Right, that's sampling error. And how much sampling error we expect on average is standard error.

Now, if we do a small number of samples, the counts might not be very accurate.

So one fundamental lesson to take away from that simple example is look at your residuals.

Consisting of accidental and systematic errors.

There is only the training data.

So, I'm gonna introduce a new formula and a new concept here, and one that will be, essential as we move forward in inferential statistics.

Variance

Error diffusion

Monochrome error diffusion

Having done that, finally, what

Not surprisingly the best complexity is obtained where the generalization error is minimum.

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.

Give or take a few years

And the way we estimate that is to rely on the principles, of the central limit theorem, and calculate standard error, by looking at the standard deviation, in our sample, and the size, of our sample.

So we've now computed the era term's delta 4 for our network.

label yi from this specific example we're looking at to compute the error term for delta L for the output there.

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.

If your hypothesis basically classified the example y correctly.

Have you allowed for any error in your calculation?

If the prediction of our function f equals our target label, and the error is zero, then no update occurs.

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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.

Values given over accidental errors.

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You're taking a poll?

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

And of course, this is the definition of the test set error if we are using linear regression and using the squared error metric.

J C V and J

The answer is this.

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.

Statistics textbooks, whether they're in Psychology, or Economics, or Sociology, or

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