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Changes between Version 25 and Version 26 of OfficialTolArchiveNetworkBysPrior


Ignore:
Timestamp:
Jun 16, 2011, 3:31:41 PM (14 years ago)
Author:
Víctor de Buen Remiro
Comment:

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  • OfficialTolArchiveNetworkBysPrior

    v25 v26  
    118118
    119119 [[LatexEquation(  C x\sim N\left(\mu,\Sigma\right) )]]
    120  [[LatexEquation(  C\in\mathbb{R}^{n\times k}\wedge\mu\in\mathbb{R}^{k}\wedge\Sigma\in\mathbb{R}^{k\times k}\wedge\mathrm{rank}\left(\Sigma\right)=k )]]
     120 [[LatexEquation(  C\in\mathbb{R}^{k\times n}\wedge\mu\in\mathbb{R}^{k}\wedge\Sigma\in\mathbb{R}^{k\times k}\wedge\mathrm{rank}\left(\Sigma\right)=k )]]
    121121
    122122which likelihood function is
    … …  
    130130The gradient is
    131131
    132  [[LatexEquation( \left(\frac{\partial L\left(x\right)}{\partial x_{i}}\right)_{i=1\ldots n}=-\Sigma^{-1}\left(Cx-\mu\right) )]]
     132 [[LatexEquation( \left(\frac{\partial L\left(x\right)}{\partial x_{i}}\right)_{i=1\ldots n}=-C^{T}\Sigma^{-1}\left(Cx-\mu\right) )]]
    133133
    134134and the hessian
    135135
    136  [[LatexEquation( \left(\frac{\partial^{2}L\left(x\right)}{\partial x_{i}\partial x_{j}}\right)_{i,j=1\ldots n}=-C\Sigma^{-1}C^{T} )]]
     136 [[LatexEquation( \left(\frac{\partial^{2}L\left(x\right)}{\partial x_{i}\partial x_{j}}\right)_{i,j=1\ldots n}=-C^{T}\Sigma^{-1}C )]]
    137137
    138138==== Hierarquical relation of simple homogenity ====