# Logistic regression

> A type of regression model that predicts a probability. Logistic regression models have the following characteristics:[^1]

A type of [regression model](https://wiki.g15e.com/pages/Regression%20model.txt) that predicts a <probability>. Logistic regression models have the following characteristics:[^1]

- The [label](https://wiki.g15e.com/pages/Label%20(machine%20learning.txt)) is [categorical](https://wiki.g15e.com/pages/Categorical%20data.txt). The term logistic regression usually refers to <binary logistic regression>, that is, to a model that calculates probabilities for labels with two possible values. A less common variant, <multinomial logistic regression>, calculates probabilities for labels with more than two possible values.
- The [loss function](https://wiki.g15e.com/pages/Loss%20function.txt) during training is [log loss](https://wiki.g15e.com/pages/Log%20loss.txt). (Multiple Log Loss units can be placed in parallel for labels with more than two possible values.)
- The model has a linear architecture, not a [deep neural network](https://wiki.g15e.com/pages/Deep%20neural%20network.txt). However, the remainder of this definition also applies to deep model that predict probabilities for categorical labels.

A logistic regression model uses the following two-step architecture:[^1]

1. The model generates a raw prediction ($y'$) by applying a linear function of input features.
2. The model uses that raw prediction as input to a [sigmoid function](https://wiki.g15e.com/pages/Sigmoid%20function.txt), which converts the raw prediction to a value between 0 and 1, exclusive.

Like any [regression model](https://wiki.g15e.com/pages/Regression%20model.txt), a logistic regression model predicts a number. However, this number typically becomes part of a [binary classification](https://wiki.g15e.com/pages/Binary%20classification.txt) model as follows:[^1]

- If the predicted number is *greater* than the [classification threshold](https://wiki.g15e.com/pages/Classification%20threshold.txt), the binary classification model predicts the [positive class](https://wiki.g15e.com/pages/Positive%20class%20(machine%20learning.txt)).
- If the predicted number is *less* than the [classification threshold](https://wiki.g15e.com/pages/Classification%20threshold.txt), the binary classification model predicts the [negative class](https://wiki.g15e.com/pages/Negative%20class%20(machine%20learning.txt)).

## See also

- [ML crash course - Logistic regression](https://wiki.g15e.com/pages/ML%20crash%20course%20-%20Logistic%20regression.txt)

## Footnotes

[^1]:https://developers.google.com/machine-learning/glossary#logistic_regression