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udlbook
2022-11-08 10:30:40 +00:00
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commit bd3b2262c4
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CM20315_Gradients_I.ipynb
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@@ -4,7 +4,8 @@
"metadata": { "metadata": {
"colab": { "colab": {
"provenance": [], "provenance": [],
"authorship_tag": "ABX9TyOVcqVtSrxHzifl2v6uaO71", "collapsed_sections": [],
"authorship_tag": "ABX9TyMDEfAZvjcjpvBNmdrYv3EW",
"include_colab_link": true "include_colab_link": true
}, },
"kernelspec": { "kernelspec": {
@@ -46,7 +47,7 @@
"Suppose that we know the current values of $\\beta_{0},\\beta_{1},\\beta_{2},\\beta_{3},\\beta_{4},\\omega_{0},\\omega_{1},\\omega_{2},\\omega_{3},\\omega_{4}$, and $x$. We could obviously calculate $y$. But we also want to know how $y$ changes when we make a small change to $\\beta_{0},\\beta_{1},\\beta_{2},\\beta_{3},\\beta_{4},\\omega_{0},\\omega_{1},\\omega_{2},\\omega_{3}$, or $\\omega_{4}$. In other words, we want to compute the ten derivatives:\n", "Suppose that we know the current values of $\\beta_{0},\\beta_{1},\\beta_{2},\\beta_{3},\\beta_{4},\\omega_{0},\\omega_{1},\\omega_{2},\\omega_{3},\\omega_{4}$, and $x$. We could obviously calculate $y$. But we also want to know how $y$ changes when we make a small change to $\\beta_{0},\\beta_{1},\\beta_{2},\\beta_{3},\\beta_{4},\\omega_{0},\\omega_{1},\\omega_{2},\\omega_{3}$, or $\\omega_{4}$. In other words, we want to compute the ten derivatives:\n",
"\n", "\n",
"\\begin{eqnarray*}\n", "\\begin{eqnarray*}\n",
"\\frac{\\partial y}{\\partial \\beta_{0}}, \\quad \\frac{\\partial y}{\\partial \\beta_{1}}, \\quad \\frac{\\partial y}{\\partial \\beta_{2}}, \\quad \\frac{\\partial \\beta_{3}}{\\partial d}, \\quad\n", "\\frac{\\partial y}{\\partial \\beta_{0}}, \\quad \\frac{\\partial y}{\\partial \\beta_{1}}, \\quad \\frac{\\partial y}{\\partial \\beta_{2}}, \\quad \\frac{\\partial y }{\\partial \\beta_{3}}, \\quad\n",
"\\frac{\\partial y}{\\partial \\beta_{4}}, \\quad \\frac{\\partial y}{\\partial \\omega_{0}}, \\quad \\frac{\\partial y}{\\partial \\omega_{1}}, \\quad \\frac{\\partial y}{\\partial \\omega_{2}}, \\quad \\frac{\\partial y}{\\partial \\omega_{3}}, \\quad\\mbox{and} \\quad \\frac{\\partial y}{\\partial \\omega_{4}}.\n", "\\frac{\\partial y}{\\partial \\beta_{4}}, \\quad \\frac{\\partial y}{\\partial \\omega_{0}}, \\quad \\frac{\\partial y}{\\partial \\omega_{1}}, \\quad \\frac{\\partial y}{\\partial \\omega_{2}}, \\quad \\frac{\\partial y}{\\partial \\omega_{3}}, \\quad\\mbox{and} \\quad \\frac{\\partial y}{\\partial \\omega_{4}}.\n",
"\\end{eqnarray*}" "\\end{eqnarray*}"
], ],