Causal Discovery

Question 1

How can you test DAG and data compatibility

Answer 1

One can find the d-separated nodes and then check in the data if those nodes are independent empirically.

Question 2

How many conditional independence relationships do you find in this graph?

Answer 2

six.

Question 3

What is causal discovery?

Answer 3

Find all conditional independence relationships in the data and construct a DAG that is compatible with these relationships.

Question 4

Can you always completely learn the DAG from data?

Answer 4

No, since the chain and fork relationships are not distinguishable but they are distinguishable from collider.

Question 5

What are some assumptions of causal discovery?

Answer 5

• Acyclicity (Having a DAG)
• Causal sufficiency (no hidden or latent variables)
• Optional: linearity and Guassian errors. Make conditional independence testing easier.
• Causal Faithfulness: You can go from d-separation to certain causal relations and reverse.

Question 6

What is the PC algorithm

Answer 6

It is a popular algorithm for causal discovery
- First determine the skeleton of the graph
- then the v-structure
- finally determine further edge orientation

Question 7

How do you determine the skeleton of a DAG?

Answer 7

• First consider the undirected complete graph
• remove the edges for conditionally independent nodes. Consider all pairs and for each pair condition on all other nodes and test independence at and alpha level.
• Store the separating set of nodes

Question 8

What is V-Structure

Answer 8

• for a triplet of nodes that are unshielded meaning that i>j>k such that i and k are not directly connected.
• determine whether there is a collider structure based on d-separation
• Given that we cannot differentiate fork and chain relation, we may have uncertainty on the direction of certain edges for which we can use arrows on both ends of the edge to represent uncertainty (partially DAG or PDAG)