How fitting.

And on this slide, I'm basically explaining all the problems you have.

We talked about the fit from data and we even talked about multivariate Gaussians.

I'm going to be fitting very complex high order polynomials that might fit the training set with much more complex functions

The algorithm is amazingly simple.

Suppose we're fitting a high order polynomial like that shown here, but to prevent overfitting, we're going to use regularization, like that shown here, so we have this regularization term to try to keep the values of the parameters small.

For this quiz we will assume a degenerative case of 3 data points and just 1 cluster center.

Suppose we fit a linear regression model with a very high order polynomial, but to prevent overfitting, we are going to use regularization as shown here.

In that case, given that we're fitting a high order polynomial, this is a usual overfitting setting.

As for the discussion of most of the learning algorithms, we're going to begin by talking about the cost function for fitting the parameters of the network.

You learned about what a Gaussian is.

So, that's Jcv of theta because with high bias we won't be fitting.

And once again here is as if we fit this parameter theta to my cross validation set, which is why I am saving aside a separate test set that I am going to use to get a better estimate of how well my a parameter vector theta will generalize to previously unseen examples.

So, we'll do that for this figure, where maybe d equals 1, were going to be fitting very simple functions where as we are the right of this this may be d equals 4 or relatively may be even larger numbers.

And so this degree of polynomial, so the parameter is no longer fit to the test set.

So I can look at my first model, my second model, fits with these different values of the regularization parameter and evaluate them on my cross validation set basically measure the average squared error of each of these parameter vectors theta on my cross validation set.

And the reason is, what we've done is, we've fit this extra the parameter d, that is this degree of polynomial, and we'll fit that parameter d using the test set.

And by having fit the parameter to the test set, this means that the performance of the hypothesis on that test set may not be a fair estimate of how well the hypothesis is likely to do on examples we haven't seen before.

As we increase the degree of the polynomial, we're going to fit our training set better and better and so, if d equals 1 that ever rose to the high training error.

So here are examples of two models with, different amounts of Baryonic matter.

And the more general principal is that, once your parameters were fit to some set of data maybe the training set, maybe something else then the error of your hypothesis as measured on that same data set, such as the training error, that's unlikely to be a good estimate of your actual generalization error, that is, of how well the hypothesis will generalize to new examples.

And in this video, we also stepped through an entire process of giving data set, we have, fitting the parameters, doing parameter estimations.

In this video, we're going to put together gradient descent with our cost function, and that will give us an algorithm for

And the key that distinguishes these two cases is if you have a high bias problem your training set error will also be high as your hypothesis just not fitting the training set well.

longer fair to evaluate my hypothesis on this test set.

left corresponds to a high bias problem, that is, if you are fitting an overly

Later. I will later. East.

And that's indeed what's seen through a number of other pieces of evidence.

low order polynomial such as a plus one, when we really needed a higher order polynomial to fit the data.

Given the following data, my first question is, can this data be fit exactly using a linear function that maps from X to Y?

What we've done is we fit that parameter d, and we'll set d equals 4, and we did so using the cross validation set.

All of them, all of them!

west central Borneo

Hiking club's office.

Often that matter, if we look at the test set error we'll get a pretty similar result as if we were to plot the cross validation error.

All of it! I said all of it!

I want to tell you everything. Everything.

We get this function over here that specifies any probability for a value X given a specific mu and sigma squared.

Mountain Time south Idaho east Oregon

Part of an internal mole hunt.

Mountain Time Alberta, east British Columbia west Saskatchewan

The four places where you saw, that we've never stopped northern Nigeria, northern India, the southern corner of Afghanistan and bordering areas of Pakistan they're going to be the toughest.

I got nothing to fear from you anyway. Lieutenant Gerard to headquarters.

I'm sorry, Ada. Lieutenant Gerard to headquarters.

sir.