You will learn exciting terms like maximum likelihood estimator and laplacian estimator.

Now, let's move to the Laplace estimator.

Then, the maximum likelihood estimator is very simple.

Or do we find a maximum likelihood estimator.

This gives us 3 7 for the maximum likelihood estimator.

That is frustrating. Somehow the maximum likelihood estimator seems reckless.

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

Thrun One of the oddities of the maximum likelihood estimator is overfitting.

Then, I want you to fit a Gaussian using the maximum likelihood estimator.

So let's not assume we have Laplacian smoothing and instead use the maximum likelihood estimator.

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

Let's now dive in and understand how to use this cryptic name maximum likelihood estimator.

We talked about the Laplace estimator, which added k fake data points, 1 for each possible outcome, and that resulted in the slightly more complex out, as shown in this formula over here. and we identified cases where the Laplace estimator is much better than the maximum likelihood estimator, specifically when there isn't much data.

Thrun I would now like to ask the exact same question for the maximum likelihood estimator.

Compute for me mu and sigma squared using the maximum likelihood estimator I just gave you.

Compute for me the mean and the variance using the maximum likelihood estimator I just gave you.

I'll ask you know for the two different estimators what is the maximum like estimator and what is the laplacian estimator for our estimate of the probability of the outcome 1 for this die, based on that data.

And as previously, we're going to prove the correctness of the maximum likelihood estimator or MLE but this time for Gaussians.

Check the box that is the most likely µ you might observed, if p is a true probability using our statistical estimator.

From a single coin flip, the maximum likelihood estimator will always assume that all future coin flips come from the same way.

Now does this mean from a single coin flip, the maximum likelihood estimator will always assume a loaded or biased, yes or no?

This is the full proof that the empirical observed variance over the data is the maximum likelihood estimator for finding the parameters of a Gaussian.

The count that we have is 1 out of 1 is rain and 1 out of 1 would give us 1 under the maximum likelihood estimator.

So, in summary, we talked about the maximum likelihood estimator, and we even derived it mathematically for those of you who had the patience to stay on.

I better derive for you the desired equation on here which is the maximum likelihood estimator all the way from the definition of the probability of the data.

From there, we can transform the expression to this expression over here where I left out a term and it finally gives you the desired proof for the maximum likelihood estimator for the mean.

By now, you might have recognized what we're really building up is a Bayes network where the parameters of the Bayes networks are estimated using supervised learning by a maximum likelihood estimator based on training data.

You might remember you add something to the numerator, like 1, and something to the denominator to make sure things normalize, and then you get different probabilities than you would get with the maximum likelihood estimator.