Glymour C, Scheines R, Spirtes P, Kelley K (1987). Discovering Causal Structure. Academic Press, San Diego.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... networks (called also belief networks, probabilistic networks) encode properties of probability distributions using directed acyclic graphs (dag) Their usage is spread among many disciplines such as Artificial Intelligence [12] Decision Analysis [6, 14] Economics [22] Genetics [23] Philosophy [4], and Statistics [9, 18] Bayesian networks are popular due to existence of numerous efficient methods of reasoning with probabilities if the joint probability distribution has an underlying dag structure [11, 12, 15, 16, 17] Spirtes, Glymour and Scheines [19] formulated a Conjecture (called ....

Glymour C., Sheines R., Spirtes P., Kelly K.: Discovering Causal Structures, Academic Press, New York,: 1987

....the dependencies can form a graph (as in the analysis of Markov fields [24] or a hypergraph (as in relational databases [19] and the task is to find the topology of these structures. Structure identification includes tasks such as finding effective representations for probability distributions [16, 7, 30], devising economical decompositions of database schema, synthesizing simple Boolean expressions for truth tables [6] and casting logical theories that render subsequent processing tractable. Despite the generality of the task, very few formal results have been established, and those that exist ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly, Discovering Causal Structure, (Academic Press, Orlando, FL 1987)

.... in deriving some statement about the probability distribution governing the data) or they can be deterministic as in deriving functional dependencies between fields in the data [20] Density estimation methods in general fall under this category, as do methods for explicit causal modeling (e.g. [13] and [14] Change and Deviation Detection These methods account for sequence information, be it time series or some other ordering (e.g. protein sequencing in genome mapping) The distinguishing feature of this class of methods is that ordering of observations is important. Scalable methods for ....

....might prevent the manager from embarking on this lossy policy. However, often these correlations can link items in a store in relationships that might seem mysterious and intriguing. Situations under which correlation can lead to causality are not straightforward and are the subject of much study [13, 19]. Association rules can be viewed as an efficient and scalable means for finding frequent marginals in the data. However, the use of these marginals in probabilistic inference requires care, as the infrequent marginals can be just as important. For a related discussion, see [24] ....

C. Glymour, R. Scheines, and P. Spirtes ABD K. Kelly. Discovering Causal Structure. Academic Press, New York, 1987.

....analysis can generally be divided into two regimes: association rules and data dependency. They are discussed subsequently. 2.3. 1 Association and Sequence Typical examples on dependency analysis are the discovery of association rules [3, 25] and the building of the dependency or causal graphs [57, 105]. They try to describe the sequential or causal relationship among data items. An interesting application of mining association rules is the analysis of supermarket transaction data which can help in the planning of market and selling strategies. In a supermarket, suppose we keep track of those ....

....et al. 148] suggest a bottom up procedure for discovering multivalued dependencies (MVDs) in observed data without knowing a priori the relationships among the attributes. A prototype system for automated database schema design has been implemented. In recent years, research by Glymour et al. [57], Pearl and Verma [105] Pearl [104] and others has resulted in major advances in the area of discovering dependency or causal graphs. As standard statistical techniques cannot distinguish causation from covariation, data precedence information or assumptions are needed to establish the direction ....

Glymour, C., Scheines, R., Spirtes, P. and Kelly, K.,. Discovering Causal Structure. New York: Academic, 1987.

....on a domain U where at each step several operators are used in order to construct a neighbourhood for a partially developed graph that is consistent with the conditional dependency relationships detected in the data. Some methods that start from a completely connected directed acyclic graph 5 [10] while other ones start from a single node and try to connect new nodes in a piecewise fashion until the whole set of variables is the graph. The decision about which variables to link to a given one can be made by resorting the evaluation function, which in turn, measures structural properties ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structures. Academic Press, San Diego, California, 1987.

....hidden) Statistical indistinguishability is less well understood when graphs can contain variables representing unmeasured common causes ( 17] p. 88) Latent (hidden) variable identification has been investigated intensely both for belief networks (e.g. 10, 6, 9, 2] and causal networks ( [12, 16, 17, 4, 5]) beside the immense research effort in traditional statistics (to mention results of Spearman on vanishing tetrad differences from the beginning of this century to recent LISREL and EQS techniques see [15] for a comparative study of these techniques with causal network approaches in AI) The ....

Glymour C., Scheines R., Spirtes P., Kelley K. (1987): Discovering causal structure, New York, Academic Press.

....and their potential use as an alternative interpretation of simultaneous equation systems. 42 11.2 Causal discovery Another and more controversial aspect of causal inference from graphical models is associated with identifying causal relationships from data. Ever since the appearance of Glymour et al. 1987) and the first version of the corresponding program TETRAD, this has been the subject of sometimes quite heated discussions (Freedman 1991, 1995; Robins and Wasserman 1999; Glymour et al. 1999) Basically there have been two different types of approach. The constraintbased approach (Spirtes et ....

Glymour, C., Scheines, R., Spirtes, P., and Kelly, K. (1987). Discovering Causal Structure. Academic Press, New York.

.... (also called belief networks or bayesian belief networks) encode properties of probability distributions using directed acyclic graphs (dag) Their usage is spread among many disciplines such as Artificial Intelligence [14] Decision Analysis [9] 17] Economics [31] Genetics [32] Philosophy [7], and Statistics [11] 22] Bayesian networks are popular due to existence of numerous efficient methods of quantitative reasoning with probabilities if the joint probability distribution has an underlying dag structure [13, 14, 18, 19, 20] Reasoning about conditional and marginal independence ....

Glymour C., Sheines R., Spirtes P., Kelly K.: Discovering Causal Structures, Academic Press, New York,: 1987

....y 2;t . On the other hand, y 1;t and y 2;t (y 2;t and y 3;t ) are contemporaneously correlated when conditioned on y 3;t (y 1;t ) In general, graphs of this sort provide a useful shortcut for expressing the contemporaneous relationships among variables. Swanson and Granger (1997) 1 See, e.g. Glymour, Scheines, Spirtes, and Kelly (1987) and Swanson and Granger (1997) for further details. formalize the use of partial correlations and DAGs for orthogonalizing the errors in VAR models, by providing a simple regression based technique for testing the adequacy of some given recursive structural model of the errors, thus avoiding ....

Glymour, C., R. Scheines, P. Spirtes, and K. Kelly (1987), Discovering Causal Structure, San Diego, Academic Press.

....the user can specify different ff values in different contexts, depending on how confident he needs to be for each individual decision. This issue is clearly related to the confidence measured used by the BN learners that use conditionalindependence tests to decide whether to include some link [GSSK87, CBL97]. Our test, however, is more fine grained (at the level of a single modification, rather than dealing with the entire cascade of decisions made by general learning algorithms) and, again, is under the control of the user. Also, some of our analyses assume we know how the eventual belief net will ....

....of queries that will be posed (see Section 2.2.2) This allows us to focus attention on producing a system that will perform well on these queries. This model, first expressed in [GGS97] differs from both of the dominant approaches, based on maximizing likelihood [Hec95] or finding independencies [GSSK87, CBL97]. Section 3 shows how the error bars for an inference from a belief net varies with the sample size; this relates to the work on determining the sample complexity for learning belief nets [Hof93, FY96, Das97] Of course, those papers dealt with the problem of identifying which of a given class of ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structure. Academic Press, Inc., London, 1987.

....numeric value distributions, regardless the size of the original database. Systems for Knowledge Discovery in Databases Matheus, Chan, Piatetsky Father s education Father s Occupation Respondent s Education First Job Occupation in 1962 Figure 4: A data dependency graph derived by TETRAD [Glymour et al. 1987] depicting the American Occupational Structure according to a 1962 survey of 20,000 people. Exact or functional dependencies have been the subject of database research since the 1970 s. Several algorithms now exist for using functional dependencies to create normalized databases that minimize ....

.... to create normalized databases that minimize redundancies and facilitate updates [Ullman, 1982] An asymptotically optimal algorithm also exists for finding the minimal set of functional dependencies in a database [Mannila and Raiha, 1987] In recent years, research by Pearl [1988, 1991] Glymour et al. 1987], and others has resulted in major advances in the area of discovering dependency or causal graphs. Because standard statistical techniques cannot distinguish causation from covariation, data precedence information or assumptions are needed to establish the direction of influence. The proposed ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structure. Academic Press, 1987.

....local search is effective for detecting strong patterns. 15.1 Introduction The problem of inferring causality from empirical observations has been well studied. Several approaches are notable for efficiently constructing complex causal models of the inter relationships between variables (e.g. [8, 3, 2]) These approaches tend to rely on correlations and co variances among the variables as the basis for inferring causality. However, for some applications, the available data are categorical observations over time (e.g. event streams or execution traces of programs) for example, patterns in ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structure. Academic Press, 1987.

....z E mail: msingh gradient.cis.upenn.edu or mgv usceast.cs.scarolina.edu International Journal of Approximate Reasoning 1995 12:111 131 c fl 1995 Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010 0888 613X 95 7. 00 112 methods are based on linearity and normality assumptions [2, 3]; others are more general but require extensive testing of independence relations [4, 5, 6, 7, 8] others yet take a Bayesian approach [9, 10, 11, 12] In this paper, we do not consider methods of the first kind, namely, those that make linearity and normality assumptions. Our work concentrates on ....

Glymour, C., Scheines, R., Spirtes, P., and Kelly, K., Discovering Causal Structure, Academic Press, San Diego, CA, 1987.

....chronological information can significantly simplify the modeling task. Such semantics should be applicable, therefore, to the organization of concurrent events or events whose chronological precedence cannot be determined with precision, e.g. old age explains disabilities ) in the spirit of Glymour [Glymour et al. 1987] and Simon [Simon, 1954] 1 See [Dechter and Pearl, 1990] for a treatment of causation in the context of categorical data. 2 Some of the popular quotes are: No causation without manipulation , Holland, 1986] No causes in, no causes out , Cartwright, 1989] No computer program can take ....

Glymour, C., Scheines, R., Spirtes, P., and Kelly, K. (1987). Discovering Causal Structure. Academic Press, New York.

....probability) is maximal [Hec95, Bun96] or which embodies the discussion in Section 6. Also, ZG99] relates the err( Delta ) and CLL Delta ( Delta ) scores, and explains why we used the first for the elq and ulqs contexts, but the second for ilq. all and only the conditional dependencies [GSSK87]. As discussed above, our goal is different: our learners seek the BN that produces the most accurate responses, over a distribution of queries. While this objective is weaker (as a BN that is a perfect model of the distribution will also have the most accurate possible responses) we argue that ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structure. Academic Press, Inc., London, 1987.

....ffl Summarization. Summarization involves techniques for searching compact descriptions for a set of data. Summarization rules, linguistic summaries [123] statistical summaries [52] and decision trees [22] are the main summarization methods used in Data Mining. ffl Dependency modelling [14, 45, 51, 90]. This task looks for a model that describes in an easily understandable way the dependencies that exist between the variables appearing in the data. Two level of analysis are performed in the learning of this kind of models. In a first level we have to find the structural dependence between ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structure. New-York: Academic Press, 1987.

....the observed variables. In addition, we need to specify how to transform the parameters of the network to the observable parameters. The transformation of the means and the transformation to obtain the observable covariance matrix can be accomplished via the trek sum rule (for a discussion, see Glymour et al. 1987). Using the trek sum rule, it is easy to show that the observable parameters are all sums of products of the network parameters. Given that the mapping from s to the observable parameters is W is a polynomial function of , it follows from Thm. 1 that the rank of the Jacobian matrix h s W ....

....that this model imposes tetrad 3 m i is the mean of X i conditional on all parents being zero, b ji corresponds to the partial regression coefficient of X i on X j given the other parents of X i , and v i corresponds to the residual variance of X i given the parents of X i . constraints (see Glymour et al. 1987). In this model the three tetrad constraints that hold in the distribution over the observed variables are cov(X 1 ; X 2 )cov(X 3 ; X 4 ) Gamma cov(X 1 ; X 3 )cov(X 2 ; X 4 ) 0 cov(X 1 ; X 4 )cov(X 2 ; X 3 ) Gamma cov(X 1 ; X 3 )cov(X 2 ; X 4 ) 0 cov(X 1 ; X 4 )cov(X 2 ; X 3 ) Gamma cov(X 1 ....

Glymour, C., Scheines, R., Spirtes, P., and Kelly, K. (1987). Discovering Causal Structure. Academic Press.

.... in deriving some statement about the probability distribution governing the data) or they can be deterministic as in deriving functional dependencies between fields in the data [101] Density estimation methods in general fall under this category, so do methods for explicit causal modeling (e.g. [58] and [63] We focus our attention specifically on density estimation. 5.2 Density Estimation Mathematical Programming Formulations In the density estimation problem [108] we are given a finite number of n dimensional data points, that is fx 1 ; x 2 ; x M g. We assume that these ....

C. Glymour, R. Scheines, and P. Spirtes ABD K. Kelly. Discovering Causal Structure. Academic Press, New York, 1987.

....event) For example, we have used DD to search for dependencies between combinations of actions of a planner and plan failure. Path Analysis (PA) is a technique for building causal models based on multiple linear regression [10,14,17,19,5] which is related to techniques for causal induction [15,9]. Our algorithm for PA builds detailed models of the interaction of various causal factors on the value of an ordinal variable. For example, we have constructed path models of environment and planner factors that directly or indirectly influence the amount of time required to finish a plan. The ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structure. Academic Press, 1987.

....patterns are connected with the more basic notions associated with causation, such as influence, manipulation, and control. The connection is made in the mechanism based account of causation. The basic idea behind this account goes back to [Simon 1977] and is stated succinctly in his forward to [Glymour et al. 1987]: The advantage of representing the system by structural equations that describe the direct causal mechanisms is that if we obtain some knowledge that one or more of these mechanisms has been altered, we can use the remaining equations to predict the consequences the new equilibrium. Here, by ....

Glymour, C., R. Scheines, P. Spirtes and K. Kelly (1987) Discovering Causal Structure, Academic Press, Orlando, FL.

....about external interventions can be organized and represented graphically and, conversely, how the graphical representation can be used to facilitate quantitative predictions of the effects of interventions. The basic idea goes back to Simon [9] and is stated succinctly in his forward to [1]: The advantage of representing the system by structural equations that describe the direct causal mechanisms is that if we obtain some knowledge that one or more of these mechanisms has been altered, we can use the remaining equations to predict the consequences the new equilibrium. Here, by ....

Glymour, C., Scheines, R., Spirtes, P., and Kelly, K., Discovering Causal Structure, Academic Press, Orlando, FL, 1987.

.... intelligent systems [8] and in decision theory to model complex decisions [9] An area not considered in this review is graphical modeling in social science which has had rich development and application, and strong interactions with the artificial intelligence and statistical communities [10], 3] 11] 12] Networks in general play the role of a high level language, as is seen in artificial intelligence, statistics, and to a lesser degree in neural networks (where biological views offer an alternative interpretation) See the survey by Ripley [13] Networks are used to build ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly, Discovering Causal Structure, Morgan Academic Press, San Diego, CA, 1987.

....and Analysis in LISP) 118] Other examples of software as algorithm for building a model from data can be found in the literature. Spirtes and Glymour s work on TETRAD suggested fitting a causal structure to statistical data by considering the measure of fit of several different structures [55]. Pearl criticized TETRAD for its failure to to employ a systematic procedure for finding a best fit structure [110] This criticism was taken to heart; the project s second incarnation, TETRAD II, approached the problem systematically [140] Cooper and Herskovits s K2 algorithm constructs a BN ....

C. Glymour, R. Scheines, P. Spirtes, and K. Kelly. Discovering Causal Structures. Academic Press, San Diego, 1987.

....is unmeasured, however, our data will only include partial correlations among the measured variables X = X 1 , X 2 , X 3 , X 4 , and there is no partial correlation involving only variables in X that is entailed to be zero by this SEM. The vanishing tetrad difference (Spearman, 1904, Glymour, et al. 1987), however, can provide extra information about the specification of this model. A tetrad difference involves two products of correlations, each of which involve the same four variables but in different permutations. In the SEM of Figure 9 there are three tetrad differences among the measured ....

....rejection of an otherwise correct RSEM. Finally, if a model produced by search is tested on the data used to find the model specification, the p value of the test is not a measure of the error probability of the model specification procedure. For a discussion of the meaning of such p values, see Glymour, et al. 1987). Where possible, models generated from one sample should be cross validated on others. 29 In the case of Build under the assumption of latent variables, more research is needed to find out how to construct (efficiently) from the PAG which represents the entire partial correlation equivalence ....

Glymour, C., Scheines, R., Spirtes, P., & Kelly, K. (1987). Discovering Causal Structure. Academic Press, San Diego, CA.

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Glymour C, Scheines R, Spirtes P, Kelley K (1987). Discovering Causal Structure. Academic Press, San Diego.

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Glymour C., Scheines R., Spirtes P., Kelly K.: `Discovering Causal Structure', Academic Press, San Diego, CA, 1987.

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Clark Glymour, Richard Scheines, Peter Spirtes, and Kevin Kelly. Discovering Causal Structures. Academic Press, 1987. 68

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Glymour, C., R. Scheines, P. Spirtes, and K. Kelly (1987), Discovering Causal Structure, San Diego, Academic Press.

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Glymour C., Scheines R., Spirtes P., Kelly K. (1987) Discovering Causal Structure. New York: Academic Press.

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Glymour, C., Scheines, R., Spirtes, P., and Kelly, K. "Discovering Causal Structure ". San Diego, CA: Academic Press, 1987.

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Glymour, C., Scheines, R., Spirtes, P., and Kelly, K. "Discovering Causal Structure". San Diego, CA: Academic Press, 1987.

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Glymour, C.; Scheines, R.; Spirtes, P.; and Kelly, K. Discovering Causal Structure, Academic Press, New York, 1987.

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