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.

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Again, validation.

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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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.

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.

Test are just the average squared error, or one half of the average squared error on my training validation and test sets without the extra regularization chart.

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I'm going to abbreviate cross validation

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.

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

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

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XiCV, YiCV to denote the i cross validation example.

learning algorithm and it is not performing as well as your are hoping, so your cross validation set error or your test set error is high.

Now that we're armed with the notion of training and validation in test sets, we can understand the concepts of bias and variance a little bit better.

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.

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

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The first is test, re test.

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.

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.

And in our discussion of how to do this we'll talk about not just how to split your data into a train and test sets but how to split your data into what we'll discover is called the train validation and test sets.

And, finally, test and test it again.

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

I wish to split these things would be to send 60 of your data to your training set, maybe 20 to your cross validation set, and 20 to your test set.

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