Merge pull request #65 from slds-lmu/update-latex-math

latex-math/basic-math.tex

@@ -1,11 +1,11 @@
 % math spaces
-\ifdefined\N                                                                
+\ifdefined\N
 \renewcommand{\N}{\mathds{N}} % N, naturals
-\else \newcommand{\N}{\mathds{N}} \fi 
+\else \newcommand{\N}{\mathds{N}} \fi
 \newcommand{\Z}{\mathds{Z}} % Z, integers
 \newcommand{\Q}{\mathds{Q}} % Q, rationals
 \newcommand{\R}{\mathds{R}} % R, reals
-\ifdefined\C 
+\ifdefined\C
   \renewcommand{\C}{\mathds{C}} % C, complex
 \else \newcommand{\C}{\mathds{C}} \fi
 \newcommand{\continuous}{\mathcal{C}} % C, space of continuous functions
@@ -19,10 +19,10 @@
 
 % basic math stuff
 \newcommand{\xt}{\tilde x} % x tilde
-\newcommand{\argmax}{\operatorname{arg\,max}} % argmax
-\newcommand{\argmin}{\operatorname{arg\,min}} % argmin
+\DeclareMathOperator*{\argmax}{arg\,max} % argmax
+\DeclareMathOperator*{\argmin}{arg\,min} % argmin
 \newcommand{\argminlim}{\mathop{\mathrm{arg\,min}}\limits} % argmax with limits
-\newcommand{\argmaxlim}{\mathop{\mathrm{arg\,max}}\limits} % argmin with limits  
+\newcommand{\argmaxlim}{\mathop{\mathrm{arg\,max}}\limits} % argmin with limits
 \newcommand{\sign}{\operatorname{sign}} % sign, signum
 \newcommand{\I}{\mathbb{I}} % I, indicator
 \newcommand{\order}{\mathcal{O}} % O, order

latex-math/basic-ml.tex

@@ -1,6 +1,7 @@
 % machine learning
 \newcommand{\Xspace}{\mathcal{X}} % X, input space
 \newcommand{\Yspace}{\mathcal{Y}} % Y, output space
+\newcommand{\Zspace}{\mathcal{Z}} % Space of sampled datapoints ! Also defined identically in ml-online.tex !
 \newcommand{\nset}{\{1, \ldots, n\}} % set from 1 to n
 \newcommand{\pset}{\{1, \ldots, p\}} % set from 1 to p
 \newcommand{\gset}{\{1, \ldots, g\}} % set from 1 to g
@@ -10,23 +11,23 @@
 \newcommand{\xtil}{\tilde{\mathbf{x}}} % vector x-tilde (bold)
 \newcommand{\yv}{\mathbf{y}} % vector y (bold)
 \newcommand{\xy}{(\xv, y)} % observation (x, y)
-\newcommand{\xvec}{\left(x_1, \ldots, x_p\right)^\top} % (x1, ..., xp) 
+\newcommand{\xvec}{\left(x_1, \ldots, x_p\right)^\top} % (x1, ..., xp)
 \newcommand{\Xmat}{\mathbf{X}} % Design matrix
 \newcommand{\allDatasets}{\mathds{D}} % The set of all datasets
-\newcommand{\allDatasetsn}{\mathds{D}_n}  % The set of all datasets of size n 
+\newcommand{\allDatasetsn}{\mathds{D}_n}  % The set of all datasets of size n
 \newcommand{\D}{\mathcal{D}} % D, data
 \newcommand{\Dn}{\D_n} % D_n, data of size n
 \newcommand{\Dtrain}{\mathcal{D}_{\text{train}}} % D_train, training set
 \newcommand{\Dtest}{\mathcal{D}_{\text{test}}} % D_test, test set
 \newcommand{\xyi}[1][i]{\left(\xv^{(#1)}, y^{(#1)}\right)} % (x^i, y^i), i-th observation
 \newcommand{\Dset}{\left( \xyi[1], \ldots, \xyi[n]\right)} % {(x1,y1)), ..., (xn,yn)}, data
-\newcommand{\defAllDatasetsn}{(\Xspace \times \Yspace)^n} % Def. of the set of all datasets of size n 
-\newcommand{\defAllDatasets}{\bigcup_{n \in \N}(\Xspace \times \Yspace)^n} % Def. of the set of all datasets 
+\newcommand{\defAllDatasetsn}{(\Xspace \times \Yspace)^n} % Def. of the set of all datasets of size n
+\newcommand{\defAllDatasets}{\bigcup_{n \in \N}(\Xspace \times \Yspace)^n} % Def. of the set of all datasets
 \newcommand{\xdat}{\left\{ \xv^{(1)}, \ldots, \xv^{(n)}\right\}} % {x1, ..., xn}, input data
 \newcommand{\ydat}{\left\{ \yv^{(1)}, \ldots, \yv^{(n)}\right\}} % {y1, ..., yn}, input data
 \newcommand{\yvec}{\left(y^{(1)}, \hdots, y^{(n)}\right)^\top} % (y1, ..., yn), vector of outcomes
 \renewcommand{\xi}[1][i]{\xv^{(#1)}} % x^i, i-th observed value of x
-\newcommand{\yi}[1][i]{y^{(#1)}} % y^i, i-th observed value of y 
+\newcommand{\yi}[1][i]{y^{(#1)}} % y^i, i-th observed value of y
 \newcommand{\xivec}{\left(x^{(i)}_1, \ldots, x^{(i)}_p\right)^\top} % (x1^i, ..., xp^i), i-th observation vector
 \newcommand{\xj}{\xv_j} % x_j, j-th feature
 \newcommand{\xjvec}{\left(x^{(1)}_j, \ldots, x^{(n)}_j\right)^\top} % (x^1_j, ..., x^n_j), j-th feature vector
@@ -40,7 +41,7 @@
 \newcommand{\preimageInducer}{\left(\defAllDatasets\right)\times\Lam} % Set of all datasets times the hyperparameter space
 \newcommand{\preimageInducerShort}{\allDatasets\times\Lam} % Set of all datasets times the hyperparameter space
 % Inducer / Inducing algorithm
-\newcommand{\ind}{\mathcal{I}} % Inducer, inducing algorithm, learning algorithm 
+\newcommand{\ind}{\mathcal{I}} % Inducer, inducing algorithm, learning algorithm
 
 % continuous prediction function f
 \newcommand{\ftrue}{f_{\text{true}}}  % True underlying function (if a statistical model is assumed)
@@ -61,8 +62,8 @@
 \newcommand{\fhDtrain}{\fh_{\Dtrain}} % fhat_Dtrain, estimate of f based on D
 \newcommand{\fhDnlam}{\fh_{\Dn, \lamv}} %model learned on Dn with hp lambda
 \newcommand{\fhDlam}{\fh_{\D, \lamv}} %model learned on D with hp lambda
-\newcommand{\fhDnlams}{\fh_{\Dn, \lamv^\ast}} %model learned on Dn with optimal hp lambda 
-\newcommand{\fhDlams}{\fh_{\D, \lamv^\ast}} %model learned on D with optimal hp lambda 
+\newcommand{\fhDnlams}{\fh_{\Dn, \lamv^\ast}} %model learned on Dn with optimal hp lambda
+\newcommand{\fhDlams}{\fh_{\D, \lamv^\ast}} %model learned on D with optimal hp lambda
 
 % discrete prediction function h
 \newcommand{\hx}{h(\xv)} % h(x), discrete prediction function
@@ -91,12 +92,12 @@
 \newcommand{\argmint}{\argmin_{\thetab \in \Theta}} % argmin theta
 
 % densities + probabilities
-% pdf of x 
+% pdf of x
 \newcommand{\pdf}{p} % p
 \newcommand{\pdfx}{p(\xv)} % p(x)
 \newcommand{\pixt}{\pi(\xv~|~ \thetab)} % pi(x|theta), pdf of x given theta
 \newcommand{\pixit}[1][i]{\pi\left(\xi[#1] ~|~ \thetab\right)} % pi(x^i|theta), pdf of x given theta
-\newcommand{\pixii}[1][i]{\pi\left(\xi[#1]\right)} % pi(x^i), pdf of i-th x 
+\newcommand{\pixii}[1][i]{\pi\left(\xi[#1]\right)} % pi(x^i), pdf of i-th x
 
 % pdf of (x, y)
 \newcommand{\pdfxy}{p(\xv,y)} % p(x, y)
@@ -134,7 +135,7 @@
 
 % probababilistic
 \newcommand{\bayesrulek}[1][k]{\frac{\P(\xv | y= #1) \P(y= #1)}{\P(\xv)}} % Bayes rule
-\newcommand{\muk}{\bm{\mu_k}} % mean vector of class-k Gaussian (discr analysis) 
+\newcommand{\muk}{\bm{\mu_k}} % mean vector of class-k Gaussian (discr analysis)
 
 % residual and margin
 \newcommand{\eps}{\epsilon} % residual, stochastic
@@ -192,4 +193,4 @@
 
 % lm
 \newcommand{\thx}{\thetab^\top \xv} % linear model
-\newcommand{\olsest}{(\Xmat^\top \Xmat)^{-1} \Xmat^\top \yv} % OLS estimator in LM 
+\newcommand{\olsest}{(\Xmat^\top \Xmat)^{-1} \Xmat^\top \yv} % OLS estimator in LM

latex-math/ml-interpretable.tex

@@ -29,8 +29,5 @@
 \newcommand{\Gspace}{\mathcal{G}} % Hypothesis space for surrogate model
 \newcommand{\neigh}{\phi_{\xv}} % Proximity measure
 \newcommand{\zv}{\mathbf{z}} % Sampled datapoints for surrogate
-\ifdefined \Zspace \else
-\newcommand{\Zspace}{\mathcal{Z}} % Space of sampled datapoints ! Also defined identically in ml-online.tex !
-\fi
 \newcommand{\Gower}{d_G} % Gower distance
 

latex-math/ml-online.tex

@@ -1,16 +1,10 @@
-\renewcommand{\l}{L}
 \newcommand{\Aspace}{\mathcal{A}}
-%\renewcommand{\Zspace}{\mathcal{Z}}
-\ifdefined \Zspace \else
-\newcommand{\Zspace}{\mathcal{Z}} % Space of sampled datapoints ! Also defined identically in ml-interpretable.tex !
-\fi
 \newcommand{\norm}[1]{\left|\left|#1\right|\right|_2}
-
-\newcommand{\llin}{\l^{\texttt{lin}}}
-\newcommand{\lzeroone}{\l^{0-1}}
-\newcommand{\lhinge}{\l^{\texttt{hinge}}}
-\newcommand{\lexphinge}{\widetilde{\l^{\texttt{hinge}}}}
-\newcommand{\lconv}{\l^{\texttt{conv}}}
+\newcommand{\llin}{L^{\texttt{lin}}}
+\newcommand{\lzeroone}{L^{0-1}}
+\newcommand{\lhinge}{L^{\texttt{hinge}}}
+\newcommand{\lexphinge}{\widetilde{L^{\texttt{hinge}}}}
+\newcommand{\lconv}{L^{\texttt{conv}}}
 \newcommand{\FTL}{\texttt{FTL}}
 \newcommand{\FTRL}{\texttt{FTRL}}
 \newcommand{\OGD}{{\texttt{OGD}}}