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| 1 | +\newcommand{\field}[1]{\mathbb{#1}} |
| 2 | +\newcommand{\set}[1]{\mathcal{#1}} |
| 3 | +\newcommand{\fY}{\set{Y}} |
| 4 | +\newcommand{\fX}{\set{X}} |
| 5 | +\newcommand{\fF}{\set{F}} |
| 6 | +\newcommand{\fD}{\set{D}} |
| 7 | + |
| 8 | +\newcommand{\R}{\field{R}} |
| 9 | +\newcommand{\Nat}{\field{N}} |
| 10 | + |
| 11 | +\renewcommand{\Pr}{\field{P}} |
| 12 | +\newcommand{\Ind}{\mathds{1}} |
| 13 | +\newcommand{\E}{\field{E}} |
| 14 | +\newcommand{\Var}{\mathrm{Var}} |
| 15 | + |
| 16 | +\DeclareMathOperator*{\argmin}{arg\,min} |
| 17 | +\DeclareMathOperator*{\argmax}{arg\,max} |
| 18 | + |
| 19 | +\DeclareMathOperator{\sign}{sign} |
| 20 | + |
| 21 | +\newcommand{\RiskD}{L_{\fD}} |
| 22 | +\newcommand{\RiskS}{L_{S}} |
| 23 | +\newcommand{\RiskSi}{L_{S_i}} |
| 24 | +\newcommand{\RiskV}{L_{V}} |
| 25 | +\newcommand{\RiskT}{L_{T}} |
| 26 | + |
| 27 | +\newcommand{\blambda}{\boldsymbol{\lambda}} |
| 28 | +\newcommand{\bnu}{\boldsymbol{\nu}} |
| 29 | +\newcommand{\btheta}{\boldsymbol{\theta}} |
| 30 | +\newcommand{\bx}{\boldsymbol{x}} |
| 31 | +\newcommand{\bX}{\boldsymbol{X}} |
| 32 | +\newcommand{\bw}{\boldsymbol{w}} |
| 33 | +\newcommand{\bu}{\boldsymbol{u}} |
| 34 | +\newcommand{\bv}{\boldsymbol{v}} |
| 35 | +\newcommand{\by}{\boldsymbol{y}} |
| 36 | +\newcommand{\bz}{\boldsymbol{z}} |
| 37 | +\newcommand{\bV}{\boldsymbol{V}} |
| 38 | +\newcommand{\bD}{\boldsymbol{D}} |
| 39 | +\newcommand{\bphi}{\boldsymbol{\phi}} |
| 40 | +\newcommand{\bPhi}{\boldsymbol{\Phi}} |
| 41 | +\newcommand{\bxi}{\boldsymbol{\xi}} |
| 42 | +\newcommand{\bbeta}{\boldsymbol{\beta}} |
| 43 | +\newcommand{\balpha}{\boldsymbol{\alpha}} |
| 44 | + |
| 45 | +\newcommand{\newdef}[1]{\textbf{#1}} |
| 46 | + |
| 47 | +\newcommand{\norm}[1]{\left\lVert#1\right\rVert} |
| 48 | + |
| 49 | +\DeclareMathOperator{\Conv}{conv} |
| 50 | +\newcommand\braces[1]{\{#1\}} |
| 51 | +\newcommand\brackets[1]{[#1]} |
| 52 | +\newcommand\dotp[1]{\langle #1 \rangle} |
| 53 | +\newcommand\Parens[1]{\mleft(#1\mright)} |
| 54 | +\newcommand\Norm[1]{\mleft\|#1\mright\|} |
| 55 | +\newcommand\Braces[1]{\mleft\{#1\mright\}} |
| 56 | +\newcommand\Brackets[1]{\mleft[#1\mright]} |
| 57 | +\newcommand\Ceil[1]{\mleft\lceil#1\mright\rceil} |
| 58 | +\newcommand\Abs[1]{\mleft|#1\mright|} |
| 59 | +\newcommand\Dotp[1]{\mleft\langle#1\mright\rangle} |
| 60 | + |
| 61 | +\newcommand{\Proj}{\ensuremath{\operatorname{Proj}}} |
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