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

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

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

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.

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

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

The sigmoid function, G of

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.

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.

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

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

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.

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

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

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.

And, by the way, the terms sigmoid function and logistic function are basically synonyms and mean the same thing.

The second bit of notational change, we're just designating the most standard convention, when using as the SVM, instead of logistic regression as a following.

And finally, the second term here is the regularization term similar to what we had for logistic regression.

E to the infinity becomes very large one over something very large becomes zero.

And in order to explain some of the math, I'm going to use z to denote failure of transpose x here.

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 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

Where instead of having basically just one logistic regression output unit, we may instead have K of them.

For example, if you wish to predict the weather anytime into the future, it's implausible to assume the further the prediction goes out, the hotter or the cooler it becomes.