 Hello, everyone. This is Alice Gao. In this video, I will discuss the de-separation definition, which we can use to determine whether an unconditional or conditional independence relationship holds or not. Here's the definition of de-separation. There are two variables x and y, and the set of observed variables e. If the observed variables e block every undirected path between x and y, then we say that e de-separates x and y. To determine whether x and y are independent, given the observed variables e, we can verify whether e de-separates x and y. If de-separation holds, then the independence relationship holds as well. Let me clarify a few things regarding the de-separation definition. First, to verify the definition, we need to consider every undirected path between x and y. The word undirected means that we do not care about the direction of the arrows on the path. As long as a series of nodes and edges connect x and y, we will consider it the path. Second, there may be multiple paths between x and y. We need to consider every path and verify that e blocks every path between x and y. Third, on each path, there could be multiple nodes between x and y. The path is blocked if at least one node blocks the path. As soon as we find one node blocking the path, we are done and we can move on to a different path. In the worst case, we need to check every node and discover that none of the nodes blocks the path. Given this definition, our task boils down to the following. Pick a path between x and y and pick a node on the path, determine whether the node blocks a path or not. This leads to our next question. What does it mean to block a path? Let me explain this in three scenarios. Interestingly, these three scenarios correspond to the three key structures that I discussed previously. In each of the three scenarios, we will look at one path between x and y and consider one node n on the path. The three scenarios differ by the direction of the two arrows on both sides of n. Scenario number one, the two arrows around n point in the same direction, forming a chain around n. I drew the arrows pointing to the right, but it's fine if they point to the left as well. In this scenario, if n is observed, then n blocks a path between x and y. This rule is similar to the first key structure that's a chain. If we observe whether alarm is going off or not, then burglary and Watson become independent. You can think of observing alarm or observing n as cutting the chain at that node. Scenario two, the two arrows around n point away from n to the two children a and b. If the arrows depict causal relationships, you can think of a and b as unreliable sensors of n. If n is observed, then n blocks the path between x and y. This rule is similar to the second key structure. If we observe alarm, then Watson and Gibbon become independent. Scenario three, the two arrows around n point toward n. a and b are both parents of n. If the arrows depict causal relationships, then a and b jointly cause n to happen. The descendants of n are also important in this scenario. The rule says that if we do not observe n, and do not observe any of n's descendants, then the path is blocked. This rule is similar to the third key structure. If alarm is not observed, then burglary and earthquake are independent. If alarm is observed, burglary and earthquake become dependent. Note that this rule is the opposite of the first two rules. The first two rules say that n blocks a path if n is observed. This third rule says that n and its descendants block the path if they're not observed. These three scenarios together define what it means for a path to be blocked. That's everything on the de-separation definition. In the next video, I will go over several examples of applying de-separation to determine whether an independent relationship holds. Let me summarize. After watching this video, you should be able to explain the de-separation definition. In particular, what does it mean for a node to block a path? Thank you very much for watching. I will see you in the next video. Bye for now.