Consisting of accidental and systematic errors.

Variance

Error diffusion

Monochrome error diffusion

Having done that, finally, what

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.

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

If your hypothesis basically classified the example y correctly.

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

Values given over accidental errors.

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.

J C V and J

The answer is this.

Yeah. I would agree with that.

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

There's always a little fluctuation from sample to sample.

If you draw a curve like this, your quadratic error becomes 2.

If I go to my output for 100 steps, I find that the y value is between 0.7 and 0.9.

The unstandardized regression coefficient, B.

It was 22 miles.

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

Of course, we won't do that. We'll just do it in R.

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.

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

Here's what I mean.

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

Sometimes there is an alternative test sets metric that might be easier to interpret, and that's the misclassification error.

Expressed through standard deviation Values given over accidental errors.

This is where the concept of ordinary lease squar es regression comes in. And the idea is very simple.

As N gets really, really large.

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.

But again what's standard errors.

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

It's really common for a car to believe to be here but it has 2 meters all the way up to 10 meters of error.

There is only the training data.

I'm just about to teach you to find out exactly where the robot is.

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.

In contrast if your algorithm is suffering from high variance then, if you look here, we'll notice that, J train, that is the training error, is going to be low.

So here we have a mean of 5.93, instead of a mean of 5.5.

We can calculate it, for. A slope, of a regression line.

And T, we just saw, the formula is the regression coefficient over standard error.

Let's enter a 3.0 for the differential term, run everything, and the y error is still large.

Right, cause this is in the denominator. So if this gets really, really large, then standard error gets really, really low.