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.

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

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

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

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.

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

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

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.

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

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

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

And if you have a high variance problem, your training set error will usually be low, that is much lower than the cross validation error.

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.

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

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.

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.

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.

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And I would then pick whichever one of these 12 models gives me the lowest error on the cross validation set.

I'm going to abbreviate cross validation

So, if your algorithm is suffering from a bias problem, the training set error would be high and you may find that the cross validation error will also be high.

And so, this is the bias regime whereas and cross validation error will be high and let me just leave all that.

Concretely, for the high bias case, that is, the case of under fitting, what we find is that both the cross validation error and the training error are going to be high.

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.

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XiCV, YiCV to denote the i cross validation example.

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And so, once again, it will often be some intermediate value of lambda that you know, subsequent just right or that works best in terms of having a small cross validation error or a small test set error.

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