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udlbook
2023-09-29 12:50:35 +01:00
parent 4a08fa44bf
commit 8c658ac321
1 changed files with 6 additions and 6 deletions
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12
Notebooks/Chap07/7_1_Backpropagation_in_Toy_Model.ipynb
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@@ -4,7 +4,7 @@
"metadata": { "metadata": {
"colab": { "colab": {
"provenance": [], "provenance": [],
"authorship_tag": "ABX9TyOwOpROPBel8eYGzp5DGRkt", "authorship_tag": "ABX9TyP5wHK5E7/el+vxU947K3q8",
"include_colab_link": true "include_colab_link": true
}, },
"kernelspec": { "kernelspec": {
@@ -55,7 +55,7 @@
"This is a composition of the functions $\\cos[\\bullet],\\exp[\\bullet],\\sin[\\bullet]$. I chose these just because you probably already know the derivatives of these functions:\n", "This is a composition of the functions $\\cos[\\bullet],\\exp[\\bullet],\\sin[\\bullet]$. I chose these just because you probably already know the derivatives of these functions:\n",
"\n", "\n",
"\\begin{eqnarray*}\n", "\\begin{eqnarray*}\n",
" \\frac{\\partial \\cos[z]}{\\partial z} = -\\sin[z] \\quad\\quad \\frac{\\partial \\exp[z]}{\\partial z} = \\exp[z] \\quad\\quad \\frac{\\partial \\sin[z]}{\\partial z} = -\\cos[z].\n", " \\frac{\\partial \\cos[z]}{\\partial z} = -\\sin[z] \\quad\\quad \\frac{\\partial \\exp[z]}{\\partial z} = \\exp[z] \\quad\\quad \\frac{\\partial \\sin[z]}{\\partial z} = \\cos[z].\n",
"\\end{eqnarray*}\n", "\\end{eqnarray*}\n",
"\n", "\n",
"Suppose that we have a least squares loss function:\n", "Suppose that we have a least squares loss function:\n",
@@ -107,8 +107,8 @@
" return beta3+omega3 * np.cos(beta2 + omega2 * np.exp(beta1 + omega1 * np.sin(beta0 + omega0 * x)))\n", " return beta3+omega3 * np.cos(beta2 + omega2 * np.exp(beta1 + omega1 * np.sin(beta0 + omega0 * x)))\n",
"\n", "\n",
"def likelihood(x, y, beta0, beta1, beta2, beta3, omega0, omega1, omega2, omega3):\n", "def likelihood(x, y, beta0, beta1, beta2, beta3, omega0, omega1, omega2, omega3):\n",
" diff = fn(x, beta0, beta1, beta2, beta3, omega0, omega1, omega2, omega3) - y ;\n", " diff = fn(x, beta0, beta1, beta2, beta3, omega0, omega1, omega2, omega3) - y\n",
" return diff * diff ;" " return diff * diff"
] ]
}, },
{ {
@@ -123,8 +123,8 @@
{ {
"cell_type": "code", "cell_type": "code",
"source": [ "source": [
"beta0 = 1.0; beta1 = 2.0; beta2 = -3.0; beta3 = 0.4;\n", "beta0 = 1.0; beta1 = 2.0; beta2 = -3.0; beta3 = 0.4\n",
"omega0 = 0.1; omega1 = -0.4; omega2 = 2.0; omega3 = 3.0;\n", "omega0 = 0.1; omega1 = -0.4; omega2 = 2.0; omega3 = 3.0\n",
"x = 2.3; y =2.0\n", "x = 2.3; y =2.0\n",
"l_i_func = likelihood(x,y,beta0,beta1,beta2,beta3,omega0,omega1,omega2,omega3)\n", "l_i_func = likelihood(x,y,beta0,beta1,beta2,beta3,omega0,omega1,omega2,omega3)\n",
"print('l_i=%3.3f'%l_i_func)" "print('l_i=%3.3f'%l_i_func)"