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12
A Guide to the Literature on Learning Probabilistic Networks From Data
, 1996
"... This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the ..."
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Cited by 190 (0 self)
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This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...
Graphs, Causality, And Structural Equation Models
, 1998
"... Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers. ..."
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Cited by 51 (14 self)
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Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.
Causal Inference in the Presence of Latent Variables and Selection Bias
 In Proceedings of Eleventh Conference on Uncertainty in Artificial Intelligence
"... This paper uses Bayesian network models for that investigation. Bayesian networks, or directed acyclic graph (DAG) models have proved very useful in representing both causal and statistical hypotheses. The nodes of the graph represent vertices, directed edges represent direct influences, and the top ..."
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Cited by 37 (5 self)
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This paper uses Bayesian network models for that investigation. Bayesian networks, or directed acyclic graph (DAG) models have proved very useful in representing both causal and statistical hypotheses. The nodes of the graph represent vertices, directed edges represent direct influences, and the topology of the graph encodes statistical constraints. We will consider features of such models that can be determined from data under assumptions that are related to those routinely applied in experimental situations:
Using Path Diagrams as a Structural Equation Modelling Tool
, 1997
"... this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. There are a number of problems associated with structural equation modeling. These problems include: ..."
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Cited by 34 (7 self)
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this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. There are a number of problems associated with structural equation modeling. These problems include:
A Polynomial Time Algorithm For Determining DAG Equivalence in the Presence of Latent Variables and Selection Bias
, 1997
"... ations. For this class of algorithms, it is impossible to determine which of two dseparation equivalent causal structures generated a given probability distribution, given only the set of conditional independence and dependence relations true of the observed distribution. We will describe a polynom ..."
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Cited by 18 (6 self)
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ations. For this class of algorithms, it is impossible to determine which of two dseparation equivalent causal structures generated a given probability distribution, given only the set of conditional independence and dependence relations true of the observed distribution. We will describe a polynomial (in the number of vertices) time algorithm for determining when two DAGs which may have latent variables or selection bias are dseparation equivalent. A DAG G entails a conditional independence relation if and only if it is true in every probability measure satisfying the local directed Markov property for G. (We place definitions and sets of variables in boldface.) Pearl, Geiger, and Verma (Pearl 1988) have shown that there is a graphical relation, dseparation, that holds among three disjoint sets of variable A, and B, and C in DAG G if and only if G entails that
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 11 (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).
Causal Inference and Reasoning in Causally Insufficient Systems
, 2006
"... The big question that motivates this dissertation is the following: under what conditions and to what extent can passive observations inform us of the structure of causal connections among a set of variables and of the potential outcome of an active intervention on some of the variables? The partic ..."
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Cited by 10 (2 self)
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The big question that motivates this dissertation is the following: under what conditions and to what extent can passive observations inform us of the structure of causal connections among a set of variables and of the potential outcome of an active intervention on some of the variables? The particular concern here revolves around the common kind of situations where the variables of interest, though measurable themselves, may suffer from confounding due to unobserved common causes. Relying on a graphical representation of causally insufficient systems called maximal ancestral graphs, and two wellknown principles widely discussed in the literature, the causal Markov and Faithfulness conditions, we show that the FCI algorithm, a sound inference procedure in the literature for inferring features of the unknown causal structure from facts of probabilistic independence and dependence, is, with some extra sound inference rules, also complete in the sense that any feature of the causal structure left undecided by the inference procedure is indeed underdetermined by facts of probabilistic independence and dependence. In addition, we consider the issue of quantitative reasoning about effects of local interventions with the FCIlearnable features of the unknown causal structure. We improve and generalize two important pieces of work in the literature about identifying intervention effects. We also provide some preliminary study of the testability of the
On testing whether an Embedded Bayesian Network represents a Probability Model
"... Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential number of independence evaluations, each of the form: "X ..."
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Cited by 4 (1 self)
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Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential number of independence evaluations, each of the form: "X is conditionally independent of Y, given Z. " In contrast, a linear number of such evaluations is required to test a standard Bayesian network (one per vertex). On the positive side, we show that if a network with hidden variables G has a tree skeleton, checking whether G represents a given probability model P requires the polynomial number of such independence evaluations. Moreover, we provide an algorithm that efficiently constructs a treestructured Bayesian network (with hidden variables) that represents P if such a network exists, and further recognizes when such a network does not exist.
1Using Path Diagrams as a Structural Equation Modelling Tool
"... Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error ” ..."
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Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error ” or “disturbance ” terms), and an associated path
A New Graphical Model for the Representative of Marginalized DAGRepresentable Relations Azaria Paz Technion IIT HAIFA and The Netanya Academic College
"... A new model for representing PDinduced relations that are derived from DAGrepresentable relations through marginalization over a subset of their variables is introduced. The new model requires polynomial space and a polynomial algorithm is given for testing whether a given triplet is represented in ..."
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A new model for representing PDinduced relations that are derived from DAGrepresentable relations through marginalization over a subset of their variables is introduced. The new model requires polynomial space and a polynomial algorithm is given for testing whether a given triplet is represented in the model. In addition a polynomial algorithm is derived for testing whether a marginalized DAGrepresentable relation is DAGrepresentable. 1