Math macro command for latex support in markdown
Number and Arrays
a
$a$
A scalar
\va
$\va$
A vector, additionally $\vzero, \vone, \vmu, \vnu, \vtheta$ for \vzero, \vone, \vmu, \vnu, \vtheta
\mA
$\mA$
A matrix
\tA
$\tA$
A tensor
\mI_n
$\mI_n$
Identity matrix with $n$ rows and $n$ columns
\mI
$\mI$
Identity matrix with dimensionality implied by context
\ve^{(i)}
$\ve^{(i)}$
Standard basis vector $[0,\dots,0,1,0,\dots,0]$ \text{diag}(\va)
$\text{diag}(\va)$
A square, diagonal matrix with diagonal entries given by $\va$
\ra
$\ra$
A scalar-valued random variable
\rva
$\rva$
A vector-valued random variables
\rmA
$\rmA$
A matrix-valued random varialbes
Sets and Graphs
\sA
$\sA$
A setNote: the command covers
sA to sZ but don't no sE since it's expectation
\R
$\R$
The set of real numbers
{0, 1}
${0, 1}$
The set containing 0 and 1
{0, 1, \dots, n}
${0, 1, \dots, n}$
The set of all integers between $0$ and $n$
[a, b]
$[a, b]$
The real interval including $a$ and $b$
(a, b]
$(a, b]$
The real interval excluding $a$ but including $b$
\sA \backslash \sB
$\sA \backslash \sB$
Set subtraction, i.e., the set containing the elements of $\sA$ not in $\sB$
\gG
$\gG$
A graph
Indexing
\eva_i
$\eva_i$
Element $i$ of vector $\va$, with indexing starting at 1
\eva_{-i}
$\eva_{-i}$
All elements of vector $\va$ except for element $i$
\emA_{i,j}
$\emA_{i,j}$
Element $i, j$ of matrix $\mA$
\mA_{i, :}
$\mA_{i, :}$
Row $i$ of matrix $\mA$
\mA_{:, i}
$\mA_{:, i}$
Column $i$ of matrix $\mA$
\etA_{i, j, k}
$\etA_{i, j, k}$
Element $(i, j, k)$ of a 3-D tensor $\tA$
\tA_{:, :, i}
$\tA_{:, :, i}$
2-D slice of a 3-D tensor
\erva_i
$\erva_i$
Element $i$ of the random vector $\rva$
Linear Algebra Operators
\mA^\top
$\mA^\top$
Transpose of matrix $\mA$
\mA^+
$\mA^+$
Moore-Penrose pseudoinverse of $\mA$
\mA \odot \mB
$\mA \odot \mB$
Element-wise (Hadamard) product of $\mA$ and $\mB$
\mathrm{det}(\mA)
$\mathrm{det}(\mA)$
Determinant of $\mA$
\sign(x)
$\sign(x)$
Sign of a variable $x$
\Tr \mA
$\Tr(\mA)$
Trace of a matrix A
Calculus
\diff y / \diff x
$\diff y / \diff x$
Derivative of $y$ with respect to $x$
\frac{\partial y}{\partial x}
$\frac{\partial y}{\partial x}$
Partial derivative of $y$ with respect to $x$
\nabla_\vx y
$\nabla_\vx y$
Gradient of $y$ with respect to $\vx$
\nabla_\mX y
$\nabla_\mX y$
Matrix derivatives of $y$ with respect to $\mX$
\nabla_\tX y
$\nabla_\tX y$
Tensor containing derivatives of $y$ with respect to $\tX$
\frac{\partial f}{\partial \vx}
$\frac{\partial f}{\partial \vx}$
Jacobian matrix $\mJ \in \R^{m\times n}$ of $f: \R^n \rightarrow \R^m$
\nabla_\vx^2 f(\vx)\text{ or }\mH(f)(\vx)
$\nabla_\vx^2 f(\vx)\text{ or }\mH(f)(\vx)$
The Hessian matrix of $f$ at input point $\vx$
\int f(\vx) d\vx
$\int f(\vx) d\vx$
Definite integral over the entire domain of $\vx$
\int_\sS f(\vx) d\vx
$\int_\sS f(\vx) d\vx$
Definite integral with respect to $\vx$ over the set $\sS$
Probabilities
\ra \bot \rb
$\ra \bot \rb$
The random variables $\ra$ and $\rb$ are independent
\ra \bot \rb \mid \rc
$\ra \bot \rb \mid \rc$
They are conditionally independent given $\rc$
P(\ra)
$P(\ra)$
A probability distribution over a discrete variable
p(\ra)
$p(\ra)$
A probability distribution over a continuous variable, or a variable of unspecified type
\ra \sim P
$\ra \sim P$
Random variable $\ra$ has distribution $P$
\E_{\rx \sim P} [ f(x) ] \text{ or } \E f(x)
$\E_{\rx \sim P} [ f(x) ] \text{ or } \E f(x)$
Expectation of $f(x)$ with respect to $P(\rx)$
\Var(f(x))
$\Var(f(x))$
Variance of $f(x)$ under $P(\rx)$
\Cov(f(x), g(x))
$\Cov(f(x), g(x))$
Covariance of $f(x)$ and $g(x)$ under $P(\rx)$
H(\rx)
$H(\rx)$
Shannon entropy of the random variable $\rx$
\KL(P \Vert Q)
$\KL(P \Vert Q)$
Kullback-Leibler divergence of $P$ and $Q$
\mathcal{N}(\vx ; \vmu , \mSigma)
$\mathcal{N}(\vx ; \vmu , \mSigma)$
Gaussian distribution over $\vx$ with mean $\vmu$ and covariance $\mSigma$
Functions
f: \sA \rightarrow \sB
$f: \sA \rightarrow \sB$
The function $f$ with domain $\sA$ and range $\sB$
f \circ g
$f \circ g$
Composition of the functions $f$ and $g$
f(\vx ; \vtheta)
$f(\vx ; \vtheta)$
A function of $\vx$ parametrized by $\vtheta$. Sometimes written as $f(\vx)$ to simplify notation
\log x
$\log x$
Natural logarithm of $x$
\sigma(x)
$\sigma(x)$
Logistic sigmoid, $\displaystyle \frac{1}{1 + \exp(-x)}$
\zeta(x)
$\zeta(x)$
Softplus, $\log(1 + \exp(x))$
| \vx |_p
$| \vx |_p$
$L^p$ norm of $\vx$
| \vx |
$| \vx |$
$L^2$ norm of $\vx$
x^+
$x^+$
Positive part of $x$, i.e., $\max(0,x)$
\bm{1}_\mathrm{condition}
$\bm{1}_\mathrm{condition}$
Is 1 if the condition is true, 0 otherwise
Custom Commands special
\bm{#1}
$\bm{x}$
Bold symbol, e.g., $\boldsymbol{x}$
\sign
$\sign$
operator, Sign , $\operatorname{sign}$
\Tr
$\Tr$
operator Trace, $\operatorname{Tr}$
\E
$\E$
Expectation, $\mathbb{E}$
\KL
$\KL$
Kullback-Leibler divergence, $D_\mathrm{KL}$
\NormalDist
$\NormalDist$
Gaussian distribution, $\mathcal{N}$
\diag
$\diag$
Diagonal matrix, $\mathrm{diag}$
\Ls
$\Ls$
Loss function, $\mathcal{L}$
\R
$\R$
Real number set, $\mathbb{R}$
\emp
$\emp$
Empirical distribution, $\tilde{p}$
\lr
$\lr$
Learning rate, $\alpha$
\reg
$\reg$
Regularization coefficient, $\lambda$
\rect
$\rect$
Rectifier activation, $\mathrm{rectifier}$
\softmax
$\softmax$
Softmax function, $\mathrm{softmax}$
\sigmoid
$\sigmoid$
Sigmoid function, $\sigma$
\softplus
$\softplus$
Softplus function, $\zeta$
\Var
$\Var$
Variance, $\mathrm{Var}$
\standarderror
$\standarderror$
Standard error, $\mathrm{SE}$
\Cov
$\Cov$
Covariance, $\mathrm{Cov}$
\tran
$\tran$
Transpose operator, $^\top$
\inv
$\inv$
Inverse operator, $^{-1}$
\diff
$\diff$
Differential operator, $\mathrm{d}$