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Chain Graph Models and their Causal Interpretations
 B
, 2001
"... Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultim ..."
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Cited by 49 (4 self)
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Chain graphs are a natural generalization of directed acyclic graphs (DAGs) and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are a number of simple and apparently plausible, but ultimately fallacious interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to awed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated as the equilibrium distribution of dynamic models with feedback. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for DAGs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feedback in econometrics. Keywords: Causal model; cha...
A SINful approach to Gaussian graphical model selection
 Journal of Statistical Planning and Inference
"... Abstract. Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed by testing these conditional independences, which are equivalent to specified zeroes among certain ..."
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Cited by 25 (5 self)
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Abstract. Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed by testing these conditional independences, which are equivalent to specified zeroes among certain (partial) correlation coefficients. For concentration graphs, covariance graphs, acyclic directed graphs, and chain graphs (both LWF and AMP), we apply Fisher’s ztransformation, ˇ Sidák’s correlation inequality, and Holm’s stepdown procedure, to simultaneously test the multiple hypotheses obtained from the Markov properties. This leads to a simple method for model selection that controls the overall error rate for incorrect edge inclusion. In practice, we advocate partitioning the simultaneous pvalues into three disjoint sets, a significant set S, an indeterminate set I, and a nonsignificant set N. Then our SIN model selection method selects two graphs, a graph whose edges correspond to the union of S and I, and a more conservative graph whose edges correspond to S only. Prior information about the presence and/or absence of particular edges can be incorporated readily. 1.
Multimodality of the likelihood in the bivariate seemingly unrelated regression model
, 2002
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Iterative conditional fitting for Gaussian ancestral graph models
 In M. Chickering and J. Halpern (Eds.), Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence
, 2004
"... Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By design, ancestral graphs encode precisely the conditional indep ..."
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Cited by 18 (6 self)
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Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By design, ancestral graphs encode precisely the conditional independence structures that can arise from Bayesian networks with selection and unobserved (hidden/latent) variables. Thus, ancestral graph models provide a potentially very useful framework for exploratory model selection when unobserved variables might be involved in the datagenerating process but no particular hidden structure can be specified. In this paper, we present the Iterative Conditional Fitting (ICF) algorithm for maximum likelihood estimation in Gaussian ancestral graph models. The name reflects that in each step of the procedure a conditional distribution is estimated, subject to constraints, while a marginal distribution is held fixed. This approach is in duality to the wellknown Iterative Proportional Fitting algorithm, in which marginal distributions are fitted while conditional distributions are held fixed. 1
Markov equivalence for ancestral graphs
, 2004
"... Ancestral graph models can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any 3JJ.cestral graph, there may be several other graphs to which it is Markov equivalent. We state and prove conditions under whic ..."
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Cited by 16 (5 self)
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Ancestral graph models can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any 3JJ.cestral graph, there may be several other graphs to which it is Markov equivalent. We state and prove conditions under which two maximal ancestral graphs are Markov equivalent to each other, thereby extending analogous results for DAGs given by other authors. 'University of W2k'lhi.ng1;on Technical No. 466. Contents
Graphical models for causal inference
 Complex Stochastic Systems. London/Boca Raton: Chapman and Hall/CRC Press. chapter
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Maximum Likelihood Estimation in Gaussian AMP Chain Graph Models and Gaussian Ancestral Graph Models
, 2004
"... The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with datageneration by natural bloc ..."
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Cited by 13 (7 self)
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The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with datageneration by natural blockrecursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm. Key words: AMP chain graph, graphical model, iterative partial maximization, multivariate normal distribution, maximum likelihood estimation 1
Effects of treatment on the treated: Identification and generalization
 In Proceedings of the TwentyFifth Conference on Uncertainty in Artificial Intelligence
, 2009
"... Many applications of causal analysis call for assessing, retrospectively, the effect of withholding an action that has in fact been implemented. This counterfactual quantity, sometimes called “effect of treatment on the treated, ” (ETT) have been used to to evaluate educational programs, critic publ ..."
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Cited by 13 (5 self)
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Many applications of causal analysis call for assessing, retrospectively, the effect of withholding an action that has in fact been implemented. This counterfactual quantity, sometimes called “effect of treatment on the treated, ” (ETT) have been used to to evaluate educational programs, critic public policies, and justify individual decision making. In this paper we explore the conditions under which ETT can be estimated from (i.e., identified in) experimental and/or observational studies. We show that, when the action invokes a singleton variable, the conditions for ETT identification have simple characterizations in terms of causal diagrams. We further give a graphical characterization of the conditions under which the effects of multiple treatments on the treated can be identified, as well as ways in which the ETT estimand can be constructed from both interventional and observational distributions. 1
Multiple testing and error control in Gaussian graphical model selection
 Statistical Science
"... Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of cond ..."
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Cited by 12 (2 self)
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Abstract. Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables ’ joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion. Key words and phrases: Acyclic directed graph, Bayesian network, bidirected graph, chain graph, concentration graph, covariance graph, DAG, graphical model, multiple testing, undirected graph. 1.
Cumulative distribution networks and the derivativesumproduct algorithm
"... We introduce a new type of graphical model called a ‘cumulative distribution network’ (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we ..."
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Cited by 12 (6 self)
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We introduce a new type of graphical model called a ‘cumulative distribution network’ (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we find that the conditional independence properties of CDNs are quite different from other graphical models. We also describe a messagepassing algorithm that efficiently computes conditional cumulative distributions. Due to the unique independence properties of the CDN, these messages do not in general have a onetoone correspondence with messages exchanged in standard algorithms, such as belief propagation. We demonstrate the application of CDNs for structured ranking learning using a previouslystudied multiplayer gaming dataset. 1