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28
Learning the structure of linear latent variable models
 Journal of Machine Learning Research
, 2006
"... We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are dseparated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the ..."
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Cited by 41 (13 self)
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We describe anytime search procedures that (1) find disjoint subsets of recorded variables for which the members of each subset are dseparated by a single common unrecorded cause, if such exists; (2) return information about the causal relations among the latent factors so identified. We prove the procedure is pointwise consistent assuming (a) the causal relations can be represented by a directed acyclic graph (DAG) satisfying the Markov Assumption and the Faithfulness Assumption; (b) unrecorded variables are not caused by recorded variables; and (c) dependencies are linear. We compare the procedure with standard approaches over a variety of simulated structures and sample sizes, and illustrate its practical value with brief studies of social science data sets. Finally, we
Spectral Methods for Learning Multivariate Latent Tree Structure
"... This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linearGaussian models, hidden Markov models, Gaussian mixture models, and Markov evol ..."
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Cited by 8 (1 self)
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This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linearGaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The setting is one where we only have samples from certain observed variables in the tree, and our goal is to estimate the tree structure (i.e., the graph of how the underlying hidden variables are connected to each other and to the observed variables). We propose the Spectral Recursive Grouping algorithm, an efficient and simple bottomup procedure for recovering the tree structure from independent samples of the observed variables. Our finite sample size bounds for exact recovery of the tree structure reveal certain natural dependencies on underlying statistical and structural properties of the underlying joint distribution. Furthermore, our sample complexity guarantees have no explicit dependence on the dimensionality of the observed variables, making the algorithm applicable to many highdimensional settings. At the heart of our algorithm is a spectral quartet test for determining the relative topology of a quartet of variables from secondorder statistics. 1
Generalized measurement models
, 2004
"... Given a set of random variables, it is often the case that their associations can be explained by hidden common causes. We present a set of welldefined assumptions and a provably correct algorithm that allow us to identify some of such hidden common causes. The assumptions are fairly general and so ..."
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Cited by 7 (4 self)
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Given a set of random variables, it is often the case that their associations can be explained by hidden common causes. We present a set of welldefined assumptions and a provably correct algorithm that allow us to identify some of such hidden common causes. The assumptions are fairly general and sometimes weaker than those used in practice by, for instance, econometricians, psychometricians, social scientists and in many other fields where latent variable models are important and tools such as factor analysis are applicable. The goal is automated knowledge discovery: identifying latent variables that can be used across diferent applications and causal models and throw new insights over a data generating process. Our approach is evaluated throught simulations and three realworld cases.
The hidden life of latent variables: Bayesian learning with mixed graph models
, 2008
"... Directed acyclic graphs (DAGs) have been widely used as a representation of conditional independence in machine learning and statistics. Moreover, hidden or latent variables are often an important component of graphical models. However, DAG models suffer from an important limitation: the family of D ..."
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Cited by 7 (3 self)
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Directed acyclic graphs (DAGs) have been widely used as a representation of conditional independence in machine learning and statistics. Moreover, hidden or latent variables are often an important component of graphical models. However, DAG models suffer from an important limitation: the family of DAGs is not closed under marginalization of hidden variables. This means that in general we cannot use a DAG to represent the independencies over a subset of variables in a larger DAG. Directed mixed graphs (DMGs) are a representation that includes DAGs as a special case, and overcomes this limitation. This paper introduces algorithms for performing Bayesian inference in Gaussian and probit DMG models. An important requirement for inference is the characterization of the distribution over parameters of the models. We introduce a new distribution for covariance matrices of Gaussian DMGs. We discuss and illustrate how several Bayesian machine learning tasks can benefit from the principle presented here: the power to model dependencies that are generated from hidden variables, but without necessarily modelling such variables explicitly.
Bayesian learning of measurement and structural models
 23rd International Conference on Machine Learning
, 2006
"... We present a Bayesian search algorithm for learning the structure of latent variable models of continuous variables. We stress the importance of applying search operators designed especially for the parametric family used in our models. This is performed by searching for subsets of the observed vari ..."
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Cited by 5 (3 self)
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We present a Bayesian search algorithm for learning the structure of latent variable models of continuous variables. We stress the importance of applying search operators designed especially for the parametric family used in our models. This is performed by searching for subsets of the observed variables whose covariance matrix can be represented as a sum of a matrix of low rank and a diagonal matrix of residuals. The resulting search procedure is relatively efficient, since the main search operator has a branch factor that grows linearly with the number of variables. The resulting models are often simpler and give a better fit than models based on generalizations of factor analysis or those derived from standard hillclimbing methods. 1.
Bayesian inference for Gaussian mixed graph models
 Proceedings of 22nd Conference on Uncertainty in Artificial Intelligence
, 2006
"... We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bidirected edges, is a representation of conditional independencies that is closed under marginalization and arises naturall ..."
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Cited by 5 (3 self)
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We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bidirected edges, is a representation of conditional independencies that is closed under marginalization and arises naturally from causal models which allow for unmeasured confounding. Monte Carlo methods and a variational approximation for such models are presented. Our algorithms for Bayesian inference allow the evaluation of posterior distributions for several quantities of interest, including causal effects that are not identifiable from data alone but could otherwise be inferred where informative prior knowledge about confounding is available. 1
On the progression and stability of adolescent identity formation. A fivewave longitudinal study in earlytomiddle and middletolate adolescence
 Child Development
, 2010
"... This study examined identity development in a 5wave study of 923 earlytomiddle and 390 middletolate adolescents thereby covering the ages of 12–20. Systematic evidence for identity progression was found: The number of diffusions, moratoriums, and searching moratoriums (a newly obtained status) ..."
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Cited by 3 (3 self)
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This study examined identity development in a 5wave study of 923 earlytomiddle and 390 middletolate adolescents thereby covering the ages of 12–20. Systematic evidence for identity progression was found: The number of diffusions, moratoriums, and searching moratoriums (a newly obtained status) decreased, whereas the representation of the highcommitment statuses (2 variants of a [fore]closed identity: ‘‘early closure’ ’ and ‘‘closure,’ ’ and achievement) increased. We also found support for the individual difference perspective: 63% of the adolescents remained in the same identity status across the 5 waves. Identity progression was characterized by 7 transitions: diffusion fi moratorium, diffusion fi early closure, moratorium fi closure, moratorium fi achievement, searching moratorium fi closure, searching moratorium fi achievement, and early closure fi achievement. Erikson (1968) theorized that one of the main tasks for adolescents is to develop a coherent sense of identity. Marcia’s (1966) identity status model has been one of the most important, and widely studied and utilized, elaborations of Erikson’s views on identity formation. Marcia distinguished four identity
Applications of causally defined direct and indirect effects in mediation analysis using SEM
 University of California
"... Judea Pearl for helpful advice This paper summarizes some of the literature on causal effects in mediation analysis. It presents causallydefined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables. The expansion to noncontinuous mediators and outcomes offers a ..."
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Cited by 3 (0 self)
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Judea Pearl for helpful advice This paper summarizes some of the literature on causal effects in mediation analysis. It presents causallydefined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables. The expansion to noncontinuous mediators and outcomes offers a broader array of causal mediation analyses than previously considered in structural equation modeling practice. A new result is the ability to handle mediation by a nominal variable. Examples with a binary outcome and a binary, ordinal or nominal mediator are given using Mplus to compute the effects. The causal effects require strong assumptions even in randomized designs, especially sequential ignorability, which is presumably often violated to some extent due to mediatoroutcome confounding. To study the effects of violating this assumption, it is shown how a sensitivity analysis can be carried out. This can be used both in planning a new study and in evaluating the results of an existing study.
Political sophistication and policy reasoning: A reconsideration
 American Journal of Political Science
, 2004
"... The sophisticationinteraction theory of mass policy reasoning, which posits that the strength of the relationship between abstract principles and policy preferences is conditional on political sophistication, dominates the study of public opinion. This article argues that the sophisticationinterac ..."
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Cited by 3 (0 self)
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The sophisticationinteraction theory of mass policy reasoning, which posits that the strength of the relationship between abstract principles and policy preferences is conditional on political sophistication, dominates the study of public opinion. This article argues that the sophisticationinteraction theory does not hold to the degree the consensus claims. Specifically, it challenges the proposition that sophistication promotes the use of domainspecific beliefs and values. Analysis of 1984, 1986, 1987, 1988, and 1990 NES data yields two compelling findings. First, a series of confirmatory factor analyses indicate that beliefs about equal opportunity, selfreliance, and limited government in the social welfare domain and about militarism and anticommunism in the foreign policy domain are structured coherently and equivalently in the minds of citizens at different levels of sophistication. Second, structural equation model results demonstrate that political sophistication does not systematically enhance the impact these principles have on policy preferences. The conventional wisdom in public opinion research holds that the ability to deduce specific policy preferences from abstract principles is conditional on political sophistication. Research shows that sophistication strengthens the relationship between liberalconservative orientations and issue positions
New dseparation identification results for learning continuous latent variable models
 Proceedings of the 22nd Interational Conference in Machine Learning
, 2005
"... Learning the structure of graphical models is an important task, but one of considerable difficulty when latent variables are involved. Because conditional independences using hidden variables cannot be directly observed, one has to rely on alternative methods to identify the dseparations that defi ..."
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Cited by 2 (2 self)
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Learning the structure of graphical models is an important task, but one of considerable difficulty when latent variables are involved. Because conditional independences using hidden variables cannot be directly observed, one has to rely on alternative methods to identify the dseparations that define the graphical structure. This paper describes new distributionfree techniques for identifying dseparations in continuous latent variable models when nonlinear dependencies are allowed among hidden variables. 1.