Log odds are a critical concept in statistical models and AI, particularly in logistic regression and other linear classification algorithms, where they are used to transform the odds of an event occurring into a linear function of predictor variables. The utility of log odds lies in their ability to handle probabilities by converting them into a continuous range over the entire real number line, thus enabling the convenient mathematical manipulation of binary outcomes. In the context of AI, log odds facilitate the interpretation of model coefficients in logistic regression, allowing practitioners to understand how changes in predictor variables affect the probability of a given outcome. Additionally, log odds play a crucial role in algorithms like Naive Bayes, where they assist in decision-making processes based on likelihood ratios.
The concept of odds and their logarithm has been used in statistics since the late 19th century, but log odds gained significant popularity with the advent of logistic regression in the mid-20th century as a robust statistical model for binary classification problems.
Key contributions to the development and popularization of logistic regression and the use of log odds include Joseph Berkson, who introduced the model as an alternative to the probit model in 1944, and David Cox, whose work in the 1960s provided deeper insights into its estimation and interpretation in practical statistical modeling contexts.