ml-interpretable.tex

%%%%%% perturbed data
\newcommand{\pert}[3]{\ifthenelse{\equal{#2}{}}{\tilde{#1}}{\ifthenelse{\equal{#3}{}}{\tilde{#1}^{#2}}{\tilde{#1}^{#2|#3}}}}	% command to express that for #1 the subset #2 was perturbed given subset #3

%%%%%% marginalized functions
\newcommand{\fj}{f_j} % marginal function f_j, depending on feature j
\newcommand{\fnj}{f_{-j}} % marginal function f_{-j}, depending on all features but j
\newcommand{\fS}{f_S} % marginal function f_S depending on feature set S
\newcommand{\fC}{f_C} % marginal function f_C depending on feature set C
\newcommand{\fhj}{\fh_j} % marginal function fh_j, depending on feature j
\newcommand{\fhnj}{\fh_{-j}} % marginal function fh_{-j}, depending on all features but j
\newcommand{\fhS}{\fh_S} % marginal function fh_S depending on feature set S
\newcommand{\fhC}{\fh_C} % marginal function fh_C depending on feature set C
\newcommand{\XSmat}{\Xmat_S} % Design matrix subset
\newcommand{\XCmat}{\Xmat_C} % Design matrix subset
\newcommand{\Xnj}{\Xmat_{-j}} % Design matrix subset -j = {1, .., j-1, j+1, ..., p}

%%%%% ICE
\newcommand{\fhice}[1]{\fh_{#1,ICE}} % ICE function

%%%%% Shapley values
\newcommand{\Scupj}{S \cup \{j\}} % coalition S but without player j
\newcommand{\Scupk}{S \cup \{k\}} % coalition S but without player k
\newcommand{\SsubP}{S \subseteq P} % coalition S subset of P
\newcommand{\SsubPnoj}{\SsubP \setminus \{j\}} % coalition S subset of P without player j
\newcommand{\SsubPnojk}{\SsubP \setminus \{j,k\}} % coalition S subset of P without player k
\newcommand{\phiij}{\hat{\phi}_j^{(i)}} % Shapley value for feature j and observation i

%%%%% LIME
\newcommand{\Gspace}{\mathcal{G}} % Hypothesis space for surrogate model
\newcommand{\neigh}{\phi_{\xv}} % Proximity measure
\newcommand{\zv}{\mathbf{z}} % Sampled datapoints for surrogate
\newcommand{\Gower}{d_G} % Gower distance