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- | [[File:dag_example.jpg|500px]] | + | [[media:cs-677sp10:dag_example.jpg|500px]] |

===DAG Example=== | ===DAG Example=== | ||

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* By Rule 4 created directed edge A $\rightarrow$ B - graph (f) | * By Rule 4 created directed edge A $\rightarrow$ B - graph (f) | ||

- | [[File:dag_example2.jpg|400px]] | + | [[media:cs-677sp10:dag_example2.jpg|400px]] |

==Creating Graph Skeleton== | ==Creating Graph Skeleton== | ||

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===PC Example=== | ===PC Example=== | ||

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(Example taken from Jensen, and Nielsen). Given the complete graph shown as (a) the first iteration (i=0) yields the following oracle queries and answers: | (Example taken from Jensen, and Nielsen). Given the complete graph shown as (a) the first iteration (i=0) yields the following oracle queries and answers: | ||

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Starting with a complete graph with six nodes (like the one shown below) use the PC algorithm and your own oracle to create a skeleton graph (the skeleton must meet the requirements needed for the next step). Using your skeleton graph and oracle, go through the steps of creating a possible DAG that uses each of the four rules at least once. List the steps and rules used to add each of your directed edges. | Starting with a complete graph with six nodes (like the one shown below) use the PC algorithm and your own oracle to create a skeleton graph (the skeleton must meet the requirements needed for the next step). Using your skeleton graph and oracle, go through the steps of creating a possible DAG that uses each of the four rules at least once. List the steps and rules used to add each of your directed edges. | ||

- | [[image:newpc_1.jpg|200px]] | + | [[media:cs-677sp10:newpc_1.jpg|200px]] |

==References== | ==References== | ||

* Koller, D. and Friedman, N. Probabilistic Graphical Models: Principles and Techniques. MIT Press, 2009. | * Koller, D. and Friedman, N. Probabilistic Graphical Models: Principles and Techniques. MIT Press, 2009. | ||

* Jensen, F. and Nielsen, T. Bayesian Networks and Decision Graphs. 2nd Edition. Springer, 2007. | * Jensen, F. and Nielsen, T. Bayesian Networks and Decision Graphs. 2nd Edition. Springer, 2007. |