{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", " \n", " \"Skills\n", " \n", "

\n", "\n", "\n", "# Non Linear Regression Analysis\n", "\n", "\n", "Estimated time needed: **20** minutes\n", " \n", "\n", "## Objectives\n", "\n", "After completing this lab you will be able to:\n", "\n", "* Differentiate between linear and non-linear regression\n", "* Use non-linear regression model in Python\n" ] }, { "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 since linear regression presumes that the data is linear. \n", "Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Importing required libraries

\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "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('Independent Variable')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. 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 $x$). For example:\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 so on. For example: $$ y = \\log(x)$$\n", " \n", "We can have a function that's even more complicated such as :\n", "$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at a cubic function's graph.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "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('Independent 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.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some other types of non-linear functions are:\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quadratic\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ Y = X^2 $$\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "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('Independent Variable')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "### Exponential\n" ] }, { "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": 9, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.arange(-5.0, 5.0, 0.1)\n", "\n", "Y= np.exp(X)\n", "\n", "plt.plot(X, Y, label='e^x') \n", "plt.plot(X, np.exp(-X), label='e^(-x)')\n", "plt.ylabel('Dependent Variable')\n", "plt.xlabel('Independent Variable')\n", "plt.title('Perbandingan e^x dan e^(-x)')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Logarithmic\n", "\n", "The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. 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 a polynomial representation of the $x$ values. In general form it would be written as \n", "\\begin{equation}\n", "y = \\log(X)\n", "\\end{equation}\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jupyterlab/conda/envs/python/lib/python3.7/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": [ "
" ] }, "metadata": {}, "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('Independent Variable')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sigmoidal/Logistic\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "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('Independent Variable')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# Non-Linear Regression example\n" ] }, { "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. \n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2025-10-20 14:01:10 URL:https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n" ] }, { "data": { "text/html": [ "
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YearValue
019605.918412e+10
119614.955705e+10
219624.668518e+10
319635.009730e+10
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" ], "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" ] }, "execution_count": 14, "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://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n", " \n", "df = pd.read_csv(\"china_gdp.csv\")\n", "df.head(6)" ] }, { "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)\n" ] }, { "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 decelerates slightly in the 2010s.\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "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:\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "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('Independent 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.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Building The Model ###\n", "Now, let's build our regression model and initialize its parameters. \n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "tags": [] }, "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:\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "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:\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "tags": [] }, "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. Optimize 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.\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " beta_1 = 690.451712, 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.\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "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?\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean absolute error: 0.03\n", "Residual sum of squares (MSE): 0.00\n", "R2-score: 0.98\n" ] } ], "source": [ "# write your code here\n", "\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(test_y,y_hat) )\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Click here for the solution\n", "\n", "```python \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(test_y,y_hat) )\n", "\n", "```\n", "\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\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\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Thank you for completing this lab!\n", "\n", "\n", "## Author\n", "\n", "Saeed Aghabozorgi\n", "\n", "\n", "### Other Contributors\n", "\n", "Joseph Santarcangelo\n", "\n", "\n", "##

© IBM Corporation 2020. All rights reserved.

\n", "\n", "\n", "\n", "\n", "\n" ] } ], "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": "3.7.12" }, "prev_pub_hash": "f873d3177bf529d2d648c46bab1627042a257e5ec6ce42ca68028520459f817e" }, "nbformat": 4, "nbformat_minor": 4 }