# Generalized Linear Models

Let the outcome belong to . We say that Expert 's prediction at step is denoted and is equal to

Here is a fixed \emph{activation function}. We have in all the cases except linear regression (see below). If the range of the function is , the experts necessarily give predictions from .

- Logistic activation function is .
- Probit activation function is

where is the cumulative distribution function of the normal distribution with zero mean and unit variance.

- Complementary log-log (comlog) activation function .

Generalized Linear Models are often used for classification purposes.

### Bibliography

- McCullagh, P., Nelder, J. Generalized Linear Models. Chapman & Hall/CRC, second edn. 1989.