Notation [26]

Every symbol, defined once.

A key to the marks that recur across the essays and plates, so no symbol has to be guessed from context.

probability [5]

$\mathbb{E}[X]$: Expectation Mean of random variable X over its distribution.
$\mathrm{Var}(X)$: Variance Expected squared deviation from the mean, $\mathbb{E}[(X-\mathbb{E}[X])^2]$ .
$\mathcal{N}(\mu,\sigma^2)$: Normal distribution Gaussian with mean $\mu$ and variance $\sigma^2$ .
$X \sim p$: Distributed as Random variable X is drawn from distribution p.
$p \propto q$: Proportional to Equal up to a constant factor (e.g. unnormalized density).

linear algebra [5]

$\mathbb{R}^n$: Real coordinate space Set of n-dimensional real-valued vectors.
$\langle\cdot,\cdot\rangle$: Inner product Bilinear form giving a scalar from two vectors (e.g. dot product).
$\|\cdot\|$: Norm Length/magnitude of a vector.
$\odot$: Hadamard product Elementwise product of equal-shaped arrays.
$\lambda$: Eigenvalue / regularization Scalar with $A v=\lambda v$ (linear algebra); weight on a penalty term (ML).

calculus [5]

$\nabla f$: Gradient Vector of first partial derivatives of scalar field f.
$\partial$: Partial derivative Rate of change of a function holding other variables fixed.
$\int$: Integral Continuous accumulation / area under a function.
$\sum$: Summation Sum of a sequence of terms over an index.
$\prod$: Product Product of a sequence of terms over an index.

deep learning [6]

$\theta$: Parameters Vector of model parameters to be learned.
$\eta$: Learning rate Step size scaling the gradient update.
$\sigma$: Sigmoid / standard deviation Logistic $\sigma(x)=1/(1+e^{-x})$ (DL); square root of variance (probability).
$\mathrm{softmax}$: Softmax Maps a vector to a probability simplex, $e^{z_i}/\sum_j e^{z_j}$ .
$\hat{y}$: Prediction Model's estimate of the target y.
$\mathcal{L}$: Loss Objective function minimized during training.

information [2]

$H(X)$: Entropy Expected information content, $-\sum p(x)\log p(x)$ .
$D_{KL}(p\,\|\,q)$: KL divergence Relative entropy from q to p, $\sum p\log(p/q)$ .

set & logic [3]