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50
Nonlinear causal discovery with additive noise models
"... The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In ..."
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Cited by 35 (16 self)
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The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuousvalued data linear acyclic causal models with additive noise are often used because these models are well understood and there are wellknown methods to fit them to data. In reality, of course, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this contribution we show that in fact the basic linear framework can be generalized to nonlinear models. In this extended framework, nonlinearities in the datagenerating process are in fact a blessing rather than a curse, as they typically provide information on the underlying causal system and allow more aspects of the true datagenerating mechanisms to be identified. In addition to theoretical results we show simulations and some simple real data experiments illustrating the identification power provided by nonlinearities. 1
Regression by dependence minimization and its application to causal inference in additive noise models
, 2009
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Estimating highdimensional intervention effects from observation data
 THE ANN OF STAT
, 2009
"... We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can ..."
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Cited by 9 (2 self)
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We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of the covariates on the response. This yields a collection of estimated causal effects for each covariate. We show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph. This local approach is computationally fast and feasible in highdimensional problems. We propose to use summary measures of the set of possible causal effects to determine variable importance. In particular, we use the minimum absolute value of this set, since that is a lower bound on the size of the causal effect. We demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production.
Distinguishing between cause and effect
, 2008
"... We describe eight data sets that together formed the CauseEffectPairs task in the Causality Challenge #2: PotLuck competition. Each set consists of a sample of a pair of statistically dependent random variables. One variable is known to cause the other one, but this information was hidden from the ..."
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Cited by 8 (7 self)
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We describe eight data sets that together formed the CauseEffectPairs task in the Causality Challenge #2: PotLuck competition. Each set consists of a sample of a pair of statistically dependent random variables. One variable is known to cause the other one, but this information was hidden from the participants; the task was to identify which of the two variables was the cause and which one the effect, based upon the observed sample. The data sets were chosen such that we expect common agreement on the ground truth. Even though part of the statistical dependences may also be due to hidden common causes, common sense tells us that there is a significant causeeffect relation between the two variables in each pair. We also present baseline results using three different causal inference methods.
Dependence minimizing regression with model selection for nonlinear causal inference under nonGaussian noise
 Proceedings of the TwentyThird AAAI Conference on Artificial Intelligence (AAAI2010
, 2010
"... The discovery of nonlinear causal relationship under additive nonGaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called leastsquares independence regression (LSIR). LSIR learns the ..."
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Cited by 8 (7 self)
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The discovery of nonlinear causal relationship under additive nonGaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called leastsquares independence regression (LSIR). LSIR learns the additive noise model through minimization of an estimator of the squaredloss mutual information between inputs and residuals. A notable advantage of LSIR over existing approaches is that tuning parameters such as the kernel width and the regularization parameter can be naturally optimized by crossvalidation, allowing us to avoid overfitting in a datadependent fashion. Through experiments with realworld datasets, we show that LSIR compares favorably with the stateoftheart causal inference method.
Estimation of causal effects using linear nonGaussian causal models with hidden variables
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Detecting the Direction of Causal Time Series
"... We propose a method that detects the true direction of time series, by fitting an autoregressive moving average model to the data. Whenever the noise is independent of the previous samples for one ordering of the observations, but dependent for the opposite ordering, we infer the former direction to ..."
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Cited by 7 (2 self)
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We propose a method that detects the true direction of time series, by fitting an autoregressive moving average model to the data. Whenever the noise is independent of the previous samples for one ordering of the observations, but dependent for the opposite ordering, we infer the former direction to be the true one. We prove that our method works in the population case as long as the noise of the process is not normally distributed (for the latter case, the direction is not identifiable). A new and important implication of our result is that it confirms a fundamental conjecture in causal reasoning — if after regression the noise is independent of signal for one direction and dependent for the other, then the former represents the true causal direction — in the case of time series. We test our approach on two types of data: simulated data sets conforming to our modeling assumptions, and real world EEG time series. Our method makes a decision for a significant fraction of both data sets, and these decisions are mostly correct. For real world data, our approach outperforms alternative solutions to the problem of time direction recovery. 1.
Causal Modelling Combining Instantaneous and Lagged Effects: an Identifiable Model Based on NonGaussianity
"... Causal analysis of continuousvalued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use nonGaussian model ..."
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Cited by 6 (4 self)
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Causal analysis of continuousvalued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use nonGaussian models. Here, we show how to combine the nonGaussian instantaneous model with autoregressive models. We show that such a nonGaussian model is identifiable without prior knowledge of network structure, and we propose an estimation method shown to be consistent. This approach also points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients. 1.
Estimation of a Structural Vector Autoregression Model Using NonGaussianity
"... Analysis of causal effects between continuousvalued variables typically uses either autoregressive models or structural equation models with instantaneous effects. Estimation of Gaussian, linear structural equation models poses serious identifiability problems, which is why it was recently proposed ..."
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Cited by 6 (4 self)
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Analysis of causal effects between continuousvalued variables typically uses either autoregressive models or structural equation models with instantaneous effects. Estimation of Gaussian, linear structural equation models poses serious identifiability problems, which is why it was recently proposed to use nonGaussian models. Here, we show how to combine the nonGaussian instantaneous model with autoregressive models. This is effectively what is called a structural vector autoregression (SVAR) model, and thus our work contributes to the longstanding problem of how to estimate SVAR’s. We show that such a nonGaussian model is identifiable without prior knowledge of network structure. We propose computationally efficient methods for estimating the model, as well as methods to assess the significance of the causal influences. The model is successfully applied on financial and brain imaging data.
Causal reasoning with ancestral graphs
, 2008
"... Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One promin ..."
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Cited by 6 (0 self)
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Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate postintervention probabilities to preintervention probabilities that are estimable from observational data. However, such causal diagrams are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on datamining can only output an equivalence class of causal diagrams (rather than a single one). This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a (partial) ancestral graph. We present two main results. The first result extends Pearl (1995)’s celebrated docalculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl’s calculus—the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (1993).