added random walk example

doc/pub/How2ReadData/ipynb/How2ReadData.ipynb

@@ -17,6 +17,7 @@
     "\n",
     "\n",
     "\n",
+    "\n",
     "## Introduction\n",
     "\n",
     "Our emphasis throughout this series of lectures  \n",
@@ -57,6 +58,7 @@
     "\n",
     "\n",
     "\n",
+    "\n",
     "## Software and needed installations\n",
     "\n",
     "We will make extensive use of Python as programming language and its\n",
@@ -91,6 +93,7 @@
     "\n",
     "etc etc. \n",
     "\n",
+    "\n",
     "## Python installers\n",
     "\n",
     "If you don't want to perform these operations separately and venture\n",
@@ -114,6 +117,7 @@
     "license.\n",
     "\n",
     "\n",
+    "\n",
     "## Installing R, C++, cython or Julia\n",
     "\n",
     "You will also find it convenient to utilize R. Although we will mainly\n",
@@ -132,6 +136,7 @@
     "\n",
     "\n",
     "\n",
+    "\n",
     "## Installing R, C++, cython, Numba etc\n",
     "\n",
     "\n",
@@ -170,6 +175,7 @@
     "[doconce](https://github.com/hplgit/doconce) you can convert a standard ascii text file into various HTML \n",
     "formats, ipython notebooks, latex files, pdf files etc with minimal edits.\n",
     "\n",
+    "\n",
     "## Simple linear regression model using **scikit-learn**\n",
     "\n",
     "We start with perhaps our simplest possible example, using **scikit-learn** to perform linear regression analysis on a data set produced by us. \n",
@@ -582,6 +588,8 @@
    "metadata": {},
    "source": [
     "Similarly, using **R**, we can perform similar studies. The following **R** code illustrates this.\n",
+    "\n",
+    "\n",
     "## Non-Linear Least squares in R"
    ]
   },
@@ -1573,6 +1581,111 @@
     "plt.grid(True)\n",
     "plt.show()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Random walk model"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.preprocessing import PolynomialFeatures\n",
+    "from sklearn.linear_model import LinearRegression\n",
+    "\n",
+    "steps=250\n",
+    "\n",
+    "distance=0\n",
+    "x=0\n",
+    "distance_list=[]\n",
+    "steps_list=[]\n",
+    "while x<steps:\n",
+    "    distance+=np.random.randint(-1,2)\n",
+    "    distance_list.append(distance)\n",
+    "    x+=1\n",
+    "    steps_list.append(x)\n",
+    "plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
+    "\n",
+    "steps_list=np.asarray(steps_list)\n",
+    "distance_list=np.asarray(distance_list)\n",
+    "\n",
+    "X=steps_list[:,np.newaxis]\n",
+    "\n",
+    "#Polynomial fits\n",
+    "\n",
+    "#Degree 2\n",
+    "poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
+    "X_poly=poly_features.fit_transform(X)\n",
+    "\n",
+    "lin_reg=LinearRegression()\n",
+    "poly_fit=lin_reg.fit(X_poly,distance_list)\n",
+    "b=lin_reg.coef_\n",
+    "c=lin_reg.intercept_\n",
+    "print (\"2nd degree coefficients:\")\n",
+    "print (\"zero power: \",c)\n",
+    "print (\"first power: \", b[0])\n",
+    "print (\"second power: \",b[1])\n",
+    "\n",
+    "z = np.arange(0, steps, .01)\n",
+    "z_mod=b[1]*z**2+b[0]*z+c\n",
+    "\n",
+    "fit_mod=b[1]*X**2+b[0]*X+c\n",
+    "plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
+    "plt.title(\"Polynomial Regression\")\n",
+    "\n",
+    "plt.xlabel(\"Steps\")\n",
+    "plt.ylabel(\"Distance\")\n",
+    "\n",
+    "#Degree 10\n",
+    "poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
+    "X_poly10=poly_features10.fit_transform(X)\n",
+    "\n",
+    "poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
+    "\n",
+    "y_plot=poly_fit10.predict(X_poly10)\n",
+    "plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
+    "\n",
+    "plt.legend()\n",
+    "plt.show()\n",
+    "\n",
+    "\n",
+    "#Decision Tree Regression\n",
+    "from sklearn.tree import DecisionTreeRegressor\n",
+    "regr_1=DecisionTreeRegressor(max_depth=2)\n",
+    "regr_2=DecisionTreeRegressor(max_depth=5)\n",
+    "regr_3=DecisionTreeRegressor(max_depth=7)\n",
+    "regr_1.fit(X, distance_list)\n",
+    "regr_2.fit(X, distance_list)\n",
+    "regr_3.fit(X, distance_list)\n",
+    "\n",
+    "X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
+    "y_1 = regr_1.predict(X_test)\n",
+    "y_2 = regr_2.predict(X_test)\n",
+    "y_3=regr_3.predict(X_test)\n",
+    "\n",
+    "# Plot the results\n",
+    "plt.figure()\n",
+    "plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
+    "plt.plot(X_test, y_1, color=\"red\",\n",
+    "         label=\"max_depth=2\", linewidth=2)\n",
+    "plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
+    "plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
+    "\n",
+    "plt.xlabel(\"Data\")\n",
+    "plt.ylabel(\"Darget\")\n",
+    "plt.title(\"Decision Tree Regression\")\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {},