Learning causal structure from observational data has attracted much attention,and it is notoriously challenging to find the underlying structure in the presenceof confounders (hidden direct common causes of two variables). In this paper,by properly leveraging the nonGaussianity of the data, we propose to estimatethe structure over latent variables with the socalled Triad constraints: we design a form of "pseudoresidual" from three variables, and show that when causal relations are linear and noise terms are nonGaussian, the causal direction between the latent variables for the three observed variables is identifiable by checking a certain kind of independence relationship. In other words, the Triad constraints help us to locate latent confounders and determine the causal direction between them. This goes far beyond the Tetrad constraints and reveals more information about the underlying structure from nonGaussian data. Finally, based on the Triad constraints, we develop a twostep algorithm to learn the causal structure corresponding to measurement models. Experimental results on both synthetic and real data demonstrate the effectiveness and reliability of our method.
more »
« less
Testability of Instrumental Variables in Linear NonGaussian Acyclic Causal Models
This paper investigates the problem of selecting instrumental variables relative to a target causal influence X→Y from observational data generated by linear nonGaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear nonGaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and realworld data show the effectiveness of the proposed method.
more »
« less
 Award ID(s):
 2134901
 NSFPAR ID:
 10380964
 Date Published:
 Journal Name:
 Entropy
 Volume:
 24
 Issue:
 4
 ISSN:
 10994300
 Page Range / eLocation ID:
 512
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this


Summary We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variablespecific error term and the other observed variables $Y_u$ with $\sigma(u) < \sigma (v)$. The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has previously been shown that when the variablespecific error terms are nonGaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in highdimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum indegree of the graph is controlled. Our theoretical analysis is couched in the setting of logconcave error distributions.more » « less

An important achievement in the field of causal inference was a complete characterization of when a causal effect, in a system modeled by a causal graph, can be determined uniquely from purely observational data. The identification algorithms resulting from this work produce exact symbolic expressions for causal effects, in terms of the observational probabilities. More recent work has looked at the numerical properties of these expressions, in particular using the classical notion of the condition number. In its classical interpretation, the condition number quantifies the sensitivity of the output values of the expressions to small numerical perturbations in the input observational probabilities. In the context of causal identification, the condition number has also been shown to be related to the effect of certain kinds of uncertainties in the structure of the causal graphical model. In this paper, we first give an upper bound on the condition number for the interesting case of causal graphical models with small “confounded components”. We then develop a tight characterization of the condition number of any given causal identification problem. Finally, we use our tight characterization to give a specific example where the condition number can be much lower than that obtained via generic bounds on the condition number, and to show that even “equivalent” expressions for causal identification can behave very differently with respect to their numerical stability properties.more » « less

de Campos, C. ; Maathuis, M. H. (Ed.)An important achievement in the field of causal inference was a complete characterization of when a causal effect, in a system modeled by a causal graph, can be determined uniquely from purely observational data. The identification algorithms resulting from this work produce exact symbolic expressions for causal effects, in terms of the observational probabilities. More recent work has looked at the numerical properties of these expressions, in particular using the classical notion of the condition number. In its classical interpretation, the condition number quantifies the sensitivity of the output values of the expressions to small numerical perturbations in the input observational probabilities. In the context of causal identification, the condition number has also been shown to be related to the effect of certain kinds of uncertainties in the structure of the causal graphical model. In this paper, we first give an upper bound on the condition number for the interesting case of causal graphical models with small “confounded components”. We then develop a tight characterization of the condition number of any given causal identification problem. Finally, we use our tight characterization to give a specific example where the condition number can be much lower than that obtained via generic bounds on the condition number, and to show that even “equivalent” expressions for causal identification can behave very differently with respect to their numerical stability properties.more » « less

Chaudhuri, Kamalika ; Jegelka, Stefanie ; Song, Le ; Szepesvari, Csaba ; Niu, Gang ; Sabato, Sivan (Ed.)Traditional causal discovery methods mainly focus on estimating causal relations among measured variables, but in many realworld problems, such as questionnairebased psychometric studies, measured variables are generated by latent variables that are causally related. Accordingly, this paper investigates the problem of discovering the hidden causal variables and estimating the causal structure, including both the causal relations among latent variables and those between latent and measured variables. We relax the frequentlyused measurement assumption and allow the children of latent variables to be latent as well, and hence deal with a specific type of latent hierarchical causal structure. In particular, we define a minimal latent hierarchical structure and show that for linear nonGaussian models with the minimal latent hierarchical structure, the whole structure is identifiable from only the measured variables. Moreover, we develop a principled method to identify the structure by testing for Generalized Independent Noise (GIN) conditions in specific ways. Experimental results on both synthetic and realworld data show the effectiveness of the proposed approach.more » « less