Very human. So again your not forced to use it and

sometimes there is a good reasons not to do it but.

It's generally a good tip to follow. So how does one actually construct a

graphical model? Do we have in our minds some monolithic P

of some set of variables, X1 up to XN and we just need to figure out how to encode

that using a graph? Well maybe implicitly, but certainly not

in any explicit form. The way in which one typically constructs

a graphical model in practice is by having some variable or sometimes set of

variables that we wish to reason about. So, for example, we might care about the

variable cancer or maybe even lung cancer.

Well, what influences, whether we have cancer.

whether somebody is going to get lung cancer.

Well if we go an ask a doctor. What is the probability for someone to

get lung cancer? The doctor is going to say, well.

You know, that depends. And you might say, what does it depend

on? An the doctor will say, well.

Whether they smoke for example. At which point.

You're likely to add the variable smoking as a parent to the lung cancer variable.

The doctor might say well but that's not the only thing, it might the probability

of cancer also depends for example on the kind of work that you do because some

kinds of work involve more dust particles getting into your lungs and so again

here's another variable which you would add as a parent.

And I even go and ask either there a doctor or an expert in a different domain

what is the probability that somebody smokes?

And if they think about it they're likely to say that depends, and what does it

depend on? Well maybe their age, gender,

maybe their, the country that they live in because certain different countries

have different smoking frequencies. And so once again, we're going to extend the

conversation backward to include more variables up to the point that we can

stop, because if you now ask for example, what is the probability of gender being

male versus female, well anybody can answer that one.

And at that point one can stop because there's no way to extend the conversation

backward. Is that enough?

Usually not because we also need to consider for example, factors that might

help us might indicate to us whether somebody's going to have can, somebody

has cancer or not. And so we might go and ask the doctor

what are some pieces of evidence that might be indicative here, and we would,

the doctor would tell us for example, coughing or maybe bloody sputum and

various other things that would be potential indicators.

And at that point, one would say, well, okay.

What is the probability of coughing given lung cancer?

And again, one would now extend the conversation backward to say.

Well, other things may cause coughing. For example, having allergies.

And so once again we would, go from here and extend backward, to construct a

graphical model that captured, all the relavent factors for answering queries

that we hear about. So, that's the structure of a graphical

model now let's talk a little bit about parameters, the values of these

parameters and what make a difference here, so here are certain things that

really do make a difference, to parameters, zeros.

Make big difference. And when we talked about diagnosis we saw

that many of the mistakes that were made in early medical expert systems were

derived from the fact that people gave zeros to things that was unlikely.

But not actually impossible. And so zeros are something to be very,

very careful about. Because you should only use something,

you should only give probability zero to something that is, impossible perhaps

because it's definitional. Otherwise, things really shouldn't have

probability zero. Other things that make a difference are a

sort of weaker versions. So for example, orders of, order of

magnitude differences, the difference between a probability of one over ten

versus one over 100 that makes a difference.

It makes a much bigger, whereas small differences like 0.54 versus 0.57 are

unlikely to make a difference to most queries.

Finally it's turned out that relative values between conditional probabilities

make a much bigger difference to the answer than the absolute probabilities.

That is, the, comparing different entries in the same CPD, relative to each other,

is a very useful way of of evaluating the graphical model and seeing whether the

value. Use that you use for those relative

ratios really make sense. Finally,

Conditional probability tables are actually quite rare acceptance small

applications. In most cases one would use structured

CPDs of the forms that we've discussed as well as the variety of other forms.

So let's talk a little bit about structured CPDs because those are

actually quite important. and we can break up of the.

The types of CPD's that we've talked about along two axes: one is whether

they're intended to deal primarily discreet or with continuous variables.

And on the other side is whether they type of structure that they encode is

context specific, where a variable might make a difference in some circumstances

and not in others, versus aggregating. Of multiple weak influences.

And so let's give off an example of each of these categories.

So for discrete and context specific, we had three cpd's as an example.

For discrete and aggregating we had sigmoid.

CPD's as well as noisy or, where noisy max or any one of those, that family.

For continuous CPD's we didn't actually talk about context specific,

representations, but one can take the, continues version of tree CPD called a

regression tree. Where one breaks up the context based on

some threshold on the continuous variables.