VeriAnalitigiNotlar.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "~~~\n",
    "Introduction: cemgil-ml-tutorial-is-bankasi2018.pdf\n",
    "\n",
    "Supervised Learning, Linear Regression: Regression.ipynb\n",
    "\n",
    "Regularization, Feature selection: RobustRegression.ipynb\n",
    "\n",
    "Classification, Logistic Regression: LogisticRegression.ipynb\n",
    "\n",
    "Naive Bayes, k-nearest neighbors, decision trees, model evaluation :\n",
    "DecisionTree.ipynb, KNN.ipynb\n",
    "\n",
    "Optimization, Gradient Descent, Newton's method, Momentum \n",
    "GradientDescent.ipynb\n",
    "\n",
    "Artificial Neural Networks (ANNs) \n",
    "Deep Learning Frameworks, PyTorch, Automatic Differentiation \n",
    "MultiLayerPerceptron.ipynb, AutomaticDifferentiation.ipynb\n",
    "\n",
    "Unsupervised Learning, k-means clustering \n",
    "\n",
    "\n",
    "Dimensionality reduction, Singular Value Decomposition, Principal Component Analysis, Recommendation systems \n",
    "~~~"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1068b7518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAACcCAYAAABvA1AIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUiMsdElqxP8Bx32imQ5WYywAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106999860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.array([10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5])-2\n",
    "y = np.array([8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68])-2\n",
    "#y = np.array([9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74])-2\n",
    "#y = np.array([7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73])-2\n",
    "\n",
    "def plot_fit(w1, w0):\n",
    "    f = w0 + w1*x\n",
    "\n",
    "    plt.figure(figsize=(6,6))\n",
    "    plt.plot(x,y,'sk')\n",
    "    plt.plot(x,f,'o-r')\n",
    "    #plt.axis('equal')\n",
    "    plt.xlim((0,15))\n",
    "    plt.ylim((0,15))\n",
    "    for i in range(len(x)):\n",
    "        plt.plot((x[i],x[i]),(f[i],y[i]),'b')\n",
    "    plt.show()\n",
    "    plt.figure(figsize=(6,2))\n",
    "    plt.bar(x,(f-y)**2/2)\n",
    "    plt.title(np.sum((f-y)**2/2))\n",
    "    plt.ylim((0,30))\n",
    "    plt.xlim((0,15))\n",
    "    plt.show()\n",
    "    \n",
    "plot_fit(0.38,3.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nyXgq9kT57DPo3RsKCuw0GpEoy86GadOgenWbety0KXSijKZiT4QtW6BnT7up9Nhj9sSe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1126a3320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([-3.98363636,  2.40272727, -0.44090909])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Setup data\n",
    "x = np.array([1,2,3,5])\n",
    "y = np.array([-2, -1, -0.7, -3])\n",
    "\n",
    "# Setup the Design matrix\n",
    "N = len(x)\n",
    "A = np.vstack( [np.ones(N), x, x**2] ).T\n",
    "# Solve the least squares problem\n",
    "w_ls,E,rank,sigma = np.linalg.lstsq(A, y)\n",
    "\n",
    "# Plot results\n",
    "xx = np.linspace(0,6,100)\n",
    "NN = len(xx)\n",
    "AA = np.vstack( [np.ones(NN), xx, xx**2] ).T\n",
    "f_pred = AA.dot(w_ls)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xx, f_pred, '-r')\n",
    "plt.show()\n",
    "w_ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6M3u/htdsXp1rpJFMqjeTaoXMqjeTaoXMqjeTaoXk6t23Oi+yCnpNqs3M8oH7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\n/wfWD2PCOSmZiAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10682f208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.73610997, -4.95454215,  3.215489  , -0.71527962,  0.04808533])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Setup data\n",
    "x = np.array([-0.5, 0, 1,2,3,5])\n",
    "y = np.array([4, 1, -2, -1, -0.7, -3])\n",
    "\n",
    "# Setup the Design matrix\n",
    "Order = 4\n",
    "A = np.array([x**p for p in range(Order+1)]).T\n",
    "# Solve the least squares problem\n",
    "w_ls,E,rank,sigma = np.linalg.lstsq(A, y)\n",
    "\n",
    "# Plot results\n",
    "xx = np.linspace(-1,6,100)\n",
    "AA = np.array([xx**p for p in range(Order+1)]).T\n",
    "f_pred = AA.dot(w_ls)\n",
    "plt.plot(x, y, 'o')\n",
    "plt.plot(xx, f_pred, '-r')\n",
    "plt.show()\n",
    "w_ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [1, 2],\n",
       "       [1, 3],\n",
       "       [1, 5]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Order = 1\n",
    "A = np.array([x**p for p in range(Order+1)]).T\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.44090909,  2.40272727, -3.98363636])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = np.polyfit(x,y, 2)\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.9047619]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.array([4, 8, 16, 30])\n",
    "N = len(z)\n",
    "\n",
    "y = z[1:].reshape(N-1,1)\n",
    "A = z[:-1].reshape(N-1,1)\n",
    "\n",
    "w_ls,E,rank,sigma = np.linalg.lstsq(A, y )\n",
    "w_ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 73.79672131]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[-1]*w_ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy as sc\n",
    "import scipy.linalg as la\n",
    "\n",
    "# Order\n",
    "L = 2\n",
    "\n",
    "def AR_model(y,L):\n",
    "    N = len(y) - L\n",
    "    A = np.hstack((np.matrix(y[L-i:L-i+N]) for i in range(1,L+1) ))\n",
    "    yy = np.matrix(y[L:(L+N+1)])\n",
    "    return A, yy\n",
    "   \n",
    "def make_AR_model(y, L):\n",
    "    B = la.toeplitz(y[:-1], y[0:L])\n",
    "    AA = B[L-1:,:]\n",
    "    yy = y[L:]\n",
    "    return AA, yy\n",
    "\n",
    "A,yy = AR_model(y, L)\n",
    "#plt.imshow(A, interpolation='nearest')\n",
    "# Solve the least squares problem\n",
    "w_ls,E,rank,sigma = np.linalg.lstsq(A, yy)\n",
    "\n",
    "f = A*w_ls\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.2 -1. ]\n",
      " [-1.7  1.2]\n",
      " [ 1.1 -1.7]]\n",
      "[-1.7  1.1 -1.9]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-0.01244109,  1.16068031])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.array([-1, 1.2, -1.7, 1.1, -1.9])\n",
    "\n",
    "L = 2\n",
    "A,y = make_AR_model(z, L)\n",
    "\n",
    "print(A)\n",
    "print(y)\n",
    "\n",
    "w_ls,E,rank,sigma = np.linalg.lstsq(A, y )\n",
    "w_ls"
   ]
  }
 ],
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