Algorithm: Gaussian Naive Bayes

Recall from my Naive Bayes post that there are several variants.  One of the variants that I'll be talking about today is Gaussian Naive Bayes.

Probability Distributions and Random Variables

Suppose I had two coins and I flipped both of them.  The possible combinations can be two heads, two tails, or one of each.  These combinations are all part of a sample space.

Now let's take this a step further.  Taking the above demonstration, we want to determine the probability that each combination would occur.

Assuming independence, we derive the following probabilities:

All of these probabilities belong in a probability distribution.

Deriving the Cost Function for Logistic Regression

In my previous post, you saw the derivative of the cost function for logistic regression as:

I bet several of you were thinking, "How on Earth could you derive a cost function like this:

Into a nice function like this:

?"

Well, this post is going to go through the math.  Even if you already know it, it's a good algebra and calculus problem. Read more