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

When we fit the parameters of our learning algorithm we think about choosing the parameters to minimize the training error.

It goes from two forty down to two hundred.

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

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

Consisting of accidental and systematic errors.

However, in practice you're often just given the training data error.

The idea is to use gradient descent.

And to make some of our, make the math a little bit easier, I'm going to actually look at, you know, 1 over M times that.

Variance

Error diffusion

It's already zero for the original setting.

Monochrome error diffusion

Having done that, finally, what

Really, that's a sum of square distances, right? Of all of these errors.

Here's one thing you could do you could take your first model and minimize the training error and this would give you some parameter vector theta, and you can then take your second model, the quadratic function and for that your training set and this will give you some other parameters vector theta.

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

This is an interesting one where we seem to have a linear relationship that is flatter than the linear regression indicates, but there is one outlier.

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.

Then you can run our command run( ) with our parameters, and whatever it outputs is our best error so far.

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.

So again, the values of the coefficients are estimated such that the model comes up with optimal predictions.

Here we start implementing the delta debugging function.

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

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.

One over here, and one over here.

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.

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.

Then you've got a really big range.

What we're going to do is apply gradient descent to minimize our squared error cost function.

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.

Here's what I mean.

I've discovered the test has a margin of error.

There's your margin of error.