[tab] math_commands.tex (latex)

\usepackage{amsmath,amsfonts,bm}


ewcommand{\figleft}{{\em (Left)}}

ewcommand{\figcenter}{{\em (Center)}}

ewcommand{\figright}{{\em (Right)}}

ewcommand{\figtop}{{\em (Top)}}

ewcommand{\figbottom}{{\em (Bottom)}}

ewcommand{\captiona}{{\em (a)}}

ewcommand{\captionb}{{\em (b)}}

ewcommand{\captionc}{{\em (c)}}

ewcommand{\captiond}{{\em (d)}}


ewcommand{
ewterm}[1]{{\bf #1}}

ewcommand*{\defeq}{\stackrel{	ext{def}}{=}}


\def\figref#1{figure~
ef{#1}}
\def\Figref#1{Figure~
ef{#1}}
\def	wofigref#1#2{figures 
ef{#1} and 
ef{#2}}
\def\quadfigref#1#2#3#4{figures 
ef{#1}, 
ef{#2}, 
ef{#3} and 
ef{#4}}
\def\secref#1{section~
ef{#1}}
\def\Secref#1{Section~
ef{#1}}
\def	wosecrefs#1#2{sections 
ef{#1} and 
ef{#2}}
\def\secrefs#1#2#3{sections 
ef{#1}, 
ef{#2} and 
ef{#3}}
\def\eqref#1{equation~
ef{#1}}
\def\Eqref#1{Equation~
ef{#1}}
\def\plaineqref#1{
ef{#1}}
\def\chapref#1{chapter~
ef{#1}}
\def\Chapref#1{Chapter~
ef{#1}}
\def
angechapref#1#2{chapters
ef{#1}--
ef{#2}}
\def\algref#1{algorithm~
ef{#1}}
\def\Algref#1{Algorithm~
ef{#1}}
\def	woalgref#1#2{algorithms 
ef{#1} and 
ef{#2}}
\def\Twoalgref#1#2{Algorithms 
ef{#1} and 
ef{#2}}
\def\partref#1{part~
ef{#1}}
\def\Partref#1{Part~
ef{#1}}
\def	wopartref#1#2{parts 
ef{#1} and 
ef{#2}}

\def\ceil#1{\lceil #1 
ceil}
\def\floor#1{\lfloor #1 
floor}
\def\1{\bm{1}}

ewcommand{	rain}{\mathcal{D}}

ewcommand{\valid}{\mathcal{D_{\mathrm{valid}}}}

ewcommand{	est}{\mathcal{D_{\mathrm{test}}}}

\def\eps{{\epsilon}}


ewcommand{\Qclass}{\mathcal{Q}}

ewcommand{
hoinit}{{
ho_0}}

ewcommand{\Pieps}{{\Pi_\epsilon}}

ewcommand{	rans}{P}

ewcommand{\backup}{\mathcal{T}}

ewcommand{\Qprime}{Q^{\prime}}

ewcommand{\Qhat}{\hat{Q}}

ewcommand{
eward}{r}

ewcommand{\policy}{\pi}

ewcommand{\mdp}{\mathcal{M}}

ewcommand{\states}{\mathcal{S}}

ewcommand{\actions}{\mathcal{A}}

ewcommand{\observations}{\mathcal{O}}

ewcommand{	ransitions}{T}

ewcommand{\grad}{{
abla}}


\def
eta{{	extnormal{$\eta$}}}
\def
a{{	extnormal{a}}}
\def
b{{	extnormal{b}}}
\def
c{{	extnormal{c}}}
\def
d{{	extnormal{d}}}
\def
e{{	extnormal{e}}}
\def
f{{	extnormal{f}}}
\def
g{{	extnormal{g}}}
\def
h{{	extnormal{h}}}
\def
i{{	extnormal{i}}}
\def
j{{	extnormal{j}}}
\def
k{{	extnormal{k}}}
\def
l{{	extnormal{l}}}
\def
n{{	extnormal{n}}}
\def
o{{	extnormal{o}}}
\def
p{{	extnormal{p}}}
\def
q{{	extnormal{q}}}
\def
r{{	extnormal{r}}}
\def
s{{	extnormal{s}}}
\def
t{{	extnormal{t}}}
\def
u{{	extnormal{u}}}
\def
v{{	extnormal{v}}}
\def
w{{	extnormal{w}}}
\def
x{{	extnormal{x}}}
\def
y{{	extnormal{y}}}
\def
z{{	extnormal{z}}}

\def
vepsilon{{\mathbf{\epsilon}}}
\def
vtheta{{\mathbf{	heta}}}
\def
va{{\mathbf{a}}}
\def
vb{{\mathbf{b}}}
\def
vc{{\mathbf{c}}}
\def
vd{{\mathbf{d}}}
\def
ve{{\mathbf{e}}}
\def
vf{{\mathbf{f}}}
\def
vg{{\mathbf{g}}}
\def
vh{{\mathbf{h}}}
\def
vu{{\mathbf{i}}}
\def
vj{{\mathbf{j}}}
\def
vk{{\mathbf{k}}}
\def
vl{{\mathbf{l}}}
\def
vm{{\mathbf{m}}}
\def
vn{{\mathbf{n}}}
\def
vo{{\mathbf{o}}}
\def
vp{{\mathbf{p}}}
\def
vq{{\mathbf{q}}}
\def
vr{{\mathbf{r}}}
\def
vs{{\mathbf{s}}}
\def
vt{{\mathbf{t}}}
\def
vu{{\mathbf{u}}}
\def
vv{{\mathbf{v}}}
\def
vw{{\mathbf{w}}}
\def
vx{{\mathbf{x}}}
\def
vy{{\mathbf{y}}}
\def
vz{{\mathbf{z}}}

\def\erva{{	extnormal{a}}}
\def\ervb{{	extnormal{b}}}
\def\ervc{{	extnormal{c}}}
\def\ervd{{	extnormal{d}}}
\def\erve{{	extnormal{e}}}
\def\ervf{{	extnormal{f}}}
\def\ervg{{	extnormal{g}}}
\def\ervh{{	extnormal{h}}}
\def\ervi{{	extnormal{i}}}
\def\ervj{{	extnormal{j}}}
\def\ervk{{	extnormal{k}}}
\def\ervl{{	extnormal{l}}}
\def\ervm{{	extnormal{m}}}
\def\ervn{{	extnormal{n}}}
\def\ervo{{	extnormal{o}}}
\def\ervp{{	extnormal{p}}}
\def\ervq{{	extnormal{q}}}
\def\ervr{{	extnormal{r}}}
\def\ervs{{	extnormal{s}}}
\def\ervt{{	extnormal{t}}}
\def\ervu{{	extnormal{u}}}
\def\ervv{{	extnormal{v}}}
\def\ervw{{	extnormal{w}}}
\def\ervx{{	extnormal{x}}}
\def\ervy{{	extnormal{y}}}
\def\ervz{{	extnormal{z}}}

\def
mA{{\mathbf{A}}}
\def
mB{{\mathbf{B}}}
\def
mC{{\mathbf{C}}}
\def
mD{{\mathbf{D}}}
\def
mE{{\mathbf{E}}}
\def
mF{{\mathbf{F}}}
\def
mG{{\mathbf{G}}}
\def
mH{{\mathbf{H}}}
\def
mI{{\mathbf{I}}}
\def
mJ{{\mathbf{J}}}
\def
mK{{\mathbf{K}}}
\def
mL{{\mathbf{L}}}
\def
mM{{\mathbf{M}}}
\def
mN{{\mathbf{N}}}
\def
mO{{\mathbf{O}}}
\def
mP{{\mathbf{P}}}
\def
mQ{{\mathbf{Q}}}
\def
mR{{\mathbf{R}}}
\def
mS{{\mathbf{S}}}
\def
mT{{\mathbf{T}}}
\def
mU{{\mathbf{U}}}
\def
mV{{\mathbf{V}}}
\def
mW{{\mathbf{W}}}
\def
mX{{\mathbf{X}}}
\def
mY{{\mathbf{Y}}}
\def
mZ{{\mathbf{Z}}}

\def\ermA{{	extnormal{A}}}
\def\ermB{{	extnormal{B}}}
\def\ermC{{	extnormal{C}}}
\def\ermD{{	extnormal{D}}}
\def\ermE{{	extnormal{E}}}
\def\ermF{{	extnormal{F}}}
\def\ermG{{	extnormal{G}}}
\def\ermH{{	extnormal{H}}}
\def\ermI{{	extnormal{I}}}
\def\ermJ{{	extnormal{J}}}
\def\ermK{{	extnormal{K}}}
\def\ermL{{	extnormal{L}}}
\def\ermM{{	extnormal{M}}}
\def\ermN{{	extnormal{N}}}
\def\ermO{{	extnormal{O}}}
\def\ermP{{	extnormal{P}}}
\def\ermQ{{	extnormal{Q}}}
\def\ermR{{	extnormal{R}}}
\def\ermS{{	extnormal{S}}}
\def\ermT{{	extnormal{T}}}
\def\ermU{{	extnormal{U}}}
\def\ermV{{	extnormal{V}}}
\def\ermW{{	extnormal{W}}}
\def\ermX{{	extnormal{X}}}
\def\ermY{{	extnormal{Y}}}
\def\ermZ{{	extnormal{Z}}}

\def\vzero{{\bm{0}}}
\def\vone{{\bm{1}}}
\def\vmu{{\bm{\mu}}}
\def\vtheta{{\bm{	heta}}}
\def\va{{\bm{a}}}
\def\vb{{\bm{b}}}
\def\vc{{\bm{c}}}
\def\vd{{\bm{d}}}
\def\ve{{\bm{e}}}
\def\vf{{\bm{f}}}
\def\vg{{\bm{g}}}
\def\vh{{\bm{h}}}
\def\vi{{\bm{i}}}
\def\vj{{\bm{j}}}
\def\vk{{\bm{k}}}
\def\vl{{\bm{l}}}
\def\vm{{\bm{m}}}
\def\vn{{\bm{n}}}
\def\vo{{\bm{o}}}
\def\vp{{\bm{p}}}
\def\vq{{\bm{q}}}
\def\vr{{\bm{r}}}
\def\vs{{\bm{s}}}
\def\vt{{\bm{t}}}
\def\vu{{\bm{u}}}
\def\vv{{\bm{v}}}
\def\vw{{\bm{w}}}
\def\vx{{\bm{x}}}
\def\vy{{\bm{y}}}
\def\vz{{\bm{z}}}

\def\evalpha{{\alpha}}
\def\evbeta{{\beta}}
\def\evepsilon{{\epsilon}}
\def\evlambda{{\lambda}}
\def\evomega{{\omega}}
\def\evmu{{\mu}}
\def\evpsi{{\psi}}
\def\evsigma{{\sigma}}
\def\evtheta{{	heta}}
\def\eva{{a}}
\def\evb{{b}}
\def\evc{{c}}
\def\evd{{d}}
\def\eve{{e}}
\def\evf{{f}}
\def\evg{{g}}
\def\evh{{h}}
\def\evi{{i}}
\def\evj{{j}}
\def\evk{{k}}
\def\evl{{l}}
\def\evm{{m}}
\def\evn{{n}}
\def\evo{{o}}
\def\evp{{p}}
\def\evq{{q}}
\def\evr{{r}}
\def\evs{{s}}
\def\evt{{t}}
\def\evu{{u}}
\def\evv{{v}}
\def\evw{{w}}
\def\evx{{x}}
\def\evy{{y}}
\def\evz{{z}}

\def\mA{{\bm{A}}}
\def\mB{{\bm{B}}}
\def\mC{{\bm{C}}}
\def\mD{{\bm{D}}}
\def\mE{{\bm{E}}}
\def\mF{{\bm{F}}}
\def\mG{{\bm{G}}}
\def\mH{{\bm{H}}}
\def\mI{{\bm{I}}}
\def\mJ{{\bm{J}}}
\def\mK{{\bm{K}}}
\def\mL{{\bm{L}}}
\def\mM{{\bm{M}}}
\def\mN{{\bm{N}}}
\def\mO{{\bm{O}}}
\def\mP{{\bm{P}}}
\def\mQ{{\bm{Q}}}
\def\mR{{\bm{R}}}
\def\mS{{\bm{S}}}
\def\mT{{\bm{T}}}
\def\mU{{\bm{U}}}
\def\mV{{\bm{V}}}
\def\mW{{\bm{W}}}
\def\mX{{\bm{X}}}
\def\mY{{\bm{Y}}}
\def\mZ{{\bm{Z}}}
\def\mBeta{{\bm{\beta}}}
\def\mPhi{{\bm{\Phi}}}
\def\mLambda{{\bm{\Lambda}}}
\def\mSigma{{\bm{\Sigma}}}

\DeclareMathAlphabet{\mathsfit}{\encodingdefault}{\sfdefault}{m}{sl}
\SetMathAlphabet{\mathsfit}{bold}{\encodingdefault}{\sfdefault}{bx}{n}

ewcommand{	ens}[1]{\bm{\mathsfit{#1}}}
\def	A{{	ens{A}}}
\def	B{{	ens{B}}}
\def	C{{	ens{C}}}
\def	D{{	ens{D}}}
\def	E{{	ens{E}}}
\def	F{{	ens{F}}}
\def	G{{	ens{G}}}
\def	H{{	ens{H}}}
\def	I{{	ens{I}}}
\def	J{{	ens{J}}}
\def	K{{	ens{K}}}
\def	L{{	ens{L}}}
\def	M{{	ens{M}}}
\def	N{{	ens{N}}}
\def	O{{	ens{O}}}
\def	P{{	ens{P}}}
\def	Q{{	ens{Q}}}
\def	R{{	ens{R}}}
\def	S{{	ens{S}}}
\def	T{{	ens{T}}}
\def	U{{	ens{U}}}
\def	V{{	ens{V}}}
\def	W{{	ens{W}}}
\def	X{{	ens{X}}}
\def	Y{{	ens{Y}}}
\def	Z{{	ens{Z}}}


\def\gA{{\mathcal{A}}}
\def\gB{{\mathcal{B}}}
\def\gC{{\mathcal{C}}}
\def\gD{{\mathcal{D}}}
\def\gE{{\mathcal{E}}}
\def\gF{{\mathcal{F}}}
\def\gG{{\mathcal{G}}}
\def\gH{{\mathcal{H}}}
\def\gI{{\mathcal{I}}}
\def\gJ{{\mathcal{J}}}
\def\gK{{\mathcal{K}}}
\def\gL{{\mathcal{L}}}
\def\gM{{\mathcal{M}}}
\def\gN{{\mathcal{N}}}
\def\gO{{\mathcal{O}}}
\def\gP{{\mathcal{P}}}
\def\gQ{{\mathcal{Q}}}
\def\gR{{\mathcal{R}}}
\def\gS{{\mathcal{S}}}
\def\gT{{\mathcal{T}}}
\def\gU{{\mathcal{U}}}
\def\gV{{\mathcal{V}}}
\def\gW{{\mathcal{W}}}
\def\gX{{\mathcal{X}}}
\def\gY{{\mathcal{Y}}}
\def\gZ{{\mathcal{Z}}}

\def\sA{{\mathbb{A}}}
\def\sB{{\mathbb{B}}}
\def\sC{{\mathbb{C}}}
\def\sD{{\mathbb{D}}}
\def\sF{{\mathbb{F}}}
\def\sG{{\mathbb{G}}}
\def\sH{{\mathbb{H}}}
\def\sI{{\mathbb{I}}}
\def\sJ{{\mathbb{J}}}
\def\sK{{\mathbb{K}}}
\def\sL{{\mathbb{L}}}
\def\sM{{\mathbb{M}}}
\def\sN{{\mathbb{N}}}
\def\sO{{\mathbb{O}}}
\def\sP{{\mathbb{P}}}
\def\sQ{{\mathbb{Q}}}
\def\sR{{\mathbb{R}}}
\def\sS{{\mathbb{S}}}
\def\sT{{\mathbb{T}}}
\def\sU{{\mathbb{U}}}
\def\sV{{\mathbb{V}}}
\def\sW{{\mathbb{W}}}
\def\sX{{\mathbb{X}}}
\def\sY{{\mathbb{Y}}}
\def\sZ{{\mathbb{Z}}}

\def\emLambda{{\Lambda}}
\def\emA{{A}}
\def\emB{{B}}
\def\emC{{C}}
\def\emD{{D}}
\def\emE{{E}}
\def\emF{{F}}
\def\emG{{G}}
\def\emH{{H}}
\def\emI{{I}}
\def\emJ{{J}}
\def\emK{{K}}
\def\emL{{L}}
\def\emM{{M}}
\def\emN{{N}}
\def\emO{{O}}
\def\emP{{P}}
\def\emQ{{Q}}
\def\emR{{R}}
\def\emS{{S}}
\def\emT{{T}}
\def\emU{{U}}
\def\emV{{V}}
\def\emW{{W}}
\def\emX{{X}}
\def\emY{{Y}}
\def\emZ{{Z}}
\def\emSigma{{\Sigma}}


ewcommand{\etens}[1]{\mathsfit{#1}}
\def\etLambda{{\etens{\Lambda}}}
\def\etA{{\etens{A}}}
\def\etB{{\etens{B}}}
\def\etC{{\etens{C}}}
\def\etD{{\etens{D}}}
\def\etE{{\etens{E}}}
\def\etF{{\etens{F}}}
\def\etG{{\etens{G}}}
\def\etH{{\etens{H}}}
\def\etI{{\etens{I}}}
\def\etJ{{\etens{J}}}
\def\etK{{\etens{K}}}
\def\etL{{\etens{L}}}
\def\etM{{\etens{M}}}
\def\etN{{\etens{N}}}
\def\etO{{\etens{O}}}
\def\etP{{\etens{P}}}
\def\etQ{{\etens{Q}}}
\def\etR{{\etens{R}}}
\def\etS{{\etens{S}}}
\def\etT{{\etens{T}}}
\def\etU{{\etens{U}}}
\def\etV{{\etens{V}}}
\def\etW{{\etens{W}}}
\def\etX{{\etens{X}}}
\def\etY{{\etens{Y}}}
\def\etZ{{\etens{Z}}}


ewcommand{\calA}{{\cal A}}

ewcommand{\calB}{{\cal B}}

ewcommand{\calC}{{\cal C}}

ewcommand{\calD}{{\cal D}}

ewcommand{\calDx}{{\cal D}_x}

ewcommand{\calE}{{\cal E}}

ewcommand{\cale}{{\cal e}}

ewcommand{\calF}{{\cal F}}

ewcommand{\calG}{{\cal G}}

ewcommand{\calH}{{\cal H}}

ewcommand{\calHX}{{\cal H}_X}

ewcommand{\calHy}{{\cal H}_y}

ewcommand{\calI}{{\cal I}}

ewcommand{\calK}{{\cal K}}

ewcommand{\calM}{{\cal M}}

ewcommand{\calN}{{\cal N}}

ewcommand{\caln}{{\cal n}}

ewcommand{\calNP}{{\cal NP}}

ewcommand{\calMp}{\calM^+}

ewcommand{\calMm}{\calM^-}

ewcommand{\calMo}{\calM^o}

ewcommand{\Ctest}{C_*}

ewcommand{\calL}{{\cal L}}

ewcommand{\calP}{{\cal P}}

ewcommand{\calq}{{\cal q}}

ewcommand{\calQ}{{\cal Q}}

ewcommand{\calR}{{\cal R}}

ewcommand{\calS}{{\cal S}}

ewcommand{\calSstar}{\calS_*}

ewcommand{\calT}{{\cal T}}

ewcommand{\calV}{{\cal V}}

ewcommand{\calv}{{\cal v}}

ewcommand{\calX}{{\cal X}}

ewcommand{\calY}{{\cal Y}}



ewcommand{\ecoli}{\mbox{{\it E. coli}}}

ewcommand{\doPearl}{\mbox{do}}

ewcommand{\data}{\calD}

ewcommand{\model}{\calM}

ewcommand{\dataTrain}{\calD_{\mbox{train}}}

ewcommand{\dataTest}{\calD_{\mbox{test}}}

ewcommand{\dataValid}{\calD_{\mbox{valid}}}

ewcommand{\futuredata}{	ilde{\calD}}

ewcommand{\algo}{\calA}

ewcommand{\fitAlgo}{\calF}

ewcommand{\predictAlgo}{\calP}

ewcommand{\err}{\mbox{err}}

ewcommand{\logit}{\mbox{logit}}

ewcommand{\parent}{\mbox{pa}}


ewcommand{\pdata}{p_{
m{data}}}

ewcommand{\ptrain}{\hat{p}_{
m{data}}}

ewcommand{\Ptrain}{\hat{P}_{
m{data}}}

ewcommand{\pmodel}{p_{
m{model}}}

ewcommand{\Pmodel}{P_{
m{model}}}

ewcommand{\ptildemodel}{	ilde{p}_{
m{model}}}

ewcommand{\pencode}{p_{
m{encoder}}}

ewcommand{\pdecode}{p_{
m{decoder}}}

ewcommand{\precons}{p_{
m{reconstruct}}}


ewcommand{\laplace}{\mathrm{Laplace}} %

ewcommand{\ind}[1]{\mathbb{I}(#1)}


ewcommand{\E}{\mathbb{E}}

ewcommand{\Ls}{\mathcal{L}}

ewcommand{\R}{\mathbb{R}}

ewcommand{\emp}{	ilde{p}}

ewcommand{\lr}{\alpha}

ewcommand{
eg}{\lambda}

ewcommand{
ect}{\mathrm{rectifier}}

ewcommand{\softmax}{\mathrm{softmax}}

ewcommand{\sigmoid}{\sigma}

ewcommand{\softplus}{\zeta}

ewcommand{\KL}{D_{\mathrm{KL}}}

ewcommand{\Var}{\mathrm{Var}}

ewcommand{\standarderror}{\mathrm{SE}}

ewcommand{\Cov}{\mathrm{Cov}}

ewcommand{
ormlzero}{L^0}

ewcommand{
ormlone}{L^1}

ewcommand{
ormltwo}{L^2}

ewcommand{
ormlp}{L^p}

ewcommand{
ormmax}{L^\infty}


ewcommand{\parents}{Pa} %

\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}

\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\Tr}{Tr}
\let\ab\allowbreak