A Gentle Introduction to Logistic Regression With Maximum Likelihood Estimation

Logistic regression is a model for binary classification predictive modeling. The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the probability of observing the outcome given the input data and the model. This function can then be optimized to find the set of parameters that results in the largest sum likelihood over the training dataset. The maximum likelihood approach to fitting a logistic regression model both aids in better understanding the form of the logistic regression model and provides a template that can be used for fitting classification models more generally.