Poisson regression is a generalized linear model for count data.
To model a dataset that is generated from a [[Poisson distribution]] Poisson Process , we only need to model the mean $\mu$ as it is the only parameters. The simplest model we can have for some given features $X$ is a linear model. However, for count data, the effects of the predictors are often multiplicative. The next simplest model we can have is
$$ \mu = \exp\left(\beta X\right). $$
The $\exp$ makes sure that the mean is positive as this is required for count data.
Planted: by L Ma;
- Fox J. Applied Regression Analysis and Generalized Linear Models. SAGE Publications; 2015. Available: https://play.google.com/store/books/details?id=cjB3BwAAQBAJ
- Rodríguez G, editor. Poisson Models for CountData. Generalized Linear Models. Available: https://data.princeton.edu/wws509/notes
- Chapter 19: Logistic and Poisson Regression by Marie Chesaniuk
- Poisson regression and non-normal loss (sklearn documentation)
- Beyond Multiple Linear Regression, Chapter 4 Poisson Regression
L Ma (2021). 'Poisson Regression', Datumorphism, 05 April. Available at: https://datumorphism.leima.is/wiki/machine-learning/linear/poisson-regression/.