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Created on Cognitive Class Labs
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width = 400, align = \"center\"></a>\n",
"# <center>Non Linear Regression Analysis</center>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression because, as the name implies, linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example on python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Importing required libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Though Linear regression is very good to solve many problems, it cannot be used for all datasets. First recall how linear regression, could model a dataset. It models a linear relation between a dependent variable y and independent variable x. It had a simple equation, of degree 1, for example y = 2*(x) + 3."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 2*(x) + 3\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"#plt.figure(figsize=(8,6))\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regressions are a relationship between independent variables $x$ and a dependent variable $y$ which result in a non-linear function modeled data. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). \n",
"\n",
"$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
"\n",
"Non-linear functions can have elements like exponentials, logarithms, fractions, and others. For example: $$ y = \\log(x)$$\n",
" \n",
"Or even, more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
"y_noise = 20 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"y = np.power(x,2)\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"Y= np.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying logarithmic map from input $x$'s to output variable $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
"\n",
"Please consider that instead of $x$, we can use $X$, which can be polynomial representation of the $x$'s. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
" This is separate from the ipykernel package so we can avoid doing imports until\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"Y = np.log(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"Y = 1-4/(1+np.power(3, X-2))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2019-11-25 05:43:53 URL:https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Year</th>\n",
" <th>Value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1960</td>\n",
" <td>5.918412e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1961</td>\n",
" <td>4.955705e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1962</td>\n",
" <td>4.668518e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1963</td>\n",
" <td>5.009730e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1964</td>\n",
" <td>5.906225e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1965</td>\n",
" <td>6.970915e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1966</td>\n",
" <td>7.587943e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1967</td>\n",
" <td>7.205703e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1968</td>\n",
" <td>6.999350e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1969</td>\n",
" <td>7.871882e+10</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Year Value\n",
"0 1960 5.918412e+10\n",
"1 1961 4.955705e+10\n",
"2 1962 4.668518e+10\n",
"3 1963 5.009730e+10\n",
"4 1964 5.906225e+10\n",
"5 1965 6.970915e+10\n",
"6 1966 7.587943e+10\n",
"7 1967 7.205703e+10\n",
"8 1968 6.999350e+10\n",
"9 1969 7.871882e+10"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"#downloading dataset\n",
"!wget -nv -O china_gdp.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/china_gdp.csv\n",
" \n",
"df = pd.read_csv(\"china_gdp.csv\")\n",
"df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the Dataset ###\n",
"This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it deaccelerates slightly in the 2010s."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,5))\n",
"x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
"plt.plot(x_data, y_data, 'ro')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing a model ###\n",
"\n",
"From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
"since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"Y = 1.0 / (1.0 + np.exp(-X))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"The formula for the logistic function is the following:\n",
"\n",
"$$ \\hat{Y} = \\frac1{1+e^{\\beta_1(X-\\beta_2)}}$$\n",
"\n",
"$\\beta_1$: Controls the curve's steepness,\n",
"\n",
"$\\beta_2$: Slides the curve on the x-axis."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. "
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"def sigmoid(x, Beta_1, Beta_2):\n",
" y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at a sample sigmoid line that might fit with the data:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f3c54fa07f0>]"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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V5tEgjEvl+qMeukgEyN9TTNa0JRw/6WHWbSMZlNoq3CVJMMK4VK4/6qGLhNnq7Yf4wQtfUO6Bv9+uMI8qgZbErYelcv1RoIuEUc7WIib89QuSE+OZc8e59OnYItwlSU2Ecalcf4IKdDMbZ2brzCzfzB7y83pLM/uHma0ws1wzmxj6UkViy+f5+7h+2pe0bdaI1+84l25tm4a7JKmpMC6V648556rewSweWA9cCBQCS4EJzrm8Cvs8DLR0zj1oZu2AdUBH51xpoONmZma67OzsEDRBJPp8vHY3d8xcRreUprxy63DaN28c7pIkSphZjnMu099rwfTQhwP5zrlNvoCeDVxZaR8HNDfvNcnNgCKgrBY1i8Ss91buZPKMHM7q0JzZk0cqzCVkggn0LkBBheeFvm0VPQucDewAVgH3Oec8lQ9kZpPNLNvMsvfu3XuGJYtEr7k5hdz72jIGpbZi1m0jaN00KdwlSQwJJtD9rQRUeZzmYmA50BkYBDxrZqed3XHOTXXOZTrnMtu1a1fjYkWi2StfbOX+OSsY1aMtM24ZTgutZS4hFkygFwKpFZ53xdsTr2gi8Kbzygc2A31CU6JI9Pvrwk38/O3VXNCnPdNuyqRJki4BkdALJtCXAr3MrJuZJQHXAvMq7bMNuADAzDoAZwGbQlmoSDRyzvHURxt4bP4aLh3QiSk3DKVxom5MIXWj2m6Cc67MzO4BFgDxwHTnXK6Z3eF7fQrwG+AlM1uFd4jmQefcvjqsWyTiOef4/QdreeGTTVw1pCtPXD1AN6aQOhXUPHTn3HznXG/nXA/n3GO+bVN8YY5zbodz7iLnXH/n3DnOuZl1WbRIpPN4HI/Oy+WFTzZx/cg0/qAwj34RtKpiIBrIEwmxco/j4TdX8ffsAm77VjceHn+27jIU7SJsVcVAdOm/SAidLPfw339fzt+zC/jRd3oqzGNFhK2qGIh66CIhcqKsnHtf/Yp/5u3mwXF9uHNsj3CXJKESYasqBqIeukgIHCstZ/KMHP6Zt5tHL++rMI81EbaqYiAKdJFaOnKijIkvfcnCDXt5/Kr+3Dy6W7hLklCLsFUVA1Ggi9TCoWMnufHFJSzdcoAnfziIHw6LrB6bhEiEraoYiMbQRc5Q0dFSbpy+hHW7innuusGMO6dTuEuSupSVFXEBXpkCXeQM7Dl8nCzfzZyn3qCbOUtkUKCL1FDhgRKypi1hb/EJ/jZxGKN6tA13SSKAAl2kRjbvO0rWX7+g+EQZM28dwZC01uEuSeT/KNBFgrRuVzFZ05bgcY7XbhvJOV1ahrskkW9QoIsEYVXhIW6cvoTE+Dheu20kvTo0D3dJIqdRoItU48vNRUx6aSktkxN59bYRpKfoZs4SmRToIlX4z7o93DEzh86tkpl5ywg6t0oOd0kiASnQRQJ4f9VOfjT7K3q1b86MW4bTtlmjcJckUiUFuogfc3MKeWDuCgaltuJvE4fTMln3/5TIp0AXqeTlRVv45bxcRvdMYeoNmTRtpF8TiQ76SRXxcc7x7Mf5/OnD9VzYtwPPTBis+39KVFGgi+AN88feW8O0zzbz/cFdeOLqASTGa+06iS76iZUGr6zcwwNzVzLts83cPCqDP10zUGHekEXBvUMDCeqn1szGmdk6M8s3s4cC7DPWzJabWa6ZfRLaMkXqxomycu559Svm5BRy3wW9+OXlfYnTzZwbrlP3Dt26FZz7+t6hURLq5pyregezeGA9cCFQCCwFJjjn8irs0wpYBIxzzm0zs/bOuT1VHTczM9NlZ2fXtn6RM3b0RBm3v5LDZ/n7+MVlfZl0nm5M0eBlZHhDvLL0dNiypb6r8cvMcpxzmf5eC2YMfTiQ75zb5DvYbOBKIK/CPtcBbzrntgFUF+Yi4XbgaCkTX1rKqu2H+OM1A7l6aNdwlySRIEruHRpIMEMuXYCCCs8Lfdsq6g20NrP/mFmOmd3o70BmNtnMss0se+/evWdWsUgtbT94jKunLCJv52H+kjVEYS5fi5J7hwYSTKD7G1CsPE6TAAwFLgUuBn5uZr1P+yLnpjrnMp1zme3atatxsSK1tWF3MVf/ZRF7ik/wyqThXNSvY7hLkkgSJfcODSSYQC8EUis87wrs8LPPB865o865fcBCYGBoShQJjZytB7jmhcWUeRyv334uI7qnhLskiTRRcu/QQIIJ9KVALzPrZmZJwLXAvEr7vAN8y8wSzKwJMAJYE9pSRc7cv9ftIWvaF7RKTuTNO0dxdqcW4S5JIlVWlvcEqMfj/RwlYQ5BnBR1zpWZ2T3AAiAemO6cyzWzO3yvT3HOrTGzD4CVgAeY5pxbXZeFiwTrzWWFPDB3JWd1bM5LE4fTrrkW2ZLYVO20xbqiaYtS15xz/OWTjTzxwTpG9UjhhRuG0ryxFtmS6FbbaYsiUafc4/jVP3KZsXgrVwzszB+vGUhSgq7+lNimQJeYc/xkOffN/ooFubu5/fzuPDiuj67+lAZBgS4x5WBJKbe+nE3OtgO6+lMaHAW6xIyCohJu/tuXFBQd45kJg7lsQOdwlyRSrxToEhOWFxzk1peXUlrmYcYtwxmpOebSAOkskUS9D1bv4tqpi0lOiufNu0YpzCV4UbxUrj/qoUvUcs4x/fMt/Pa9PAZ2bcW0mzJ1I2cJ3qmlcktKvM9PLZULUXUxUUXqoUtUKvc4Hp2Xy2/ezWNcv47MnjxSYS4188gjX4f5KSUl3u1RSj10iTrFx09y3+zlfLx2D5PP785DmpYoZyLKl8r1R4EuUaWgqIRbX84mf+8Rfvu9c7h+ZHq4S5JolZbm/2YWUbJUrj8acpGosXRLEd977nN2HjrGjEnDFeZSO1G+VK4/CnSJCnNzCsn66xJaJCfy9t2jGd2zbbhLkmgX5Uvl+qNAl4jm8Th+//5a7p+zgmHdWvP2XaPp3q5ZuMuSaBNoemIUL5Xrj8bQJWIdPn6SH/tOfmaNSOPRK/qRGK8+iNRQDE5PDES/HRKR8vcc4XvPfs7C9Xv59ZX9+O33zlGYy5mJwemJgaiHLhHno7zd/Pjvy2mUEMesW0foVnFSOzE4PTEQBbpEDI/H8ey/8/nzh+vp36UlL9wwlM6tksNdlkS7GJyeGIjew0pEKD5+kjtn5fDnD9fzX4O7MOeOcxXmEhoxOD0xEPXQJezW7jrMnTOXsa2ohJ9f1pdJozMw05WfEiKnTnw+8oh3mCUtzRvmMXZCFBToEmZvLivk4bdW0aJxIq/dNpLh3dqEuySJRVlZMRnglQU15GJm48xsnZnlm9lDVew3zMzKzezq0JUosehEWTmPvLWK//f6CgZ2bcW7PzpPYS5SS9X20M0sHngOuBAoBJaa2TznXJ6f/R4HFtRFoRI7Cg+UcPesZawoPMQdY3pw/0W9SdCURJFaC2bIZTiQ75zbBGBms4ErgbxK+90LvAEMC2mFElM+WL2LB+auwDl44YahXNyvY7hLEokZwQR6F6CgwvNCYETFHcysC/B94DtUEehmNhmYDJAWg1OGJLDjJ8v53fw1zFi8lQFdW/LMhMGkpzQNd1kiMSWYQPc33cBVev4k8KBzrryq2QnOuanAVIDMzMzKx5AYtXHvEe559SvW7DzMred144FxfUhK0BCLSKgFE+iFQGqF512BHZX2yQRm+8K8LTDezMqcc2+HpEqJWm/kFPLzd1bTKCGO6Tdn8p0+HcJdkkjMCibQlwK9zKwbsB24Friu4g7OuW6nHpvZS8C7CvOG7VDJSX72zmr+sWIHI7q14alrB9OxZeNwlyUS06p93+ucKwPuwTt7ZQ3wunMu18zuMLM76rpAiT6L8vcx7qmFvL9qJ/9zYW9evW2kwlzqR6BlchuIoC4scs7NB+ZX2jYlwL43174siUYnysr544J1/PXTzXRv25Q37xrFgK6twl2WNBQNaJncQMy58JybzMzMdNnZ2WH53hJ6a3cd5sezl7N2VzHXj0zj4fFn0yRJFyJLPcrI8L8IV3q69+YVMcLMcpxzmf5e02+c1EpZuYcXFm7iqY820CI5QSc+JXwa0DK5gSjQ5Yyt3XWYn8xZyarth7h0QCd+fUU/Upo1CndZ0lA1oGVyA1GgS42dLPcw5T8befrjDbRonMjzWUMY379TuMuShu6xx745hg4xu0xuIAp0qZHcHYd4YO5Kcncc5vKBnfnVFf1o0zQp3GWJNKhlcgNRoEtQSkrLePKjDbz42WZaN0lkyvVDGHeOeuUSYRrIMrmBKNClWv9eu4efvb2a7QePMWF4Kg+O60OrJuqVi0QaBboEtOfwcX71bh7vrdxJz/bNeP32c7VmuUgEU6DLacrKPcxYvJX//Wg9J8o8/M+Fvbl9TA8tqCUS4fQbKt+weON+Ln36M379bh6DUlvxwX3f4t4LeinMJfI08Mv8/VEPXQDYcfAYj81fw3srd9K1dTIv3DCUi/p20M2aJTLpMn+/dOl/A3estJxpn27i+f9sxOMcd43tye1jutM4MT7cpYkE1kAu8/dHl/7Laco9jre+2s4fF6xj1+HjjOvXkUcuPZvUNk3CXZpI9XSZv18K9Abosw37+N38NeTtPMzAri15esJgzV6R6KLL/P1SoDcga3Ye5vEP1vKfdXvp0iqZpycM5rL+nYiL0zi5RBld5u+XAr0B2LT3CP/70Qb+sWIHzRsn8PD4Ptx4bobGySV66TJ/vxToMazwQAlP/2sDbyzbTlJ8HHeN7cHk87vrKk+JLrNm+Q/uBn6Zvz8K9Bi04+Axpnyykde+3IaZcdO5Gdw5tgftmmtpW4kymp5YI5q2GEO27S/hL5/kMzenEOfgmsxU7v1OTzq3Sg53aSJnpgFPTwxE0xZjXP6eYp7/90beWbGD+Djj2mFp3D6mO11bawqiRDlNT6yRoALdzMYBTwHxwDTn3O8rvZ4FPOh7egS40zm3IpSFyulyth5g2qeb+CB3F40T4pk0OoPbvtWd9i0ah7s0kdDQ9MQaqTbQzSweeA64ECgElprZPOdcXoXdNgNjnHMHzOwSYCowoi4KbujKPY4P83YxdeEmlm07SMvkRO4e25NJ53XTjSYkuvk7+anpiTUSTA99OJDvnNsEYGazgSuB/wt059yiCvt/AXQNZZECR0+UMTenkOmfb2br/hJS2yTzqyv6cfXQrjRtpJEziXKBTn5Oner90PTEoASTBF2AggrPC6m6930L8L6/F8xsMjAZIE1vmYKSv+cIryzewhvLtnPkRBmD01rx0Lg+XNSvI/G6IEhixSOPfLMXDt7njzziPfmpAA9KMIHuLzX8To0xs2/jDfTz/L3unJuKdziGzMzM8EyviQJl5R4+WrOHV77Ywuf5+0mKj+PSAZ244dx0hqS1Dnd5IqGnk58hEUygFwKpFZ53BXZU3snMBgDTgEucc/tDU17DUlBUwuvZBczNKWTnoeN0btmYn1x8Fj8clkrbZppDLjGk8nh5mzaw309s6J18jQQT6EuBXmbWDdgOXAtcV3EHM0sD3gRucM6tD3mVMez4yXIW5O7i9ewCPs/fjxmc36sdj17Rjwv6tCchXjeWkBjjb7w8MRGSkqC09Ov9dPKzxqoNdOdcmZndAyzAO21xunMu18zu8L0+BfgFkAI877shQlmgie8CzjmWbTvIO8u3887yHRw6dpIurZL5fxf25uqhXXUhkMQ2f+PlJ09CSgo0a6aTn7UQ1PQI59x8YH6lbVMqPL4VuDW0pcWeTXuP8PbyHbyzfDtb95fQKCGOi/p15IeZqYzqkaJVDyX2+JuKGGhcvKgI9u2r3/pijOa71bHCAyW8v2oX767cwYrCQ5jB6B5tufc7vbi4XweaN04Md4kioVE5vMePh5dfPn0qosbL64wCvQ4UFJUwf9VO5q/ayYrCQwCc06UFj4w/m8sHdqZjS13JKTHG37j4lClQea2okhJITvaOj+tioZBToIeAc468nYf5KG8PH67ZxerthwHo36UlD47rw/j+HUlPaRrmKkVCxN8wir9x8UAL/xUVwSuv6GKhOqDVFs/QibJylmwq4qM1u/kobzc7Dh3HDAantuLifh0Z37+T7s8psadyTxxO721XpwGvlBgKWm0xRLbuP8on6/fyybq9LNq4n2Mny2mcGMe3erXjx9/tzbf7tDDVNigAAAnxSURBVNea4xI7gu2Jl5RAfDyUl59+DLNv9tQ1tFKnFOhVOFhSyhebili0cR8L1+9ly37vD3JamyZck9mVMb3bMbpnW93KTaJfsCc0A/XEy8v9j4vfdBPMn6+hlXqiQK/gyIkylm4pYvHG/SzauI/cHYdxDpIT4zm3RwoTR3djTO92ZLTVeLhEKX+9bgj+hGagnnh6+tc9eIV32DToMfS9xSfI3lLE0i0HWLqliLydhyn3OJLi4xic1opRPdoyqmcKA7u2IilBV2xKFAkmuMHbi05O9j+NMBB/PfGpUxXe9URj6HgXvFq7q5ivCg6yfNtBvtp2gE37jgLQKCGOQamtuGtsD4Z3a0NmehuSkzSMIlEq0FK0ycn+x79rekJTPfGIFZOB7vE4thaVsGr7IVZvP8TybQdZuf0gx096AEhpmsTgtFb8YFgqwzLa0L9LS/XAJXpV7o0fOVL74IbAJzSzshTgESrqA/1kuYeNe4+wZudhcrcfZtX2Q+TtOEzxiTIAkuLj6NelBROGpzEotRVD0lrTtXUyvjVnRKKbv954TaWkwLFjOqEZA6Iu0LfsO8qHebtZs/Mwa3YVk7+nmJPl3l5EUkIcZ3dqwZWDO9O/S0vO6dKS3h2ak6gVCyUWBDuNMJBAwf3UU97HGkaJelEX6Gt3FfPY/DV0aNGIPh1bMKZ3O87u1JyzO7WgW9umCm+JTYHGxYMN82CCWwEe9aJulsux0nKOnSzXDZElNgSajeKvJ+5vOCXQNEItRRuzqprlEnWBLhLxgg1pOL2XnZjoPRlZ+UYPVfXENY2wQakq0DU+IbFt1izIyIC4OO/nWbOq3l7bY5waGtm61TtDZOtWmDgRJk365rbJk+G++/zf6KFimMPXF/T4k57uDe/0dO8fglPPFeYNk3MuLB9Dhw51Imdk5kzn0tOdM/N+njnT//Y773SuSRPnvDHq/WjSJPD2mTNrf4yUlG9uC+VHoJqlQQGyXYBcVaA3dMGGo7+wq2rfUBwj0LZgA9bMfzDGx/vfnpJS+2PU1cep9vv7t5MGRYEeaqH4xYqEIK1JOCYmOpeUFNy+oThGoH0D9YDrO2BD8eHvD0igdiu8xafWgQ6MA9YB+cBDfl434Gnf6yuBIdUd84wCvb57iP621+TteiiGAuoySEMRjoH2DcUx6uojFN+vJr38qkK6Jj+jIs7VLtCBeGAj0B1IAlYAfSvtMx543xfsI4El1R23xoFek95kXYZjoLfg/n6RQzUUUFdBGksfgdpd+d/6TMa/a3IMhbTUsdoG+rnAggrPfwr8tNI+LwATKjxfB3Sq6rg1DvT09LoLtroMx2gM2EjuodfkD+ep7TV591bbY4jUsdoG+tXAtArPbwCerbTPu8B5FZ7/C8is6rg1DvRAvdpY+qjvIK1JOEbKGPqZDJvVhEJaIlxtA/0aP4H+TKV93vMT6EP9HGsykA1kp6Wl1awVkdRD9/cWvKbj0cG+ja/LIA3FrJNA+4biGApXkdPExpBLpIyhB3oLfib1RUKQikhUqW2gJwCbgG4VTor2q7TPpZVOin5Z3XGjdpZLVUFYl0MBIiKu6kAPai0XMxsPPOmb8TLdOfeYmd0B4JybYt7FxZ/FO72xBJjonKtyoRat5SIiUnO1vgWdc24+ML/StikVHjvg7toUKSIitaPFuUREYoQCXUQkRijQRURihAJdRCRGhO2ORWa2FziDW5QD0BbYF8JyIlGstzHW2wex30a1LzzSnXPt/L0QtkCvDTPLDjRtJ1bEehtjvX0Q+21U+yKPhlxERGKEAl1EJEZEa6BPDXcB9SDW2xjr7YPYb6PaF2GicgxdREROF609dBERqUSBLiISIyIm0M1supntMbPVFbYNNLPFZrbKzP5hZi0qvDbA91qu7/XGvu1Dfc/zzexp30qQYVeT9plZlpktr/DhMbNBvtcisn1Q4zYmmtnLvu1rzOynFb4mIttYw/YlmdnffNtXmNnYCl8Tqe1LNbN/+/4/cs3sPt/2Nmb2oZlt8H1uXeFrfuprxzozu7jC9ohrY03bZ2Ypvv2PmNmzlY4Vce0Dql8Pvb4+gPOBIcDqCtuWAmN8jycBv3Ffr9G+Ehjoe54CxPsef4n3phyGd432S8Ldtpq2r9LX9Qc2VXgeke07g//D64DZvsdNgC1ARiS3sYbtuxv4m+9xeyAHiIvw9nUChvgeNwfWA32BJ4CHfNsfAh73Pe6L9/4IjfDeL2FjJP8enkH7mgLnAXdw+m03I659zrnI6aE75xYCRZU2nwUs9D3+ELjK9/giYKVzboXva/c758rNrBPQwjm32Hn/1WcA36v76qtXw/ZVNAF4DSCS2wc1bqMDmppZApAMlAKHI7mNNWxfX7y3YsQ5twc4CGRGePt2OueW+R4XA2uALsCVwMu+3V7m63qvxPtH+YRzbjOQDwyP1DbWtH3OuaPOuc+A4xWPE6ntgwgacglgNXCF7/E1QKrvcW/AmdkCM1tmZg/4tncBCit8faFvW6QK1L6Kfogv0Im+9kHgNs4FjgI7gW3AH51zRURfGwO1bwVwpZklmFk3YKjvtahon5llAIOBJUAH59xO8IYi3ncc4K27oMKXnWpLxLcxyPYFErHti/RAnwTcbWY5eN8ilfq2J+B9K5Tl+/x9M7sA79ufyiJ5Xmag9gFgZiOAEufcqTHbaGsfBG7jcKAc6Iz37fr/mFl3oq+Ngdo3He8vejbeu30tAsqIgvaZWTPgDeDHzrnDVe3qZ5urYntEqEH7Ah7Cz7aIaF9QdywKF+fcWrzDK5hZb7z3LgXvL8onzrl9vtfm4x3bnAl0rXCIrsCOeiu4hqpo3ynX8nXvHLztjpr2QZVtvA74wDl3EthjZp8DmcCnRFEbA7XPOVcG/Pep/cxsEbABOEAEt8/MEvGG3Szn3Ju+zbvNrJNzbqdvuGGPb3sh33xXeaotEftzWsP2BRKx7YvoHrqZtfd9jgN+Bpy67d0CYICZNfGNwY4B8nxvl4rNbKTvrPONwDthKD0oVbTv1LZrgNmntkVb+6DKNm4DvmNeTfHeXHxttLUxUPt8P5tNfY8vBMqccxH9M+qr50VgjXPuzxVemgfc5Ht8E1/XOw+41swa+YaVeuG9QXxEtvEM2udXpLYPiKhZLq/hHU89ifcv4C3AfXjPRK8Hfo/vylbf/tcDuXjHMJ+osD3Tt20j3htXW323JUTtGwt84ec4Edm+mrYRaAbM8f0f5gE/ifQ21rB9GcA6vCfePsK75Gmkt+88vEMHK4Hlvo/xeGeR/QvvO4x/AW0qfM0jvnaso8JMj0hs4xm2bwveE+FHfP/nfSO1fc45XfovIhIrInrIRUREgqdAFxGJEQp0EZEYoUAXEYkRCnQRkRihQBcRiREKdBGRGPH/ARnGfxvy3p3RAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"beta_1 = 0.10\n",
"beta_2 = 1990.0\n",
"\n",
"#logistic function\n",
"Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
"\n",
"#plot initial prediction against datapoints\n",
"plt.plot(x_data, Y_pred*15000000000000.)\n",
"plt.plot(x_data, y_data, 'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our task here is to find the best parameters for our model. Lets first normalize our x and y:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimal values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
"\n",
"popt are our optimized parameters."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" beta_1 = 690.447527, beta_2 = 0.997207\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regresssion model."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(1960, 2015, 55)\n",
"x = x/max(x)\n",
"plt.figure(figsize=(8,5))\n",
"y = sigmoid(x, *popt)\n",
"plt.plot(xdata, ydata, 'ro', label='data')\n",
"plt.plot(x,y, linewidth=3.0, label='fit')\n",
"plt.legend(loc='best')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice\n",
"Can you calculate what is the accuracy of our model?"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.05\n",
"Residual sum of squares (MSE): 0.00\n",
"R2-score: 0.96\n"
]
}
],
"source": [
"# write your code here\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"y_hat = sigmoid(test_x, *popt)\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(y_hat , test_y) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click __here__ for the solution.\n",
"\n",
"<!-- Your answer is below:\n",
" \n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(y_hat , test_y) )\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Want to learn more?\n",
"\n",
"IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: [SPSS Modeler](http://cocl.us/ML0101EN-SPSSModeler).\n",
"\n",
"Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at [Watson Studio](https://cocl.us/ML0101EN_DSX)\n",
"\n",
"### Thanks for completing this lesson!\n",
"\n",
"Notebook created by: <a href = \"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>\n",
"\n",
"<hr>\n",
"Copyright &copy; 2018 [Cognitive Class](https://cocl.us/DX0108EN_CC). This notebook and its source code are released under the terms of the [MIT License](https://bigdatauniversity.com/mit-license/).​"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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