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Notebook/chapter08.ipynb

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@@ -132,19 +132,19 @@
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" <br><br>\n",
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" $$\n",
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" \\begin{align*}\n",
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" \\mu_{x_m\\to f_s}(x_m)=\\prod_{\\ell \\in \\mathrm{ne}(x_m)\\,\\verb|\\|f_s}\\mu_{f_{\\ell}\\to x_m}(x_m)\n",
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" \\mu_{x_m\\to f_s}(x_m)=\\prod_{\\ell \\in \\mathrm{ne}(x_m)\\backslash f_s}\\mu_{f_{\\ell}\\to x_m}(x_m)\n",
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" \\end{align*}\n",
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" $$\n",
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"<br><br>\n",
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" 2. A message from a factor node $f_s$ to a variable node $x$ is the product of the factor with messages from all other nodes, marginalized over all variables except the one associated with $x$\n",
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" <br><br>\n",
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" $$\n",
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" \\begin{align*}\n",
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" \\mu_{f_s\\to x}(x)=\\sum_{x_1}\\cdots \\sum_{x_M}f_s(x,x_1,\\cdots,x_M)\\prod_{m\\in \\mathrm{ne}(f_s)\\,\\verb|\\|x}\\mu_{x_m\\to f_s}(x_m)\n",
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" \\mu_{f_s\\to x}(x)=\\sum_{x_1}\\cdots \\sum_{x_M}f_s(x,x_1,\\cdots,x_M)\\prod_{m\\in \\mathrm{ne}(f_s)\\backslash x}\\mu_{x_m\\to f_s}(x_m)\n",
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" \\end{align*}\n",
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" $$\n",
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" <br><br>\n",
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"where $\\mathrm{ne}(f_s)\\,\\verb|\\|x$ denotes the set of factor nodes that are neighbours of $f_s$ with node $x$ removed\n",
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"where $\\mathrm{ne}(f_s)\\backslash x$ denotes the set of factor nodes that are neighbours of $f_s$ with node $x$ removed\n",
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" <br><br>\n",
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" \n",
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" \n",

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