Now let's consider the model selection problem.

Some crazy guy is giving a commencement speech.

It seems like a reasonable fit to the data, because, you know, it

Cats fit on the windowsill

Children fit in the snow

I don't fit in anywhere I go ?

like vacuum tube technologies, and relay based technologies.

A city fit for a king

Here is what we see coming.

So this seems reasonable so far.

It did not let up.

So the we have the neutron.

Either way they were going to eat it.

1 WATCH Here is a friar, and slaughter'd Romeo's man,

lambda is large, then you have a high bias problem and you might not fit your training set so well.

We keep the inner slope, but change the outer slope.

We must try to get rid of it, the sister now said decisively to the father, for the mother, in her coughing fit, was not listening to anything.

And the hose on that van is just about a perfect match...

So Jawbone is a project that you're familiar with, and it has a humanistic technology.

And fit in all the right places with lots and lots of star sapphires.

So, if you take this training set and fill a straight

In later videos, we will build on this to talk about how to prevent in the problems of overfitting and underfitting as well.

So, you can fit things like, you know, access a

But somehow adding that example out there caused linear regression to change in straight line fit to the data from this magenta line out here to this blue line over here, and caused it to give us a worse hypothesis.

Suppose you like to decide what degree of polynomial to fit to a data set, sort of what features to include to give you a learning algorithm.

Concretely, if you fit some set of parameters theta 0, theta 1, theta 2 and so on to your training set then, the fact that your hypothesis does well in the training set, well, this doesn't mean much in terms of predicting how well your hypothesis will generalize to new examples not seen in the training set.

So, for example, we could test the full model, We could test the fit of that relative to a model that takes out the direct effect.

Now, so this is how we fit the parameters to this data.

X1 through X M, we then fit the parameters, mu 1 through mu n, and sigma squared 1 through sigma squared n, and so these were the formulas similar to the formulas we have in the previous video, that we're going to use the estimate each of these parameters, and just to give some interpretation, mu J, that's my average value of the j feature.

We've already seen a lot of times the problem of overfitting, in which just because the

If we have a very high degree of polynomial, our training error is going to be really low.

This hypothesis, h(x), with these values of theta zero, theta one, it's really not such a good fit to the data.

He trusts to you to set them free, Exactly as we were.

And the Vaucouleurs profile looks like a straight line in those coordinates.

But settling isn't always such a bad thing.

Nonetheless, if you obtain a surface brightness profile of the many, many ellipticals and then if you fit Sersic law to all of them and plot the value of the

One of the things we'll talk about later is how to choose and how to decide do you want to fit a straight line to the data or do you want to fit the quadratic function to the data and there's no fair picking whichever one gives your friend the better house to sell.

You are encouraged to experiment with the different styles until you find one which best suits your pattern of work.

So there, the model would have been all three equations.

We could trade off the relative way between how much we want to fit the training set well, as minimizing A, versus how much we care about keeping the values of the parameters small.

An ill beseeming semblance for a feast.

Here we see Hubble diagrams with the main trend line subtracted a particular model subtracted and then residuals fit for variety fodder models.

Therefore, when we see that, we see an opportunity to have a business that addresses the need of that segment.

The image will be scaled to fit the desktop. It will be stretched to fit all four corners.

line of the ellipses like these, but you certainly cannot fit a more complex data set like that shown here.