The next thing we did was we looked at sizes.

And essentially a size of a base network is the number of numbers in the conditional probability table.

And if you write down the math that this idea entails, you're going to get exactly that.

And you're also going to get amazing size differences between the full joint probability distribution and the Bayesian network.

That translates into basically, oh, that's not what is coming.

That translates into the tractability of networks that are starting to get interesting.

The network for the burglary, that's kind of chosen because it fits on one slide.

And it's complex enough that you see anything at all.

Real networks start at kind of 50 nodes where you're really gaining something.

And that's about the size where humans tend to develop problems.

And that's where, of course, machines also develop problems unless you do something clever.

Okay. But first we looked at a different problem, namely where do we get the CPTs from, the conditional probability tables.

What I wanted to show you is that with a couple of assumptions, you can get CPTs almost for free.

For instance, in deterministic situations, here in this network, we have a

Definitional dependence of those events to the others.

This is not something that is actually somewhere given outside in the world.

But we understand the mechanism very, very well.

And there are many things where we understand the mechanisms extremely well.

Because we've made them. We've defined what a European is to be, in this case, rather small set.

We define what the students are.

And how they're determined and how we compute them.

So here we have a bullion dependency and here we have a numeric dependency.

But it's still deterministic.

And we looked at the case where instead of having fully deterministic dependencies, we kind of had not fully general dependencies either.

So that is something, this example here, was that we had something which we call a noisy disjunction,

Which is essentially a numeric dependence, but there are these dampening factors.

Am I still on mute?

Oh, yes. Good. Sorry.

Okay. So here basically we have a quasi deterministic dependency where we have these dampening factors, inhibition factors.

Let's just say, well, and probabilistically in.6 cases of having a flu, you get a fever.

Not deterministic because you don't know whether you actually will develop a fever.

But the important thing is that you have these inhibition factors that are independent for every one.

So you kind of get a quasi linear behavior here, which is better than exponential, easy to model.

And then there's, you can imagine that I'm only showing you the very simplest of these tricks.

There's a whole book of tricks where we have these kind of distribution patterns that are determined by various parameters.

And the idea is always the same.

You have a pattern. It's determined by a couple of parameters.

So you can compute the whole distribution of the pattern by just a couple of values.

And that's more compact. And that's good.

That's good because it's easier to compute with and it's easier to assess.

In this case, to assess the full CPT here, you would in particular have to find patients who have a cold and a flu and a malaria at the same time.

Malaria comes on somewhere in the warm countries and flu comes on in, well, a cold comes on in the colder countries.

So it's very difficult to get these numbers.

But if you only need the inhibition factors, those are much easier to come by.

And then, of course, you get, and that's the kind of simple thing here, you only have to know three values to get two to the three numbers.

And of course, it's much more convincing if instead of three, we can do 100 or something like this, which is kind of a very normal thing.

And if you do these tricks and so on, you can build within the lifetime of one project or something like that,

networks that have kind of these characteristics, right, 500 nodes, a thousand links.

You can write that down, talking to the doctors, reading literature for two or three years, and then you have a network like that.

And then you can actually use that in production and do diagnosis with that.