I just drew in magenta. The curve that I just drew purple and magenta.

Armed with these definitions, we are now ready to build the support vector machine.

Which of these would be a good algorithm or technique for doing this classification into things like people, places, and drugs.

And that's called the support vector machine, and compared to both the logistic regression and neural networks, the

And the term logistic function, that's what give rise to the name logistic progression.

So here's a quick quiz for you.

The cost function we use for the neural network is going to be a generalization of the one that we use for logistic regression.

For logistic regression, we used to minimize the cost function j of theta that was minus 1 over m of this cost function and then plus this extra regularization term here, where this was a sum from j equals 1 through n, because we did not regularize the bias term theta zero.

In the next video we'll start working out the details of the logistic regression algorithm.

Except that we don't sum over the terms corresponding to these bias values

And it will compute the test error as follows.

How about if we were doing a classification problem and say using logistic regression instead.

And so this builds in an extra safety factor or safety margin factor into the support vector machine.

My cost function, j of theta is now going to be the following is minus one over m of a sum of a similar term to what we have in logistic regression.

Let F of XP, or linear function, and the output of logistic regression is obtained by the following function

That's the term that a single training example contributes to the overall objective function for logistic regression.

less than 0 because that corresponds to hypothesis of outputting a value close to 0.

E to the negative Z. This called the sigmoid function or the logistic function.

logistic regression and we're seeing what the mathematical formula is defining the hypothesis for logistic regression.

First, we're going to get rid of the 1 over m terms and this just, this just happens to be a slightly different convention that people use for support vector machines compared to for logistic regression.

We'll come back to that again in multiple regression, and in lecture nine in R. And then, the importance of this distinction between unstandardi zed and standardized regression coefficients.

Another thing I did here is I standardized everything, just to make this a little easier on us.

Now it's about eighteen.

We already have linear regression and we have logistic regression, so why do we need, you know, neural networks?

After decades of civil war, order was restored.

We have x of 1, 2, and 3 and y of 4, 7, and 13.

And the reason we did that is so that we could see exactly how the regression coefficients are estimated in a multiple regression.

Now let's look at the simple regression with active years in the equation.

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

And that's true of any sample statistic.

Consider a supervised learning classification problem where you have a training set like this.

It doesn't matter that much but that's the new cost function we're going to use where y is equal to 1 and you can imagine you should do something pretty similar to logistic regression but it turns out that this will give the support vector machine computational advantage that will give us later on an easier optimization problem, that will be easier for stock trades and so on.

And then, we can have multiple predictors and multiple regression coefficients.

And I want to tell you something called the decision boundary and we'll look at some visualizations together to try to get a better sense of what this hypothesis function of

Either way it's up to you.

That's ordinary least squares, is the approach we'll take at first.

It gets even easier if we want to look at the standardized regression coefficient.

This is when I put active years in the regression equation by itself and I use the scale function and R to get the standardized regression coefficient.

Machine and where you minimize that function then what you have is the parameters

But that's just the name it was given for historical reasons so don't be confused by that.

What are these numbers, what does this mean?

But again, now that we're in multiple regression, this is not the same as the correlation coefficient.

But for the sake of time, I didn't wanna go through that here.

Than looking at either one alone. And, the other thing that this segment.

Again, the regression constant now is zero because we've standardized.