# Logistic regression

I am working through Googleâ€™s Machine Learning Crash Course. The notes in this post cover the â€śLogistic Regressionâ€ť module.

â€śLogistic regressionâ€ť generates a probability (a value between 0 and 1). Itâ€™s also very efficient.

Note the glossary defines logistic regression as a classification model, which is weird since it has â€śregressionâ€ť in the name. I suspect this is explained by â€śYou can interpret the value between 0 and 1 in either of the following two ways: â€¦ a binary classification problem â€¦ As a value to be compared against a classification threshold …â€ť

The â€śsigmoidâ€ť function, aka â€ślogisticâ€ť function/transform, produces a bounded value between 0 and 1.

Note the sigmoid function is just `y = 1 / 1 + e ^ - đťžĽ` where đťžĽ is our usual linear equation. I suppose weâ€™re transforming the linear output into a logistic form.

Regularization (notes) is important in logistic regression. â€śWithout regularization, the asymptotic nature of logistic regression would keep driving loss towards 0 in high dimensionsâ€ť, esp L2 regularization and stopping early.

The â€ślogitâ€ť, aka â€ślog-oddsâ€ť, function is the inverse of the logistic function.

The loss function for logistic regression is â€ślog lossâ€ť.