Logistic regression is a statistical and machine learning method for classification that estimates the probability of a binary outcome by passing a weighted sum of input features through the logistic (sigmoid) function, which maps any value to a probability between 0 and 1.
The weights are learned from labeled examples, and a threshold on the estimated probability, often 0.5, turns it into a yes-or-no decision. Multinomial logistic regression extends the method to more than two classes. Logistic regression is a core method for text classification and is closely related to artificial neural networks, which can be viewed as logistic regression classifiers stacked on top of each other.
History
Joseph Berkson applied the logistic function to bio-assay data in a 1944 paper that used the term logit, by analogy with Bliss’s probit. D. R. Cox’s 1958 paper “The Regression Analysis of Binary Sequences” treated regression of a binary outcome on independent variables and reviewed earlier work.
Sources
- Application of the Logistic Function to Bio-Assay, Berkson, Journal of the American Statistical Association 39(227), 1944. Retrieved October 7, 2026.
- The Regression Analysis of Binary Sequences, Cox, Journal of the Royal Statistical Society, Series B 20(2), 1958. Retrieved October 7, 2026.
- Speech and Language Processing, Chapter 4, Logistic Regression and Text Classification, Jurafsky and Martin, Stanford University. Retrieved October 7, 2026.