## Introduction to generalized linear model

As the name suggested, generalized linear model (GLM) is a generalization of the linear regression model. In a classic linear model, with input $latex X$, the output $latex Y$ is modeled by $latex Y|X \sim \mathcal{N} (B X, \sigma^2 I)$. GLM extends the model in two ways, first instead of having the mean as simple…

## Dual positive semi-definite cone

The set of all positive semi-definite matrices $latex \mathcal S^+$ forms a cone. Because for any two matrices $latex A$ and $latex B$ in $latex \mathcal S^+$. $latex \theta_1 A + \theta_2 B$ is still PSD and thus in $latex \mathcal S^+$. PSD is self-dual In the context of cone, $latex \mathcal S^+$ is self-dual….