An Algorithm for Fast Recovery of Sparse Causal Graphs
TL;DR: An asymptotically correct algorithm whose complexity for fixed graph connectivity increases polynomially in the number of vertices, and may in practice recover sparse graphs with several hundred variables.
Abstract: Previous asymptotically correct algorithms for recovering causal structure from sample probabilities have been limited even in sparse causal graphs to a few variables. We describe an asymptotically...
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Book•
01 Jan 1993
TL;DR: The authors axiomatize the connection between causal structure and probabilistic independence, explore several varieties of causal indistinguishability, formulate a theory of manipulation, and develop asymptotically reliable procedures for searching over equivalence classes of causal models.
Abstract: What assumptions and methods allow us to turn observations into causal knowledge, and how can even incomplete causal knowledge be used in planning and prediction to influence and control our environment? In this book Peter Spirtes, Clark Glymour, and Richard Scheines address these questions using the formalism of Bayes networks, with results that have been applied in diverse areas of research in the social, behavioral, and physical sciences. The authors show that although experimental and observational study designs may not always permit the same inferences, they are subject to uniform principles. They axiomatize the connection between causal structure and probabilistic independence, explore several varieties of causal indistinguishability, formulate a theory of manipulation, and develop asymptotically reliable procedures for searching over equivalence classes of causal models, including models of categorical data and structural equation models with and without latent variables. The authors show that the relationship between causality and probability can also help to clarify such diverse topics in statistics as the comparative power of experimentation versus observation, Simpson's paradox, errors in regression models, retrospective versus prospective sampling, and variable selection. The second edition contains a new introduction and an extensive survey of advances and applications that have appeared since the first edition was published in 1993.
4,863 citations
TL;DR: This paper presents a Bayesian method for constructing probabilistic networks from databases, focusing on constructing Bayesian belief networks, and extends the basic method to handle missing data and hidden variables.
Abstract: This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.
3,971 citations
TL;DR: An examines methodologies suited to identify such symptom networks and discusses network analysis techniques that may be used to extract clinically and scientifically useful information from such networks (e.g., which symptom is most central in a person's network).
Abstract: In network approaches to psychopathology, disorders result from the causal interplay between symptoms (e.g., worry → insomnia → fatigue), possibly involving feedback loops (e.g., a person may engage in substance abuse to forget the problems that arose due to substance abuse). The present review examines methodologies suited to identify such symptom networks and discusses network analysis techniques that may be used to extract clinically and scientifically useful information from such networks (e.g., which symptom is most central in a person's network). The authors also show how network analysis techniques may be used to construct simulation models that mimic symptom dynamics. Network approaches naturally explain the limited success of traditional research strategies, which are typically based on the idea that symptoms are manifestations of some common underlying factor, while offering promising methodological alternatives. In addition, these techniques may offer possibilities to guide and evaluate therape...
1,824 citations
Cites methods from "An Algorithm for Fast Recovery of S..."
...Figure 7 (see Table 1 for the accompanying legend) provides a graphical representation of the result of applying the PC algorithm (Spirtes & Glymour 1991) to the NCS-R depression data using the R-package PcAlg (Kalisch et al. 2012)....
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TL;DR: Algorithms that use an information-theoretic analysis to learn Bayesian network structures from data, requiring only polynomial numbers of conditional independence tests in typical cases are provided.
804 citations
Cites background or methods from "An Algorithm for Fast Recovery of S..."
...For example, when compared to the PC algorithm (which also uses dependency analysis to learn Bayesian net structures; [48], see Section 7), we found that TPDA typically uses fewer CI tests than PC uses, but these tests are often more complex....
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...This basic “try each subset” algorithm is used by essentially all other dependency-analysis based algorithms, including the SGS algorithm [47], the Verma–Pearl algorithm [56] and the PC algorithm [48]....
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...PC [48] General Bayesian nets No O(Nk+2) K is the maximum degree of any node in the true structure; Can orient edges; enhanced from SGS algorithm; efficient...
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...) However, this method is quite popular among Bayesian network learning algorithms due to its efficiency and reliability [48,56]....
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Proceedings Article•
01 Jan 1991TL;DR: In this paper, the theory of inferred causation is discussed, where causal ordering is defined as the ordering at which subsets of variables can be solved independently of others; in other systems, it follows the way a disturbance is propagated from one variable to others.
Abstract: Publisher Summary This chapter discusses the theory of inferred causation. The study of causation is central to the understanding of human reasoning. Inferences involving changing environments require causal theories that make formal distinctions between beliefs based on passive observations and those reflecting intervening actions. In applications such as diagnosis, qualitative physics, and plan recognition, a central task is that of finding a satisfactory explanation to a given set of observations, and the meaning of explanation is intimately related to the notion of causation. In some systems, causal ordering is defined as the ordering at which subsets of variables can be solved independently of others; in other systems, it follows the way a disturbance is propagated from one variable to others. An empirical semantics for causation is important for several reasons. The notion of causation is often associated with those of necessity and functional dependence; causal expressions often tolerate exceptions, primarily because of missing variables and coarse description. Temporal precedence is normally assumed essential for defining causation, and it is one of the most important clues that people use to distinguish causal from other types of associations.
767 citations
References
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Proceedings Article•
27 Jul 1990
TL;DR: The canonical representation presented here yields an efficient algorithm for determining when two embedded causal models reflect the same dependency information, which leads to a model theoretic definition of causation in terms of statistical dependencies.
Abstract: Scientists often use directed acyclic graphs ( dags) to model the qualitative structure of causal theories, al lowing the parameters to be estimated from observa tional data. Two causal models are equivalent if there is no expirement which could distinguish one from the other. A canonical representation for causal models is presented which yields an efficient graphical crite rion for deciding equivalence, and provides a theoret ical basis for extracting causal structures from em pirical data. This representation is then extended to the more general case of an embedded causal model, that is, a dag in which only a subset of the vari[Verma and Pearl 90]. One problem that has arisen in the course of these studies is that of non uniqueness; it is quite common for two different causal models to be experimentally indistinguishable, hence, equally predictive. Formally, let a causal the ory be a pair T =< D, e >, where D is a dag, called the causal model ofT, and e a set of parameters com patible with D (i.e., sufficient for forming a probabil ity distribution for which D is a Bayesian network). We say that two causal models D1 and D2 are equiv alent if for every theory T1 =< D1, 81 > there is a theory T2 =< D2, 82 > such that T1 and T2 describe the same probability distribution, and vice versa. ables are observable. The canonical representation / b "-.. presented here yields an efficient algorithm for detera "-.. a � /c mining when two embedded causal models are equiv· "' alent, and leads to a model theoretic definition of b "-.. / b causation in terms of statistical dependencies. "' c a"' /
1,286 citations
"An Algorithm for Fast Recovery of S..." refers background in this paper
...&dquo; Figure i ALARM network 67 Verma and Pearl (1990) have suggested an improvement on the sGs algorithm....
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...Verma and Pearl (1990) subsequently proved the correctness of the algorithm and offered a variant that outputs a pattern rather than a collection of graphs....
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Book•
01 Jan 1975
1,235 citations
"An Algorithm for Fast Recovery of S..." refers background in this paper
...Methodology texts routinely recommend generating the set of admissible causal structures from &dquo;substantive theory&dquo; (see Joreskog & Sorbom, 1984; Duncan, 1975)....
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814 citations
TL;DR: An overview of structural equation models, and their potential for advancing neuropsychological theory and practice is provided to help researchers assess the relevance of these advanced statistical techniques to their own research, and begin the process of successful application.
Abstract: This paper provides an overview of structural equation models, and their potential for advancing neuropsychological theory and practice. Four topics are covered: (1) an overview of the various classes of models, and an introduction to the terminology and diagrams used to describe them, (2) an outline of the steps involved in applying structural equation modeling to any research problem, (3) an overview of the information used in assessing model fit, and a discussion of the role of significance tests in structural models, and (4) an outline of the advantages and disadvantages of structural equation models, and their potential contribution to neuropsychology. The paper is intended to help researchers (1) assess the relevance of these advanced statistical techniques to their own research, and (2) begin the process of successful application.
337 citations
Proceedings Article•
27 Jul 1990
TL;DR: Kutato as mentioned in this paper is a system that takes as input a database of cases and produces a belief network that captures many of the dependence relations represented by those data, incorporating a module for determining the entropy of belief networks and a module based on entropy calculations.
Abstract: Kutato is a system that takes as input a database of cases and produces a belief network that captures many of the dependence relations represented by those data. This system incorporates a module for determining the entropy of a belief network and a module for constructing belief networks based on entropy calculations. Kutato constructs an initial belief network in which all variables in the database are assumed to be marginally independent. The entropy of this belief network is calculated, and that arc is added that minimizes the entropy of the resulting belief network. Conditional probabilities for an arc are obtained directly from the database. This process continues until an entropy-based threshold is reached. We have tested the system by generating databases from networks using the probabilistic logic-sampling method, and then using those databases as input to Kutato. The system consistently reproduces the original belief networks with high fidelity.
149 citations