Spirtes, P., Meek, C., and Richardson, T. Causal inference in the presence of latent variables and selection bias. In Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence. P. Besnard and S. Hanks, Eds. Morgan Kaufmann Publishers, San Mateo, Calif., 1995, pp. 499--506.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....frequencies of the search procedure are known something usually obtainable only through extensive Monte Carlo exploration. Our impression is that the error rates of search procedures proposed and used in the data mining and statistical literatures are rarely estimated in this way. See [10] and [11] for Monte Carlo test design for search procedures. When the probabilities of various models are entirely subjective, model averaging gives at least coherent estimates. Hypothesis Testing Hypothesis testing can be viewed as one sided estimation in which, for a specific hypothesis and any sample ....

....algorithms implemented in the TETRAD II program [6, 10] give the correct result asymptotically in this case and in all cases in which the Markov and faithfulness conditions hold. The results are also robust against the three problems with causal inference noted in the previous paragraph [11]. However, the statistical decisions made by the algorithms are not really optimal, and the implementations are limited to the multinomial and multinormal families of probability distributions. A review of Bayesian search procedures for causal models is given in [2] Prediction ....

Spirtes, P., Meek, C., and Richardson, T. Causal inference in the presence of latent variables and selection bias. In Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence. P. Besnard and S. Hanks, Eds. Morgan Kaufmann Publishers, San Mateo, Calif., 1995, pp. 499--506.

....and parameters can (and cannot) be learned from conditional independence tests are described, when there is selection; a special case Bayesian analysis of causal modeling under selection also is proposed. A general algorithm for causal discovery using conditional independence tests is developed in (Spirtes, et al. 1995). The unique contribution of the current paper is to describe a general Bayesian method for causal modeling and discovery under selection. 1 Throughout the paper we use as synonyms the nouns sample and selection, the verbs sample and select, and the terms sampled and selected. 2 In this ....

Spirtes, P., Meek, C. and Richardson, T. (1995) Causal inference in the presence of latent variables and selection bias, In: Proceedings of the Conference on Uncertainty in Artificial Intelligence 499-506.

....causal relationships. 3 Technical Challenges Many researchers are now concentrating on learning in more expressive probabilistic models, including hybrid (discrete and continuous) models [ Lauritzen and Wermuth, 1989 ] mixed (undirected and directed) models [ Buntine, 1994; Cooper, 1995; Spirtes et al. 1995 ] dynamic Bayesian network models representing stochastic processes [ Russell et al. 1995 ] and stochastic grammars [ Stolcke and Omohundro, 1993 ] Another important problem is the specification of prior distributions over parameters most current work makes strong assumptions such as ....

....world. For example, the fact that a patient drops out of a drug study may suggest that the he or she could not tolerate the effects of the drug. Several researchers have developed basic principles and methods for dealing with such situations, including Rubin (1978) Robins (1986) Cooper (1995) Spirtes et al. 1995), and Chickering (1995) but more work needs to be done to connect these basic principles with graphical models and to make these methods more efficient. A second challenge is the creation of simple but expressive probability distributions for the local interaction models in a Bayesian network. ....

Spirtes, P., Meek, C., and Richardson, T. (1995). Causal inference in the presence of latent variables and selection bias. In Proceedings of Eleventh Conference on Uncertainty in Artificial Intelligence, Montreal, QU, pages 499--506. Morgan Kaufmann.

....nor possible in most applications of data mining. Fortunately, recent research in statistics and Bayesian learning communities provide some avenues of attack. Two classes of technique have arisen: Bayesian causal discovery, which focuses on learning complete causal models for small data sets [8, 12, 14, 15, 16, 17, 21, 22, 23, 25, 26, 27], and an offshoot of the Bayesian learning method called constraint based causal discovery, which use the data to limit sometimes severely the possible causal models [11, 26, 24] While techniques in the first class are still not practical on very large data sets, a limited version of the ....

P. Spirtes, C. Meek, and T. Richardson. Causal inference in the presence of latent variables and selection bias. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, pages 499--506, 1995.

....used to represent causality in this manner, but these networks have a different interpretation to the probabilistic networks considered here. Causality, networks and learning causlity are not covered in this review. Learning and identification of causality is considered in [56] 3] 57] 58] [59]. TABLE II A sample database in a relational table case A B C 1 T F T 2 T T T 3 F T T 4 F T T III. Some simple examples, and some basic concepts As an example of learning, consider data about three binary variables, A; B; C. This data would take the form of a table, as given in the simple ....

.... with identification algorithms [33] But Bayesian methods do equivalent things in the large sample case to the independence tests used by identification algorithms, and the strict ordering is not entirely necessary for the Bayesian algorithms [32] 37] A variety of hybrid algorithms exist [59], 104] 12] 73] that provide a rich source of ideas for future development. X. Constructing learning software For a variety of network structures with latent variables and different parametric nodes (Logistic, Poisson, and other forms) the BUGS program can generate Gibbs samplers ....

P. Spirtes, C. Meek, and T. Richardson, "Causal inference in the presence of latent variables and selection bias", In Besnard and Hanks [158], pp. 499--506.

....index searches cannot suggest adding or removing a latent variable, for example. Also, these searches output a single SEM, rather than an equivalence class of SEMs. Another search strategy based upon maximizing a score is to search not RSEMs themselves, but covariance equivalence classes of RSEMs (Spirtes and Meek, 1995). 8 Some of this literature is published in the annual proceedings of the conferences on Uncertainty in Artificial Intelligence, Knowledge Discovery in Data Bases, and the bi annual conference on Artificial Intelligence and Statistics. Examples of important papers in this tradition include: ....

....errors a partial correlation r A,B.C is entailed to be zero if and only if A and B are d separated by C in the directed graph associated with R (Pearl 1988) More details about their discovery, which is considerably more general than the description given here, are given in section 8.1. Spirtes (1995) showed that these connections between graphical structure and vanishing partial correlations hold as well for nonrecursive SEMs, i.e. in a SEM with uncorrelated errors a partial correlation r A,B.C is entailed to be zero if and only if A and B are d separated given C. The if part of the ....

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Spirtes, P., Meek, C., and Richardson, T. (1995) Causal inference in the presence of latent variables and selection bias. Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, ed. by Philippe Besnard and Steve Hanks, Morgan Kaufmann Publishers, Inc., San Mateo, CA, 499-506.

....methods for handling missing data where absence is independent of state are simpler than those where absence and state are dependent. Here, we concentrate on the simpler situation. Readers interested in the more complicated case should see Rubin (1978) Robins (1986) Cooper (1995) and Spirtes et al. 1995). Continuing with our example using discrete multinomial likelihoods, suppose we observe a single incomplete case. Let Y ae X and Z = XnY denote the observed and unobserved variables in the case, respectively. Under the assumption of parameter independence, we can compute the posterior ....

Spirtes, P., Meek, C., and Richardson, T. (1995). Causal inference in the presence of latent variables and selection bias. In Proceedings of Eleventh Conference on Uncertainty in Artificial Intelligence, Montreal, QU, pages 499--506. Morgan Kaufmann.

....however, if the number of variables in a database is large, then it is not computationally feasible to calculate the posterior probability of each causal DAG, due to the astronomically large number of such DAGs. 2 PARTIAL SOLUTION The following theorem follows simply from Cooper (1997) and Spirtes et al. 1995). A measured variable V is exogenous if there is no variable which is a direct cause of V. A variable is exogenous in a causal DAG if there is no arrow directed into it. We assume that there is no causal relation between the sampling mechanism and the measured variables (i.e. there is no ....

P. Spirtes, C. Meek and T. Richardson, "Causal inference in the presence of latent variables and selection bias", Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence, ed. by Philippe Besnard and Steve Hanks, Morgan Kaufmann Publishers, Inc., San Mateo, 1995.

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