We study again our die. You observe the following sequence 1, 2, 3, 2.

I will now teach you about estimators.

The initial probability for rain is 0 because we are just encountering 1 initial day and it's sunny.

However I'd like to do this with Laplacian smoothing with k 1.

There's many different ways to implement this.

There is 5 data points.

Here is our sequence. There's a couple of sunny days 5 in total a rainy day, 3 sunny days, 2 rainy days.

Please use Laplacian smoothing for this with K equals 1.

One technique to deal with the overfitting problem is called Laplace smoothing.

So, here's another quiz.

Narrator And the answer is there's 8 different messages of which 3 are spam.

In 3 cases, A is followed by A over here, over here, and over here.

And very certainly, the answer is yes.

What this says is based on the outcome, we believe for the parameter µ.

In both of the transitions we go from rain to sun. There is no instance of rain to rain.

The last R over here has no outbound transition, so it doesn't really count in our statistic.

And in the second box, give me an estimator that has one fake data point.

Let's look at these numbers again.

So 55 say A and 45 say B.

For example, for the prior probability, we found that 3 8 messages are spam.

Let me ask you again. Suppose you make 111 coin flips.

let me explain it to you.

If we look at the numbers over here, we get 0.5833 and 0.5986.

You might remember all this work with Laplace smoothing, but for now we keep it simple, just maximum likelihood.

The sum over all E of the mu is mu equals sum over i, xi.

Let's assume we fit all the 23 parameters of the Bayes network as explained using maximum likelihood.

The word perfect occurs in movie, but the word storm has never been seen before.

Linear regression? Do we compute confidence intervals?

We took the product of the individual exponentials and moved it up straight in here where it becomes a sum.

For is, to be 1 9, but for today, it's 0.

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Supposed suicide.

Now, if k equals 0, we get our maximum likelihood estimator.

Now I want take a second to convince ourselves this is indeed the maximum likelihood estimate of the mean and the variance.

I just want to tell you what you've learned, because you did amazingly well.

I was a little bit fast, but this is relatively straight forward mathematics.

In particular, what if I use an unbiased coin like this one?

W 0, where 0 is your iteration number, and then you up with it iteratively.

Stop estimating backup size

Simple extrapolation.

This is equivalent to assuming we have a couple of fake training examples where we add k to each observation count.

We find that along the main diagonal our uncertainty has shrunk substantially.

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