Merge pull request #21 from slds-lmu/RF-notation

Rf notation

basic-math.tex

@@ -42,9 +42,11 @@
 \newcommand{\sumik}{\sum\limits_{i=1}^k} % summation from i=1 to k
 \newcommand{\sumkg}{\sum\limits_{k=1}^g} % summation from k=1 to g
 \newcommand{\sumjg}{\sum\limits_{j=1}^g} % summation from j=1 to g
+\newcommand{\summM}{\sum\limits_{m=1}^M} % summation from m=1 to M
 \newcommand{\meanin}{\frac{1}{n} \sum\limits_{i=1}^n} % mean from i=1 to n
 \newcommand{\meanim}{\frac{1}{m} \sum\limits_{i=1}^m} % mean from i=1 to n
 \newcommand{\meankg}{\frac{1}{g} \sum\limits_{k=1}^g} % mean from k=1 to g
+\newcommand{\meanmM}{\frac{1}{M} \sum\limits_{m=1}^M} % mean from m=1 to M
 \newcommand{\prodin}{\prod\limits_{i=1}^n} % product from i=1 to n
 \newcommand{\prodkg}{\prod\limits_{k=1}^g} % product from k=1 to g
 \newcommand{\prodjp}{\prod\limits_{j=1}^p} % product from j=1 to p

ml-ensembles.tex

@@ -2,12 +2,25 @@
 \newcommand{\bl}[1][m]{b^{[#1]}} % baselearner, default m
 \newcommand{\blh}[1][m]{\hat{b}^{[#1]}} % estimated base learner, default m 
 \newcommand{\blx}[1][m]{b^{[#1]}(\xv)} % baselearner, default m
+\newcommand{\blf}[1][m]{f^{[#1]}} % baselearner: scores, default m
+\newcommand{\blfh}[1][m]{\hat{f}^{[#1]}} % estimated baselearner: scores, default m
+\newcommand{\blfhx}[1][m]{\hat{f}^{[#1]}(\xv)} % estimated baselearner: scores of x, default m
+\newcommand{\bll}[1][m]{h^{[#1]}} % baselearner: hard labels, default m
+\newcommand{\bllh}[1][m]{\hat{h}^{[#1]}} % estimated baselearner: hard labels, default m
+\newcommand{\bllhx}[1][m]{\hat{h}^{[#1]}(\xv)} % estimated baselearner: hard labels of x, default m
+\newcommand{\blp}[1][m]{\pi^{[#1]}} % baselearner: probabilities, default m
+\newcommand{\blph}[1][m]{\hat{\pi}^{[#1]}} % estimated baselearner: probabilities, default m
+\newcommand{\blphxk}[1][m]{\hat{\pi}_{k}^{[#1]}(\xv)} % estimated baselearner: probabilities of x for class k, default m
 \newcommand{\fM}{f^{[M]}(\xv)} % ensembled predictor
 \newcommand{\fMh}{\hat f^{[M]}(\xv)} % estimated ensembled predictor
 \newcommand{\ambifM}{\Delta\left(\fM\right)} % ambiguity/instability of ensemble
 \newcommand{\betam}[1][m]{\beta^{[#1]}} % weight of basemodel m
 \newcommand{\betamh}[1][m]{\hat{\beta}^{[#1]}} % weight of basemodel m with hat
 \newcommand{\betaM}{\beta^{[M]}} % last baselearner
+\newcommand{\ib}{\mathrm{IB}} % In-Bag (IB)
+\newcommand{\ibm}{\ib^{[m]}} % In-Bag (IB) for m-th bootstrap
+\newcommand{\oob}{\mathrm{OOB}} % Out-of-Bag (OOB)
+\newcommand{\oobm}{\oob^{[m]}} % Out-of-Bag (OOB) for m-th bootstrap
 
 % ml - boosting
 \newcommand{\fm}[1][m]{f^{[#1]}} % prediction in iteration m