How fitting.

It's a big push.

I'm going to be fitting very complex high order polynomials that might fit the training set with much more complex functions

Let the floaters push you!

And on this slide, I'm basically explaining all the problems you have.

We talked about the fit from data and we even talked about multivariate Gaussians.

They are both dynamic, they move.

The algorithm is amazingly simple.

Suppose we're fitting a high order polynomial like that shown here, but to prevent overfitting, we're going to use regularization, like that shown here, so we have this regularization term to try to keep the values of the parameters small.

We shall see.

We're going to expand our company huge.

So the response to these two kinds of concerns has been two

And I thought that if I push...

We had to push at the last mile.

Also in this case had to think of the wind,

Suppose we fit a linear regression model with a very high order polynomial, but to prevent overfitting, we are going to use regularization as shown here.

As for the discussion of most of the learning algorithms, we're going to begin by talking about the cost function for fitting the parameters of the network.

For this quiz we will assume a degenerative case of 3 data points and just 1 cluster center.

How should I know where?

So, that's Jcv of theta because with high bias we won't be fitting.

Electron finds its position it comes close.

So, we'll do that for this figure, where maybe d equals 1, were going to be fitting very simple functions where as we are the right of this this may be d equals 4 or relatively may be even larger numbers.

To draw a chimney we could approach it in many ways, but we'll use this method

But to continue was difficult, particularly because he was so unusually wide.

For example, to draw from this corner SketchUp snaps to this point and shows you a green endpoint.

Now draw an edge connecting the two lines to complete a surface.

In that case, given that we're fitting a high order polynomial, this is a usual overfitting setting.

And so this degree of polynomial, so the parameter is no longer fit to the test set.

You learned about what a Gaussian is.

The tiny legs on one side hung twitching in the air above, and the ones on the other side were pushed painfully into the floor.

SketchUp shows a red dot indicating you are on the edge. Click to start and draw down to a lower edge, also showing a red dot.

Draw a rectangle and split it in half, then use push pull to create some steps.

We shall see.

May I have a cigarette? he asked.

And the more general principal is that, once your parameters were fit to some set of data maybe the training set, maybe something else then the error of your hypothesis as measured on that same data set, such as the training error, that's unlikely to be a good estimate of your actual generalization error, that is, of how well the hypothesis will generalize to new examples.

And once again here is as if we fit this parameter theta to my cross validation set, which is why I am saving aside a separate test set that I am going to use to get a better estimate of how well my a parameter vector theta will generalize to previously unseen examples.

It opens our minds to what is possible and even more uniquely it pushes us, and I do believe that MlT pushes us harder than probably any other institution in the world.

So here are examples of two models with, different amounts of Baryonic matter.

left corresponds to a high bias problem, that is, if you are fitting an overly

Gregor seemed to entertain them more than the violin recital.

And the key that distinguishes these two cases is if you have a high bias problem your training set error will also be high as your hypothesis just not fitting the training set well.

It was the knob of a door.

So I can look at my first model, my second model, fits with these different values of the regularization parameter and evaluate them on my cross validation set basically measure the average squared error of each of these parameter vectors theta on my cross validation set.

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Now draw another circle on a different surface to see how the orientation aligns to whatever you are drawing on.