The next thing really works with this second example with the Brazilian, where in learning

you really want to bias yourself to certain, in a way, learnable predicates, which you

want to prefer, A, because they generalize better, and B, because it restricts your hypothesis

space and actually lets you learn with far fewer examples.

That's what we're doing now.

And of course that can be combined with other learning techniques, as we'll see in the end,

or as we did see yesterday in the end by combining these relevance judgments with decision tree

learning.

And the idea here is that we often have pairs of predicates that determine each other and

as such give a very strong relevance statement.

In essence here we have that the nationality fully determines the language, and you can

write that down in logic, which makes for a relatively complicated formula.

What you're really interested in is if we have this determination, nationality over

language, then we only need to and should learn and only need to concentrate on nationality.

So in a way, if I have that determination, then I have a functional dependency on the

two, and I don't have any new information in language.

So we shouldn't actually learn that.

Now the question of course is how do we find out about determinations?

And the answer of course is we're going to learn them.

If we have them, they actually give us great speed ups in learning because they cut down

on the hypothesis tree.

The question is how do you learn them?

And the answer is by looking at the data.

If I have a bunch of data, then what we're interested in is actually the minimal, by

some version of minimal determinations, and this here has actually one, which is the material

and the temperature together determine the conductance.

What's happening here is we're actually using predicates, and the and here, which is the

customary thing to write, you should really read as an intersection.

And is something that acts on true and false like things.

And material and temperature aren't true and false like things.

They are actually predicates or functions or whatever.

So we have to have, so we're using, I just wanted to make you aware that we're using

a slightly interesting operator here.

And it's essentially intersection.

You can figure out exactly what this is.

And once you realize this, a relatively simple generate and test algorithm works.

You look at, and that's what we have here.

We have material and temperature.

We can cut any subset of predicates into a new compound predicate.

And so we essentially have to learn or take into account or under consideration actually

any combination of the other predicates, and that gives us an exponential algorithm.

But it's very simple.

You start with single, you start with single predicate determinations.

Then you go for two subset determinations, and you work your way up all the way.

So you look at those, and then you just basically see whether any determination is, proposed

determination is consistent with the data you have.

And for that, you essentially check things that look like the nationality things.

If two things have the same value in the antecedent, and you have a third one here, you can check

whether the values are equal as well.

And you can implement that with, as I've done it here, with a very simple hash table where