In this particular example, it

Clearly a linear regression model is a very poor one to explain this data over here.

Let's look at some examples.

So, this term here.

So why do we need yet another learning algorithm?

You know, you can end up here or here.

In the original version of

Because I squared, I multiplied the second derivative of y with respect I multiplied it times itself.

Y is either zero or one, but if you are using

And I'll quickly review the linear algebra you need in order to implement and use the more powerful versions of linear regression.

Tropic of Cancer

Tropic of Capricorn

And taking gradient descent, and the square cost function, and putting them together. That will give us our first

If you want to apply logistic regression to this problem, one thing you could do is apply

If pixels are negative, we just ignore the negative sign and map back to the absolute value.

There is really no residual error over here.

And, just to give this another name, this is also called multivariate linear regression.

For such situations there is a model called logistic regression, which uses a slightly more complicated model than linear regression, which goes as follows .

No? Nonlinear equations?

How about our Gaussian kernel that we discussed in class of size 5 by 5?

First is our gradient kernel here minus 1, 1.

linear regression.

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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 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.

In this video, let's talk about how to fit the parameters of that hypothesis.

Thrun It's interesting to see how to minimize a loss function using gradient descent.

These are the x values, these are y values.

Now we plug in W1 0.9 4 x 20 equals 0.5.

So here's a quick quiz for you.

Now the second thing we have to figure out is this linear or is this a non linear differential equation?

First what I'd like to show you is just, what do I mean by linear and nonlinear.

But if you implement the algorithm written up here then you have a working implementation of linear regression with multiple features.

Once again, we're looking for function f that maps our vector x into y.

And hopefully it will recognize that that is a car.

The line of 25.2 0.67x y.

That minimizes J of theta one.

In the first instance, in the first example before I added this extra training example, previously linear regression was just getting lucky and it got us a hypothesis that, you know, worked well for that particular example, but usually apply

Let's for now just consider the one dimensional case.

So in this video, I'm going to talk about gradient descent for minimizing some arbitrary function J. And then in

Because if you are minimizing quadratic error, outliers penalize you over proportionately.

They move they go up, they go down.

You have your order, so what is the order of my differential equation?

So, using a vectorized implementation, you should be able to get a much more efficient implementation of linear regression.

Now, there are many different ways to apply linear functions in machine learning.