Logistic Regression from SCRATCH
I have tried to get together a simple approach to write Logistic Regression from scratch.
Above image summarizes quite a lot of information. We walk into logistic regression with a constraint that y_pred should be in {0,1}.
- The most obvious intuition is to have a probability function(denoted by p in above image) and call the values below 0.5 as 0 and 1 otherwise. The value of p = 0.5 implies b0+b1.x = 0 which becomes decision boundary for our space.
- The probability function is called sigmoid function which although is common for probability estimates but can be derived by assuming Y ~ Bernoulli(1, p) where Y is getting 1 in random sampling once. (Hint : Since Bernoulli is an member of Exponential Family thereby estimate p as a function of natural parameter.)
- The loss function here is of the form
Which can be directly obtained by Maximum Likelihood Estimate after assuming Y ~Bernoulli(1, p) ,where m is number of observations, and p is the matrix of sigmoid function results for each observations and y is the matrix of actual observed 0 or 1 values.
- Currently the repository attached at the end contains batch gradient descent as a way of minimize loss function.
which is a equation for all Generalized Linear Models.
- Another numerical method for solving for Logistic Regression is Newton’s Method which is not portrayed currently here.
If this article isn’t enough to satisfy your intellect goals,
Don’t worry!! Just visit my repository, it mentions all the articles, links I referred to while learning this topic.
I would really appreciate you to leave a note if you followed till the end. Any recommendation and thoughts are welcomed.
Cheers to learning!!! 💪
Shaily Jain
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