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Update 04_Regularisation.ipynb

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Pawel Swietojanski 2015-11-02 11:21:57 +00:00
parent dc115a1796
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04_Regularisation.ipynb
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@ -86,9 +86,9 @@
"Hence, the gradient of the cost w.r.t parameter $w_i$ is given as follows:\n", "Hence, the gradient of the cost w.r.t parameter $w_i$ is given as follows:\n",
"\n", "\n",
"(5) $\n", "(5) $\n",
"\\begin{align*}\\frac{\\partial E^n}{\\partial w_i} &= \\frac{\\partial (E^n_{\\text{train}} + \\beta_{L_2} E_{L_2}) }{\\partial w_i} \n", "\\begin{align*}\\frac{\\partial E^n}{\\partial w_i} &= \\frac{\\partial (E^n_{\\text{train}} + \\beta_{L_2} \frac{1}[2} E^n_{L_2}) }{\\partial w_i} \n",
" = \\left( \\frac{\\partial E^n_{\\text{train}}}{\\partial w_i} + \\beta_{L_2} \\frac{\\partial\n", " = \\left( \\frac{\\partial E^n_{\\text{train}}}{\\partial w_i} + \\beta_{L_2} \\frac{\\partial\n",
" E_{L_2}}{\\partial w_i} \\right) \n", " \frac{1}{2}E^n_{L_2}}{\\partial w_i} \\right) \n",
" = \\left( \\frac{\\partial E^n_{\\text{train}}}{\\partial w_i} + \\beta_{L_2} w_i \\right)\n", " = \\left( \\frac{\\partial E^n_{\\text{train}}}{\\partial w_i} + \\beta_{L_2} w_i \\right)\n",
"\\end{align*}\n", "\\end{align*}\n",
"$\n", "$\n",