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  1. % Sets
  2. \newcommand{\N}{\mathbb{N}}
  3. \newcommand{\Z}{\mathbb{Z}}
  4. \newcommand{\R}{\mathbb{R}}
  5. \newcommand{\D}{\mathcal{D}}
  6. \newcommand{\T}{\mathcal{T}}
  7. \newcommand{\Ell}{\mathcal{L}}
  8. % Random Variable
  9. \newcommand{\rv}[1]{\bm{#1}}
  10. \newcommand{\map}[1]{#1^{\text{MAP}}}
  11. % Matrix
  12. \newcommand{\mat}[1]{\bm{#1}}
  13. \newcommand{\inv}{^{\raisebox{.2ex}{$\scriptscriptstyle-\mkern-1.5mu1$}}}
  14. \newcommand{\tran}{^{\mkern-1.5mu\raisebox{.2ex}{$\scriptscriptstyle\mathsf{T}$}}}
  15. \newcommand{\itran}{^{\raisebox{.2ex}{$\scriptscriptstyle-\mkern-1.5mu\mathsf{T}$}}}
  16. \newcommand{\Eye}{\mat{\mathrm{I}}}
  17. % Pseudo Inputs
  18. \newcommand{\ps}[1]{\bar{#1}}
  19. \newcommand{\psmat}[1]{\ps{\mat{#1}}}
  20. % Nicer empty set
  21. \renewcommand{\emptyset}{\varnothing}
  22. % Math operators
  23. % General
  24. \DeclareMathOperator{\id}{id}
  25. \DeclareMathOperator*{\argmax}{argmax}
  26. \DeclareMathOperator*{\argmin}{argmin}
  27. \DeclareMathOperator{\atanTwo}{atan2}
  28. \DeclareMathOperator{\sgn}{sgn}
  29. \DeclareMathOperator{\diag}{diag}
  30. \DeclareMathOperator{\tr}{tr}
  31. \DeclareMathOperator*{\maximize}{maximize}
  32. \DeclareMathOperator*{\minimize}{minimize}
  33. \DeclareMathOperator{\subjectto}{subject\ to}
  34. \DeclareMathOperator{\Oh}{\mathcal{O}}
  35. \newcommand{\Powerset}[1]{2^{#1}}
  36. \newcommand*{\diff}{\mathop{}\!\mathrm{d}}
  37. \DeclarePairedDelimiter{\abs}{\vert}{\vert}
  38. % Probabilities
  39. \DeclareMathOperator{\E}{\mathbb{E}}
  40. \DeclareMathOperator{\cov}{cov}
  41. \DeclareMathOperator{\var}{var}
  42. \DeclareMathOperator{\corr}{\varrho}
  43. \DeclareMathOperator{\p}{p}
  44. \DeclareMathOperator{\q}{q}
  45. \DeclareMathOperator{\KLdiv}{KL}
  46. \DeclareMathOperator{\K}{\mathcal{K}}
  47. \DeclareMathOperator{\Q}{\mathcal{Q}}
  48. \DeclareMathOperator{\Norm}{\mathcal{N}}
  49. \DeclareMathOperator{\Uni}{\mathbb{U}}
  50. \DeclareMathOperator{\Ind}{\mathbb{I}}
  51. \DeclareMathOperator{\GP}{\mathcal{GP}}
  52. \DeclareMathOperator{\SPGP}{\mathcal{SPGP}}
  53. \DeclareMathOperator{\indep}{\perp\mkern-9.5mu\perp}
  54. \DeclareMathOperator{\nindep}{\centernot{\indep}}
  55. \providecommand\given{}
  56. \DeclarePairedDelimiterX{\Cond}[1]{(}{)}{
  57. \renewcommand\given{%
  58. \nonscript\,
  59. \delimsize\vert
  60. \nonscript\,
  61. \mathopen{}
  62. \allowbreak}
  63. #1
  64. }
  65. \makeatletter
  66. \newcommand{\Fun}{\@ifstar\@sfun\@fun}
  67. \newcommand{\@fun}[1]{#1\Cond}
  68. \newcommand{\@sfun}[1]{#1\Cond*}
  69. \makeatother
  70. \newcommand{\Prob}{\p\Cond}
  71. \newcommand{\aProb}{\tilde{\p}\Cond}
  72. \newcommand{\Variat}{\q\Cond}
  73. \newcommand{\Gaussian}{\Norm\Cond}
  74. \newcommand{\Uniform}{\Uni\Cond}
  75. \newcommand{\Indicator}{\Ind\Cond}
  76. \DeclarePairedDelimiterX{\KLdelim}[2]{(}{)}{%
  77. #1\,\delimsize\|\,#2%
  78. }
  79. \newcommand{\KL}{\KLdiv\KLdelim}
  80. \DeclarePairedDelimiterXPP{\Moment}[2]{#1}{[}{]}{}{
  81. \renewcommand\given{%
  82. \nonscript\,
  83. \delimsize\vert
  84. \nonscript\,
  85. \mathopen{}
  86. \allowbreak}
  87. #2
  88. }
  89. \providecommand\with{}
  90. \DeclarePairedDelimiterX{\Set}[1]{\{}{\}}{
  91. \renewcommand\with{%
  92. \nonscript\,
  93. \delimsize\vert
  94. \nonscript\,
  95. \mathopen{}
  96. \allowbreak}
  97. #1
  98. }