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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x10aa6a190>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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wd+/ekHmr4+PjvWVBpzY9duxYhdKTmvTp04f77ruPe++9l59++on+/fvz9NNP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\neMx5m5s4kQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a8fb350>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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EMMTknquuHGpqq4HQUhtpQmtrBAXLPHwO3CYSV5JiOpAJdAc+Br4NaWcEtr7R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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10aa33fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"def basic_linear_reg(x, y):\n",
" # linear reg on 2 axes\n",
" length = len(x)\n",
" sum_x = sum(x)\n",
" sum_y = sum(y)\n",
" sum_xsq = sum(map(lambda a: a * a, x))\n",
" sum_xy = sum(map(lambda a, b: a * b, x, y))\n",
" \n",
" a = (sum_xy - sum_x * sum_y / length) / (sum_xsq - sum(x) ** 2 / length)\n",
" b = (sum_y - a * sum_x) / length\n",
" return [a, b]\n",
"\n",
"x = np.random.uniform(0, 100, 1000)\n",
"y = np.log(x) + np.random.normal(0, 0.3, 1000)\n",
"\n",
"plt.figure(1)\n",
"plt.scatter(x, y, label=\"log(x) with some noise\")\n",
"plt.plot(np.arange(1, 100), np.log(np.arange(1, 100)), c=\"chartreuse\", label=\"log(x) true function\")\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"f(x) = log(x)\")\n",
"plt.legend(loc=\"best\")\n",
"plt.title(\"A Basic Log Function\")\n",
"\n",
"plt.figure(2)\n",
"reg = basic_linear_reg(x, y)\n",
"r_x, r_y = zip(*((i, i*reg[0] + reg[1]) for i in range(100)))\n",
"plt.plot(r_x, r_y, c='g', label=\"linear regression\")\n",
"plt.scatter(x, y - (x * reg[0] + reg[1]), c='red', label=\"residuals\")\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.legend(loc=\"best\")\n",
"\n",
"plt.figure(3)\n",
"r_x, r_y = zip(*((i, i*reg[0] + reg[1]) for i in range(100)))\n",
"plt.plot(r_x, r_y, c='g', label=\"linear regression\")\n",
"plt.scatter(x, y - (x * reg[0] + reg[1]), c='red', label=\"residuals\")\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.legend(loc=\"best\")"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x10dc52fd0>"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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TGcl4bQfUxBYGZ1+Wrc+Pv0XuHvmAtLnsNrn4yTh5uRx5aBty37YYufG/p8tF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\n/hvfRu04h+1AKRBnjIkEPFiViTXWdhGZBwQXxlR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"text/plain": [
"<matplotlib.figure.Figure at 0x10ad2eb90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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5CW8Uv8Gt594aatMEQWhEBB2u0VovAqJdsCWiWHtgLenJ6XRp1YXebXtTML+A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\nKrX9VAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10caacb90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"from sklearn.ensemble import RandomForestRegressor\n",
"from sklearn.learning_curve import learning_curve\n",
"\n",
"rfg = RandomForestRegressor()\n",
"r_x = np.array(r_x)\n",
"rfg.fit(x.reshape(-1, 1), y)\n",
"\n",
"plt.plot(r_x, rfg.predict(r_x.reshape(-1, 1)), c=\"yellow\", label = \"random forest fit\")\n",
"plt.plot(np.arange(1, 100), np.log(np.arange(1, 100)), c=\"chartreuse\", label=\"log(x) true function\")\n",
"plt.scatter(x, y, label=\"log(x) with some noise\")\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"\n",
"plt.figure(2)\n",
"plt.plot(r_x, rfg.predict(r_x.reshape(-1, 1)), c=\"green\", label = \"random forest fit\")\n",
"plt.scatter(x, y - rfg.predict(x.reshape(-1, 1)), c=\"r\", label = \"residual\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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