I am a student and I am studying machine learning. I am focusing on probabilistic generative models for classification and I am having some troubles understanding this topic.
In the slide of my professor it is written the following:
which I don't understand.
So far, I have understood that in the generative probailistic models, we ant to estimate $P(C_i|x)$, which is the probability of having class $i$ given a data $x$, using the likelihood and the Bayes theorem.
So, it starts by writing the Bayes rule, but the the slides says that we can write this as a sigmoid, but why?
If I have to try to give an answer to it, I would say because the sigmoid gives a number from $0$ to $1$, and so a probability, but it is just a guess I am doing.
Moreover, it continues by saying that we can use a gaussian distribution for $P(x|C_i)$, and so $P(x|C_i)=N(\mu ,\sigma )$, and so :
I don't understand what it is doing, can somebody please help me?
I don't know if my question is clear so sorry if it is not but I am really confused. If it is not lcear please tell me I will try to edit it. Thanks in advance.
Note: if it can be useful, this has been taken from the Bishop book at page 197