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## 4.6 Software Packages for Learning

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Based on considerations such as those illustrated in Section 4.4.1, Spirtes et al. [1993, 2000] developed an algorithm which finds the DAG faithful to *P* from the conditional independencies in *P* when there is a DAG faithful to *P*. Spirtes et al. [1993, 2000] further developed an algorithm which learns a DAG in which *P* is embedded faithfully from the conditional independencies in *P* when such a DAG exists. These algorithms have been implemented in the Tetrad software package [Scheines et al., 1994], which can be downloaded for free from the following site:

http://www.phil.cmu.edu/projects/tetrad/.

In 1997 Meek developed a heuristic search algorithm called **Greedy Equivalent Search (GES)** which has the following property: if there were a DAG faithful to *P*, the limit, as the size of the data set approaches infinity, of the probability of finding a DAG faithful to *P* is equal to 1. The Tetrad software package also has a module which uses that algorithm along with the **Bayesian information criterion (BIC)** to learn a Bayesian network from data.