Okay, so quiz is over.

distribution. So just for situating where we are in the course, we're doing

machine learning, learning agents, motivated by probabilistic agents, agents

that have a Bayesian network as a world representation. Of course, a learning

agent should be able to learn certain parts of that network, right? It might

just be that the agent designer got it wrong or that parts of the world are

changing, that the probabilities of certain connection in the Bayesian

network are changing. We have things that change fast. We have things that change

slowly. Think about the weather changing, changes between days,

but also kind of the underlying mechanisms are changing with all of that

we're putting into the atmosphere. So we know to learn, agents need to learn

about this and that's exactly the problem we're trying to tackle. And so

the topic in a way is parameter learning, parameters of the Bayesian

networks. There are techniques for learning about kind of different

network topologies that could also be something that could be changing, that

certain, that you're learning that certain causalities exist that you didn't

think about, but that's not what we're doing right now. We're learning the

parameters and the idea here is that we kind of drill in on this candy bags

example we were looking at. And rather than knowing that we have five different

bags, that was what we looked at last week, we now look at a new bag which

instead of being one of five hypotheses, we have a parameter. And basically the

main difference here is that from having a finite hypothesis space to deal with,

we have a continuous one. Much bigger hypothesis space, learning becomes

difficult and if you think about it in this extremely, extremely simple setting,

we have a single parameter in a very, very small Bayesian network. We have a

single flavor variable and it has a single parametric, a single parametric

probability table here. And so the new facet is this parameter and so we

basically do what we've done before. We unwrap and in candies, we get C cherries

and L which is N minus C lines and we assume IID observations so we can just

basically compute the likelihood. Remember the likelihood was what's the

probability of seeing the data given some hypothesis only that it's no longer

H1 to H5 but H theta. Okay and we can compute this very simply because we have

IID so all the continue, all the, we can basically get rid of all of the

dependencies here because they're independent. Okay so what we're doing is

we're optimizing the log likelihood by and we transform this by using a

logarithm and then we looked at the details and since we have this very

simple parameter which is a probability what we're getting out is what we've

been expecting anyway. Namely that we have the probability of C over N, right?

Just the average we've seen so far. That's the parameter that's going to

come out which is fine which basically tells us ha there's a likely good

likelihood that the computations we did are the right thing. So this is kind of

the warm-up exercise for the whole thing. Right so we basically write down an

expression for the likelihood of the data as a function of the parameters. We

write down the derivative of the log likelihood with respect to every

parameter of which we have one and then we find the parameter values where

derivatives are zero. In a way that's we you've probably been doing for to

graduate from high school right? Nothing really new here. So let's try

something more interesting. The next thing that's better than a Bayesian

network with one variable is a Bayesian network with two variables right? We

make it a little bit more complicated. We have the flavor variable with a prior