Contents

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]
E[X]\mathbb{E}[X]
Expectation Mean of random variable X over its distribution.
Var(X)\mathrm{Var}(X)
Variance Expected squared deviation from the mean, E[(XE[X])2]\mathbb{E}[(X-\mathbb{E}[X])^2].
N(μ,σ2)\mathcal{N}(\mu,\sigma^2)
Normal distribution Gaussian with mean μ\mu and variance σ2\sigma^2.
XpX \sim p
Distributed as Random variable X is drawn from distribution p.
pqp \propto q
Proportional to Equal up to a constant factor (e.g. unnormalized density).
linear algebra [5]
Rn\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.
λ\lambda
Eigenvalue / regularization Scalar with Av=λvA v=\lambda v (linear algebra); weight on a penalty term (ML).
calculus [5]
f\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]
θ\theta
Parameters Vector of model parameters to be learned.
η\eta
Learning rate Step size scaling the gradient update.
σ\sigma
Sigmoid / standard deviation Logistic σ(x)=1/(1+ex)\sigma(x)=1/(1+e^{-x}) (DL); square root of variance (probability).
softmax\mathrm{softmax}
Softmax Maps a vector to a probability simplex, ezi/jezje^{z_i}/\sum_j e^{z_j}.
y^\hat{y}
Prediction Model's estimate of the target y.
L\mathcal{L}
Loss Objective function minimized during training.
information [2]
H(X)H(X)
Entropy Expected information content, p(x)logp(x)-\sum p(x)\log p(x).
DKL(pq)D_{KL}(p\,\|\,q)
KL divergence Relative entropy from q to p, plog(p/q)\sum p\log(p/q).
set & logic [3]
argmax\arg\max
Argmax Argument that maximizes a function.
\circ
Function composition (fg)(x)=f(g(x))(f\circ g)(x)=f(g(x)).
\in
Element of Membership: object belongs to a set.