Class1_Intro to Gradient Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    #return x[0]**2+x[1]**2\n",
    "    return (x[0]-2)**2+(x[1]-3**2)\n",
    "\n",
    "def df(x):\n",
    "    return np.array([2*(x[0]-2),2*(x[1]-3)]) # 2 dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.array([-3.0, 8.0]) # initial guess\n",
    "lr=0.1 # learning rate\n",
    "iter1=1000 # 반복 횟수 많을수록 정확 (100번은 많이 벗어남, 10000번은 거의 근접)\n",
    "x=x0\n",
    "history=np.ones([iter1, 3])\n",
    "for i in range(0,iter1):\n",
    "    x = x - lr * df(x) # next x\n",
    "    history[i, 0:2]=np.array(x)\n",
    "    history[i,2]=f(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[14.         -5.38603583 -5.95175638 -5.99502372 -5.99946803 -5.99994291\n",
      " -5.99999387 -5.99999934 -5.99999993 -5.99999999 -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.         -6.         -6.\n",
      " -6.         -6.         -6.         -6.        ]\n"
     ]
    }
   ],
   "source": [
    "print(history[::10,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.67200000e+01 2.99008000e+01 1.91365120e+01 1.22473677e+01\n",
      " 7.83831532e+00 5.01652180e+00 3.21057395e+00 2.05476733e+00\n",
      " 1.31505109e+00 8.41632698e-01 5.38644927e-01 3.44732753e-01\n",
      " 2.20628962e-01 1.41202536e-01 9.03696229e-02 5.78365586e-02\n",
      " 3.70153975e-02 2.36898544e-02 1.51615068e-02 9.70336437e-03]\n"
     ]
    }
   ],
   "source": [
    "print(history[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20d1c466108>]"
      ]
     },
     "execution_count": 5,
     "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": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(history[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17db1d68e88>]"
      ]
     },
     "execution_count": 31,
     "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": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(history[:,2]) # f(x) value는 iteration이 진행될수록 0으로 수렴해야 함\n",
    "# 더 이상 개선이 없을 때의 x 값"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20d1e66f3c8>]"
      ]
     },
     "execution_count": 6,
     "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": [
    "plt.plot(history[:,0], history[:,1], \"bo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17db1e41508>]"
      ]
     },
     "execution_count": 33,
     "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": [
    "plt.plot(history[:,0], history[:,1], \"bo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 54,  70],\n",
       "       [ 86, 102],\n",
       "       [118, 134]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np .sum(X, axis=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([ [[0,1,2,3],[4,5,6,7]], \n",
    "              [[8,9,10,11],[12,13,14,15]],\n",
    "              [[16,17,18,19],[20,21,22,23]]     ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [4, 5, 6, 7]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0,:,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0,0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2, 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[1,1,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[24, 27, 30, 33],\n",
       "       [36, 39, 42, 45]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(X, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6, 22],\n",
       "       [38, 54],\n",
       "       [70, 86]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(X, axis=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[49 56 63]\n",
      " [56 64 72]\n",
      " [63 72 81]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "X1 = np . array ([[7 ,8 ,9]])\n",
    "X2 = np . array ( [ [ 7 ] , [ 8 ] , [ 9 ] ] )\n",
    "X3 = np . array ([7 ,8 ,9])\n",
    "print(X1*X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[49 56 63]\n",
      " [56 64 72]\n",
      " [63 72 81]]\n"
     ]
    }
   ],
   "source": [
    "print(X2*X3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[49 64 81]]\n"
     ]
    }
   ],
   "source": [
    "print(X1*X3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson Regression with boston data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data manipulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "       'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='<U7')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "boston = datasets.load_boston()\n",
    "X_train = boston['data']\n",
    "y_train = boston['target'] #number of car accidents\n",
    "boston.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "y = np.round_(y_train, decimals=0, out=None) #make into integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 13) (506,)\n"
     ]
    }
   ],
   "source": [
    "print(X_train.shape, y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* X_train does not contain the column of 1's. In the following, we add the column of 1's into the model matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 14)\n"
     ]
    }
   ],
   "source": [
    "my_ones = np.ones([506,1])\n",
    "X = np.concatenate((my_ones, X_train), axis=1)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "poisson_model = sm.GLM(y, X, family=sm.families.Poisson()) #Find W based on MLE\n",
    "poisson_results = poisson_model.fit();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                  506\n",
      "Model:                            GLM   Df Residuals:                      492\n",
      "Model Family:                 Poisson   Df Model:                           13\n",
      "Link Function:                    log   Scale:                          1.0000\n",
      "Method:                          IRLS   Log-Likelihood:                -1416.0\n",
      "Date:                Wed, 21 Oct 2020   Deviance:                       362.69\n",
      "Time:                        11:21:00   Pearson chi2:                     389.\n",
      "No. Iterations:                     5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          3.7780      0.232     16.268      0.000       3.323       4.233\n",
      "x1            -0.0103      0.002     -4.699      0.000      -0.015      -0.006\n",
      "x2             0.0010      0.001      1.900      0.057   -3.29e-05       0.002\n",
      "x3             0.0022      0.003      0.829      0.407      -0.003       0.008\n",
      "x4             0.0922      0.035      2.664      0.008       0.024       0.160\n",
      "x5            -0.6932      0.182     -3.812      0.000      -1.050      -0.337\n",
      "x6             0.1225      0.018      6.735      0.000       0.087       0.158\n",
      "x7             0.0004      0.001      0.627      0.531      -0.001       0.002\n",
      "x8            -0.0490      0.009     -5.614      0.000      -0.066      -0.032\n",
      "x9             0.0154      0.003      4.827      0.000       0.009       0.022\n",
      "x10           -0.0005      0.000     -3.114      0.002      -0.001      -0.000\n",
      "x11           -0.0359      0.006     -6.281      0.000      -0.047      -0.025\n",
      "x12            0.0005      0.000      3.195      0.001       0.000       0.001\n",
      "x13           -0.0314      0.003    -12.235      0.000      -0.036      -0.026\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "print(poisson_results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "yhat = poisson_results.mu #prediction for each observation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# yhat = poisson_results.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.725663858781825"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((y_train-yhat)**2)  #Calculation of MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Calculate MSE again!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = poisson_results.params # Estimated parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "16.725663858781825"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_yhat = np.exp(np.dot(X, W) )\n",
    "print(my_yhat.shape)\n",
    "\n",
    "np.mean((y_train-my_yhat)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Draw plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1cba731df48>]"
      ]
     },
     "execution_count": 66,
     "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": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(yhat,y_train, 'o')\n",
    "plt.plot([0, 60], [0,60], 'r-')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}