I can't believe you gave up your mop for this suit.

How fitting.

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This offer is open for five days.

This offer is available for five days.

This offer is good for five days.

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

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The algorithm is amazingly simple.

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

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

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

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The New Guys is offering him the cover.

I don't think he understood that I wasn't asking for funding.

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.

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.

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

You learned about what a Gaussian is.

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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.

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.

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.

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I had a job waiting for me in San Francisco when he got an offer from ConAgra.

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.

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

And the reason is, what we've done is, we've fit this extra the parameter d, that is this degree of polynomial, and we'll fit that parameter d using the test set.

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I'll give you a couple of more examples on irrational decision making.

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

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

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As we increase the degree of the polynomial, we're going to fit our training set better and better and so, if d equals 1 that ever rose to the high training error.

And in this video, we also stepped through an entire process of giving data set, we have, fitting the parameters, doing parameter estimations.

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.

In this video, we're going to put together gradient descent with our cost function, and that will give us an algorithm for

low order polynomial such as a plus one, when we really needed a higher order polynomial to fit the data.

And by having fit the parameter to the test set, this means that the performance of the hypothesis on that test set may not be a fair estimate of how well the hypothesis is likely to do on examples we haven't seen before.

longer fair to evaluate my hypothesis on this test set.

Given the following data, my first question is, can this data be fit exactly using a linear function that maps from X to Y?

And that's indeed what's seen through a number of other pieces of evidence.

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.