity: good models capture the equilibrium behavior represented in the data while controlling the true number of PSNE, including those potentially unobserved. We provide a generalization bound for MLE. We discuss several optimization algorithms including convex loss minimization (CLM), sigmoidal approximations and exhaustive search. We formally prove that games in our hypothesis space have a small true number of PSNE, with high probability; thus, CLM is sound. We illustrate our approach, show and discuss promising results on synthetic data and the U.S. congressional voting records. 1
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering
"... We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; e ..."
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We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; even in the simplest case, cyclic structural equation models imply constraints on the noise. We give a formalization of an alternative Markov chain equilibrium semantics which requires not only the causal graph, but also a sample order. We show how the resulting equilibrium is a function of the sample ordering, both theoretically and empirically. 1