That was theory.

Say I would give you an exercise.

Give me a graphical model of P-POP or something.

What would you do?

How would you construct a Bayesian network?

Yes.

Exactly.

Yes.

First thing, say we already done that.

What do we do?

Yeah.

We need to know where are our arrows and which are the nodes.

Exactly.

So what we do is we'll just start off with the nodes.

And then we fix some order of nodes.

And then we go through this.

That's one way of doing it.

Starting with the first variable.

And then, so the thing, the critical thing here is that we choose a set of parents.

Or in other words, what are the nodes already present that influence the node that's in my hand right now?

And you can do this by looking at the conditional probabilities.

So if I'm holding XI here, that's my current variable.

And I'm looking at what is the probability distribution of that variable given all the variables I've already seen that are already in my graph.

If that's this reduced givens probability, then I know I have a parent.

OK, so we're looking for parents out there.

There's an influence.

This really says if there is an influence of some XJ that's already in my graph, 2XI, then it's a parent.

Otherwise, I can leave it out.

I would like to leave it out.

So if I've identified a parent, I'm going to add a node.

And of course, with the new node, I'm going to take this beast, which I have to assess or estimate or hope for the best.

And then I add that as the as the CPD.

And of course, there's one choice here, really.

The choice here is the ordering of the variables.

And that choice matters.

So in particular, the size of the Bayesian networks and we'll define that in a minute is not actually a fixed is not order independent.

OK, let's say we have this order.

Let's do this together.

Mary calls.

Let me.

So that we remember this, and I'm going to go back to the construction algorithm.

So let's go through this.

So we've done I've done.

Step two for you.

Now we do. Step three together.

Yeah, what do we do?

We're starting out with I equals one. OK.

And now we're choosing a minimal sets of parents of X one, which is in the set X one to X zero, meaning the empty set.

That choice is dead easy.

For all of those, we add an edge. Well, there are none of those.