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

Z, also called the logistic function, looks like this.

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

When we plot the logistic function it looks like this

So, for logistic regression, we had two terms to our objective function.

logistic regression.

logistic regression.

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

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

logistic regression with a

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

Let's start talking about logistic regression.

light of logistic regression, the Support

like we had for logistic progression.

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

K equals one through four of basically the logistic regression algorithms cost function but summing that cost function over each of my four output units in turn.

If you look at the cost function of logistic regression, what you find is that each example x, y, contributes a term like this to the overall cost function.

So, in logistic regression we have our familiar form of the hypotheses there and the sigmoid activation function shown on the right.

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

So, it's a pretty close approximation to the cost function used by logistic regression except that it is now made out of two line segments.

This first hidden unit here, has its value computed as follows is a a(2)1 is equal to the sigmoid function, or the sigmoid activation function also called the logistic activation function, applied to this sort of linear combination of its inputs.

It's the same objective function as we always use but we just logistic regression, except that now is define using our m subscript test, test examples.

We're going to model a neuron as just a logistic unit.

Now let's think about what we will like the logistic regression to do.

Could we use Naive Bayes, k Nearest Neighbors, Support Vector Machines, Logistic Regression.

Finally, one last bit of terminology when we talk about neural networks, sometimes we'll say that this is a neuron an artificial neuron with a sigmoid or a logistic activation function.

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.

Function

function

Function

Function

Function

Form is function. Form is function.

logistic regression, I'm going to modify this a little bit, and make the hypothesis

Logistic Regression is actually a classification algorithm that we apply to settings where the

logistic regression sees a positive example with y equals 1 it tries to set theta transpose x to be very large because that corresponds to this term in a cost function being small.

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

A plus B. So for logistic regression if we send a very large value of

So, simple logistic regression together with adding in maybe the quadratic or the cubic features

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

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