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

I'm going to abbreviate cross validation

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

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

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.

XiCV, YiCV to denote the i cross validation example.

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.

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

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

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

Validation

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

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 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.

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Again, validation.

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

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.

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.

So the setting of a cross validation error being high corresponds to either this regime or this regime.

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Next I can take all of these hypotheses, all of these parameters, and use my cross validation set to evaluate them.

And I would then pick whichever one of these 12 models gives me the lowest error on the cross validation 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 so, this is the bias regime whereas and cross validation error will be high and let me just leave all that.

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Cross now. Cross now.

Just select the training error, except measure it on the cross validation data set, and here's my test set error, same as before.

I'm going to measure j subscript cv, to see how well each of these hypothesis do on my cross validation set and then

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.

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.

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.

Cross

Cross

Cross