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ml-ensembles.tex
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ml-ensembles.tex
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% ml - bagging, random forest
\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
\newcommand{\fmh}[1][m]{\hat{f}^{[#1]}} % prediction in iteration m
\newcommand{\fmd}[1][m]{f^{[#1-1]}} % prediction m-1
\newcommand{\fmdh}[1][m]{\hat{f}^{[#1-1]}} % prediction m-1
\newcommand{\errm}[1][m]{\text{err}^{[#1]}} % weighted in-sample misclassification rate
\newcommand{\wm}[1][m]{w^{[#1]}} % weight vector of basemodel m
\newcommand{\wmi}[1][m]{w^{[#1](i)}} % weight of obs i of basemodel m
\newcommand{\thetam}[1][m]{\thetav^{[#1]}} % parameters of basemodel m
\newcommand{\thetamh}[1][m]{\hat{\thetav}^{[#1]}} % parameters of basemodel m with hat
\newcommand{\blxt}[1][m]{b(\xv, \thetav^{[#1]})} % baselearner, default m
\newcommand{\ens}{\sum_{m=1}^M \betam \blxt} % ensemble
\newcommand{\rmm}[1][m]{\tilde{r}^{[#1]}} % pseudo residuals
\newcommand{\rmi}[1][m]{\tilde{r}^{[#1](i)}} % pseudo residuals
\newcommand{\Rtm}[1][m]{R_{t}^{[#1]}} % terminal-region
\newcommand{\Tm}[1][m]{T^{[#1]}} % terminal-region
\newcommand{\ctm}[1][m]{c_t^{[#1]}} % mean, terminal-regions
\newcommand{\ctmh}[1][m]{\hat{c}_t^{[#1]}} % mean, terminal-regions with hat
\newcommand{\ctmt}[1][m]{\tilde{c}_t^{[#1]}} % mean, terminal-regions
\newcommand{\Lp}{L^\prime}
\newcommand{\Ldp}{L^{\prime\prime}}
\newcommand{\Lpleft}{\Lp_{\text{left}}}
% ml - boosting iml lecture
\newcommand{\ts}{\thetav^{\star}} % theta*
\newcommand{\bljt}{\bl[j](\xv, \thetav)} % BL j with theta
\newcommand{\bljts}{\bl[j](\xv, \ts)} % BL j with theta*