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 \(q\)