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2021-05-27 20:46:48 +02:00
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"import numpy as np\n",
"import plotly.express as px\n",
"from statsmodels.nonparametric.kernel_regression import KernelReg\n",
"import plotly.graph_objs as go\n",
"import pandas as pd "
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"source": [
"# Plot the x and y values \n",
"px.scatter(x=new_x,y=fun_y(new_x), title='Figure 1: Visualizing the generated data')"
]
},
{
"cell_type": "code",
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"metadata": {},
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"cell_type": "code",
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"metadata": {},
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"source": [
"#fig = px.scatter(x=new_x,y=fun_y(new_x), title='Figure 2: Statsmodels fit to generated data')\n",
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"cell_type": "code",
"execution_count": 85,
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"kernel_x = np.arange(-xwidth,xwidth, 0.1)\n",
"bw_manual = 2\n",
"\n",
"def gauss_const(h):\n",
" \"\"\"\n",
" Returns the normalization constant for a gaussian\n",
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" num = - 0.5*np.square((xi- ker_x))\n",
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"col2= gauss_exp(kernel_x, input_x, bw_manual)\n",
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" <td>3.147371e-22</td>\n",
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" Input_x kernel_x gaussian_const gaussian_exp full_gaussian_value bw\n",
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"source": [
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"data = {'Input_x': [input_x for x in range(col2.shape[0])],\n",
" 'kernel_x': kernel_x,\n",
" 'gaussian_const': [col1 for x in range(col2.shape[0])],\n",
" 'gaussian_exp': col2,\n",
" 'full_gaussian_value': col3,\n",
" 'bw':[bw_manual for x in range(col2.shape[0])],\n",
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"single_pt_KE = pd.DataFrame(data=data)\n",
"single_pt_KE"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
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"## Plotting gaussian for all input x points \n",
"kernel_fns = {'kernel_x': kernel_x}\n",
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" input_string= 'x_value_{}'.format(np.round(input_x,2)) \n",
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" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>39.7</td>\n",
" <td>-19</td>\n",
" <td>0.398942</td>\n",
" <td>-220.5</td>\n",
" <td>6.902029e-97</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>39.7</td>\n",
" <td>-18</td>\n",
" <td>0.398942</td>\n",
" <td>-200.0</td>\n",
" <td>5.520948e-88</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>39.7</td>\n",
" <td>-17</td>\n",
" <td>0.398942</td>\n",
" <td>-180.5</td>\n",
" <td>1.624636e-79</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>39.7</td>\n",
" <td>-16</td>\n",
" <td>0.398942</td>\n",
" <td>-162.0</td>\n",
" <td>1.758750e-71</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>39.7</td>\n",
" <td>-15</td>\n",
" <td>0.398942</td>\n",
" <td>-144.5</td>\n",
" <td>7.004182e-64</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>39.7</td>\n",
" <td>-14</td>\n",
" <td>0.398942</td>\n",
" <td>-128.0</td>\n",
" <td>1.026163e-56</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>39.7</td>\n",
" <td>-13</td>\n",
" <td>0.398942</td>\n",
" <td>-112.5</td>\n",
" <td>5.530710e-50</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>39.7</td>\n",
" <td>-12</td>\n",
" <td>0.398942</td>\n",
" <td>-98.0</td>\n",
" <td>1.096607e-43</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>39.7</td>\n",
" <td>-11</td>\n",
" <td>0.398942</td>\n",
" <td>-84.5</td>\n",
" <td>7.998828e-38</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>39.7</td>\n",
" <td>-10</td>\n",
" <td>0.398942</td>\n",
" <td>-72.0</td>\n",
" <td>2.146384e-32</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>39.7</td>\n",
" <td>-9</td>\n",
" <td>0.398942</td>\n",
" <td>-60.5</td>\n",
" <td>2.118819e-27</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>39.7</td>\n",
" <td>-8</td>\n",
" <td>0.398942</td>\n",
" <td>-50.0</td>\n",
" <td>7.694599e-23</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>39.7</td>\n",
" <td>-7</td>\n",
" <td>0.398942</td>\n",
" <td>-40.5</td>\n",
" <td>1.027977e-18</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>39.7</td>\n",
" <td>-6</td>\n",
" <td>0.398942</td>\n",
" <td>-32.0</td>\n",
" <td>5.052271e-15</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>39.7</td>\n",
" <td>-5</td>\n",
" <td>0.398942</td>\n",
" <td>-24.5</td>\n",
" <td>9.134720e-12</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>39.7</td>\n",
" <td>-4</td>\n",
" <td>0.398942</td>\n",
" <td>-18.0</td>\n",
" <td>6.075883e-09</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>18</th>\n",
" <td>39.7</td>\n",
" <td>-3</td>\n",
" <td>0.398942</td>\n",
" <td>-12.5</td>\n",
" <td>1.486720e-06</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>39.7</td>\n",
" <td>-2</td>\n",
" <td>0.398942</td>\n",
" <td>-8.0</td>\n",
" <td>1.338302e-04</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>39.7</td>\n",
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" <td>0.398942</td>\n",
" <td>-4.5</td>\n",
" <td>4.431848e-03</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>39.7</td>\n",
" <td>0</td>\n",
" <td>0.398942</td>\n",
" <td>-2.0</td>\n",
" <td>5.399097e-02</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>39.7</td>\n",
" <td>1</td>\n",
" <td>0.398942</td>\n",
" <td>-0.5</td>\n",
" <td>2.419707e-01</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td>39.7</td>\n",
" <td>2</td>\n",
" <td>0.398942</td>\n",
" <td>-0.0</td>\n",
" <td>3.989423e-01</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>39.7</td>\n",
" <td>3</td>\n",
" <td>0.398942</td>\n",
" <td>-0.5</td>\n",
" <td>2.419707e-01</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td>39.7</td>\n",
" <td>4</td>\n",
" <td>0.398942</td>\n",
" <td>-2.0</td>\n",
" <td>5.399097e-02</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>26</th>\n",
" <td>39.7</td>\n",
" <td>5</td>\n",
" <td>0.398942</td>\n",
" <td>-4.5</td>\n",
" <td>4.431848e-03</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>39.7</td>\n",
" <td>6</td>\n",
" <td>0.398942</td>\n",
" <td>-8.0</td>\n",
" <td>1.338302e-04</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>28</th>\n",
" <td>39.7</td>\n",
" <td>7</td>\n",
" <td>0.398942</td>\n",
" <td>-12.5</td>\n",
" <td>1.486720e-06</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>39.7</td>\n",
" <td>8</td>\n",
" <td>0.398942</td>\n",
" <td>-18.0</td>\n",
" <td>6.075883e-09</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>30</th>\n",
" <td>39.7</td>\n",
" <td>9</td>\n",
" <td>0.398942</td>\n",
" <td>-24.5</td>\n",
" <td>9.134720e-12</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>31</th>\n",
" <td>39.7</td>\n",
" <td>10</td>\n",
" <td>0.398942</td>\n",
" <td>-32.0</td>\n",
" <td>5.052271e-15</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>32</th>\n",
" <td>39.7</td>\n",
" <td>11</td>\n",
" <td>0.398942</td>\n",
" <td>-40.5</td>\n",
" <td>1.027977e-18</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>33</th>\n",
" <td>39.7</td>\n",
" <td>12</td>\n",
" <td>0.398942</td>\n",
" <td>-50.0</td>\n",
" <td>7.694599e-23</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>34</th>\n",
" <td>39.7</td>\n",
" <td>13</td>\n",
" <td>0.398942</td>\n",
" <td>-60.5</td>\n",
" <td>2.118819e-27</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>35</th>\n",
" <td>39.7</td>\n",
" <td>14</td>\n",
" <td>0.398942</td>\n",
" <td>-72.0</td>\n",
" <td>2.146384e-32</td>\n",
" <td>1</td>\n",
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" <th>36</th>\n",
" <td>39.7</td>\n",
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" <td>0.398942</td>\n",
" <td>-84.5</td>\n",
" <td>7.998828e-38</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>37</th>\n",
" <td>39.7</td>\n",
" <td>16</td>\n",
" <td>0.398942</td>\n",
" <td>-98.0</td>\n",
" <td>1.096607e-43</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>38</th>\n",
" <td>39.7</td>\n",
" <td>17</td>\n",
" <td>0.398942</td>\n",
" <td>-112.5</td>\n",
" <td>5.530710e-50</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>39</th>\n",
" <td>39.7</td>\n",
" <td>18</td>\n",
" <td>0.398942</td>\n",
" <td>-128.0</td>\n",
" <td>1.026163e-56</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>40</th>\n",
" <td>39.7</td>\n",
" <td>19</td>\n",
" <td>0.398942</td>\n",
" <td>-144.5</td>\n",
" <td>7.004182e-64</td>\n",
" <td>1</td>\n",
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" <tr>\n",
" <th>41</th>\n",
" <td>39.7</td>\n",
" <td>20</td>\n",
" <td>0.398942</td>\n",
" <td>-162.0</td>\n",
" <td>1.758750e-71</td>\n",
" <td>1</td>\n",
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],
"text/plain": [
" Input_x kernel_x gaussian_const gaussian_exp full_gaussian_value bw\n",
"0 39.7 -21 0.398942 -264.5 5.370560e-116 1\n",
"1 39.7 -20 0.398942 -242.0 3.174282e-106 1\n",
"2 39.7 -19 0.398942 -220.5 6.902029e-97 1\n",
"3 39.7 -18 0.398942 -200.0 5.520948e-88 1\n",
"4 39.7 -17 0.398942 -180.5 1.624636e-79 1\n",
"5 39.7 -16 0.398942 -162.0 1.758750e-71 1\n",
"6 39.7 -15 0.398942 -144.5 7.004182e-64 1\n",
"7 39.7 -14 0.398942 -128.0 1.026163e-56 1\n",
"8 39.7 -13 0.398942 -112.5 5.530710e-50 1\n",
"9 39.7 -12 0.398942 -98.0 1.096607e-43 1\n",
"10 39.7 -11 0.398942 -84.5 7.998828e-38 1\n",
"11 39.7 -10 0.398942 -72.0 2.146384e-32 1\n",
"12 39.7 -9 0.398942 -60.5 2.118819e-27 1\n",
"13 39.7 -8 0.398942 -50.0 7.694599e-23 1\n",
"14 39.7 -7 0.398942 -40.5 1.027977e-18 1\n",
"15 39.7 -6 0.398942 -32.0 5.052271e-15 1\n",
"16 39.7 -5 0.398942 -24.5 9.134720e-12 1\n",
"17 39.7 -4 0.398942 -18.0 6.075883e-09 1\n",
"18 39.7 -3 0.398942 -12.5 1.486720e-06 1\n",
"19 39.7 -2 0.398942 -8.0 1.338302e-04 1\n",
"20 39.7 -1 0.398942 -4.5 4.431848e-03 1\n",
"21 39.7 0 0.398942 -2.0 5.399097e-02 1\n",
"22 39.7 1 0.398942 -0.5 2.419707e-01 1\n",
"23 39.7 2 0.398942 -0.0 3.989423e-01 1\n",
"24 39.7 3 0.398942 -0.5 2.419707e-01 1\n",
"25 39.7 4 0.398942 -2.0 5.399097e-02 1\n",
"26 39.7 5 0.398942 -4.5 4.431848e-03 1\n",
"27 39.7 6 0.398942 -8.0 1.338302e-04 1\n",
"28 39.7 7 0.398942 -12.5 1.486720e-06 1\n",
"29 39.7 8 0.398942 -18.0 6.075883e-09 1\n",
"30 39.7 9 0.398942 -24.5 9.134720e-12 1\n",
"31 39.7 10 0.398942 -32.0 5.052271e-15 1\n",
"32 39.7 11 0.398942 -40.5 1.027977e-18 1\n",
"33 39.7 12 0.398942 -50.0 7.694599e-23 1\n",
"34 39.7 13 0.398942 -60.5 2.118819e-27 1\n",
"35 39.7 14 0.398942 -72.0 2.146384e-32 1\n",
"36 39.7 15 0.398942 -84.5 7.998828e-38 1\n",
"37 39.7 16 0.398942 -98.0 1.096607e-43 1\n",
"38 39.7 17 0.398942 -112.5 5.530710e-50 1\n",
"39 39.7 18 0.398942 -128.0 1.026163e-56 1\n",
"40 39.7 19 0.398942 -144.5 7.004182e-64 1\n",
"41 39.7 20 0.398942 -162.0 1.758750e-71 1"
]
},
"execution_count": 128,
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{
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"source": [
"XXX = np.sort(np.array(fires_thefts.x))\n",
"YYY = np.array(fires_thefts.y)\n",
"\n",
"\n",
"bw_manual =3\n",
"kernel_x = np.arange(-20,20, 0.1)\n",
"\n",
"input_x = XXX[0]\n",
"col1 = gauss_const(bw_manual)\n",
"col2 = gauss_exp(kernel_x, input_x, bw_manual)\n",
"col3 = kernel_function(bw_manual, kernel_x, input_x)\n",
"\n",
"\n",
"## Plotting gaussian for all input x points \n",
"kernel_fns = {'kernel_x': kernel_x}\n",
"for input_x in XXX: \n",
" input_string= 'x_value_{}'.format(np.round(input_x,2)) \n",
" kernel_fns[input_string] = kernel_function(bw_manual, kernel_x, input_x)\n",
"\n",
"kernels_df = pd.DataFrame(data=kernel_fns)\n",
"y_all = kernels_df.drop(columns='kernel_x')\n",
"px.line(kernels_df, x='kernel_x', y=y_all.columns, title='Gaussian for all input points', range_x=[-5,100])\n",
"\n",
"ypred_single = single_y_pred(bw_manual, XXX[0], XXX, YYY)\n",
"\n",
"Y_pred = []\n",
"for input_x in XXX: \n",
" w = []\n",
" Y_single = single_y_pred(bw_manual, input_x, XXX, YYY)\n",
" Y_pred.append(Y_single)\n",
" \n",
"\n",
"# Dataframe for a single observation point x_i. In the code x_i comes from new_x\n",
"data = {'Input_x': [input_x for x in range(col2.shape[0])],\n",
" 'kernel_x': kernel_x,\n",
" 'gaussian_const': [col1 for x in range(col2.shape[0])],\n",
" 'gaussian_exp': col2,\n",
" 'full_gaussian_value': col3,\n",
" 'bw':[bw_manual for x in range(col2.shape[0])],\n",
" }\n",
"single_pt_KE = pd.DataFrame(data=data)\n",
"single_pt_KE\n",
"\n",
"\n",
"data= {'x': XXX, 'y': YYY, 'y_manual': np.array(y_all)}\n",
"fig = px.scatter(x=XXX,y=YYY)\n",
"#fig.add_trace(go.Scatter(x=new_x, y=pred_y, name='Statsmodel KR', mode='lines'))\n",
"fig.add_trace(go.Scatter(x=XXX, y=np.array(Y_pred), name='Manual KR', mode='lines'))"
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}
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Reference in New Issue Copy Permalink