Symbols

$\log(x)$ Natural logarithm of x

$\mathbf{x, y}$ Vectors are bold lowercase, thus we write a column vector as $\mathbf{x}=[x_1,\dots,x_n]^T$

$\mathbf{X, Y}$ Matrices are bold uppercase

$X, Y$ Random variables are specified as upper case Roman letters

$\boldsymbol{\theta}$ Greek lowercase characters are generally used for model parameters.

$\hat \theta$ Point estimate of $\boldsymbol{\theta}$

$\mathbb{E}[X|Y]$ Expectation of $X$ with respect to $Y$

$\textrm{var}[X|Y]$ Variance of $X$ with respect to $Y$

$\textrm{cov}[X,Y]$ Covariance matrix of $X$ and $Y$

$X \sim p$ Random variable $X$ is distributed as p

$p(\cdot)$ Probability density or probability mass function

$p(y \mid \boldsymbol{x})$ Probability (density) of $y$ given $\boldsymbol{x}$.

$\mathcal{N}(\mu, \sigma^2)$ A Gaussian (or normal) distribution with mean $\mu$ and standard deviation $\sigma$

$\mathbb{KL}(p \parallel q)$ Kullback-Leibler divergence from $p$ to $q$