Skip to content

Instantly share code, notes, and snippets.

Show Gist options
  • Save Hamid264/81310c07ffb447c70931c79495fe8876 to your computer and use it in GitHub Desktop.
Save Hamid264/81310c07ffb447c70931c79495fe8876 to your computer and use it in GitHub Desktop.
Created on Skills Network Labs
Display the source blob
Display the rendered blob
Raw
{
"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",
"\n",
"<h1><center>Non Linear Regression Analysis</center></h1>"
]
},
{
"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": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>"
]
},
{
"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 = $2x$ + 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": 7,
"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 corresponding 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": 8,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2020-07-28 20:22:42 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": 8,
"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 decelerate slightly in the 2010s."
]
},
{
"cell_type": "code",
"execution_count": 9,
"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": 10,
"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": 11,
"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": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fc4638eb160>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"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": 13,
"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": 14,
"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 regression model."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"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": null,
"metadata": {},
"outputs": [],
"source": [
"# write your code here\n",
"\n",
"\n"
]
},
{
"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": [
"<h2>Want to learn more?</h2>\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: <a href=\"http://cocl.us/ML0101EN-SPSSModeler\">SPSS Modeler</a>\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 <a href=\"https://cocl.us/ML0101EN_DSX\">Watson Studio</a>\n",
"\n",
"<h3>Thanks for completing this lesson!</h3>\n",
"\n",
"<h4>Author: <a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a></h4>\n",
"<p><a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.</p>\n",
"\n",
"<hr>\n",
"\n",
"<p>Copyright &copy; 2018 <a href=\"https://cocl.us/DX0108EN_CC\">Cognitive Class</a>. This notebook and its source code are released under the terms of the <a href=\"https://bigdatauniversity.com/mit-license/\">MIT License</a>.</p>"
]
}
],
"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": "3.6.11"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment