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cross validation, and I am going to abbreviate cross validation as CV.

Sometimes it's also called the validation set, instead of cross validation set.

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I'm going to abbreviate cross validation

So, now that we have defined the training validation or cross validation and test sets, we can also define the training error, cross validation error, and test error.

As for the cross validation error, we end up with a figure like this.

Next, let's look at the cross validation error.

XiCV, YiCV to denote the i cross validation example.

We won't be doing well on the cross validation set.

Let's take a look at the next step in searching for a business model, and that's customer validation.

Whereas in contrast your error on a cross validation set or your cross function like cross validation set, will be much bigger than your training set error.

I'm going to pick the hypothesis with the lowest cross validation error.

For some data sets you will really see these poor source of trends and by looking at the plot of the whole or cross validation error, you can either manually, automatically try to select a point that minimizes the cross validation error and select the value of lambda corresponding to low cross validation error.

And so our training set will now be only, maybe 60 of the data, and our cross validation set or our validation set will have some number of examples.

Information Breakpoint validation has caused one or more breakpoints to be re created.

The same form and the same validation. You've seen all this code before.

So for this example, let's say for the sake of argument that it was my fourth order polynomial that had the lowest cross validation error.

He thought, I know how to drive why do I need the state's validation?

And so, this is what the cross validation error and what the training error may look

This is the same form we used in unit 2, and it has the same validation.

CV, and the second piece of this data, I'm going to call the cross validation set

I'm going to denote that M subscript cv, so that's the number of cross validation examples.

And then j subscript cv is my cause validation error is pretty much what you'd expect.

Let's look at the training error and cause validation error and plot them on this figure.

And similarly, I'm then also going to define the cross validation set error when the test set error, as before to be the average sum of squared errors on the cross validation and the test sets.

I'll just warn you that just sometimes people do you know, use the same data for the purpose of the validation set and for the purpose of the test sets.

So when theta with the model selection problem like this is, instead of using the test set to select the model, we're instead going to use validation set or the cross validation set to select the model.

And finally, up to 50 to 70 of software development effort is spent on validation and debugging.

And finally, up to 50 to 70 of software development effort is spent on validation and debugging.

Whereas, your cross validation error, assuming that this say the squared error which we're trying to minimize.

So, that was model selection and how you can take your data and split it into a train validation and test set, and use your cross validation data to select model and evaluate it on the test set.

Concretely, let our training error and cross validation error be defined as in the previous videos, just say, the squared error, the average squared error as measured on the 20 sets or as measured on the cross validation set.