Generalized Linear Models

GLMs = generalized linear models
GLMS are a class of models that map high-dimensional inputs into a scalar output.
The expected value is some function of an additive combination of parameters.
It combines a linear filter + a nonlinear function + noise
linear regression, logistic regression, and Poisson regression, are all just special cases of GLMs.
- linear:

Y_{i} \sim N o r m a l (μ_{i}, σ) $ $ $ $ μ_{i} = α + β_{X} X_{i} + β_{Z} Z_{i}

- logistic:

Y_{i} \sim B e r n o u l l i (p_{i})

l o g i t (p_{i}) = α + β_{X} X_{i} + β_{Z} Z_{i}

- Poisson:
$$ Y_i \sim Poisson (\lambda) $$$$\lambda = \exp(\alpha + \beta_X X_i + \beta_Z Z_i)$$