# A Gentle Introduction to Logistic Regression With Maximum Likelihood Estimation

Last Updated on October 28, 2019

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. This is particularly true as the negative of the log-likelihood function used in the procedure can be shown to be equivalent to cross-entropy loss function.

In this post, you will discover logistic regression with maximum likelihood estimation.

After reading this post, you will know:

- Logistic regression is a linear model for binary classification predictive modeling.
- The linear part of the model predicts the log-odds of an example belonging

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