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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 \n",
"import KernelRegression"
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"x = np.arange(0,xwidth,1)# we want to add some noise to the x values so that dont sit at regular intervals\n",
"x_residuals = np.random.normal(scale=0.2, size=[x.shape[0]])# new_x is the range of x values we will be using all the way through\n",
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"num_points = x.shape[0]\n",
"residuals = np.random.normal(scale=2.0, size=[num_points])# We will be using fun_y to generate y values all the way through\n",
"fun_y = lambda x: -(x*x) + residuals"
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"array([ 0.32486907, 0.87764872, 1.89436565, 2.78540628, 4.17308153,\n",
" 4.53969226, 6.34896235, 6.84775862, 8.06380782, 8.95012592,\n",
" 10.29242159, 10.58797186, 11.93551656, 12.92318913, 14.22675389,\n",
" 14.78002175, 15.96551436, 16.82442832, 18.00844275, 19.11656304])"
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"x = np.arange(0,xwidth,1)# we want to add some noise to the x values so that dont sit at regular intervals\n",
"x_residuals = np.random.normal(scale=0.2, size=[x.shape[0]])# new_x is the range of x values we will be using all the way through\n",
"new_x = x + x_residuals# We generate residuals for y values since we want to show some variation in the data\n",
"num_points = x.shape[0]\n",
"residuals = np.random.normal(scale=2.0, size=[num_points])# We will be using fun_y to generate y values all the way through\n",
"fun_y = lambda x: -(x*x) + residuals"
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"# We are selecting a single point and calculating the Kernel value\n",
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"## Plotting gaussian for all input x points \n",
"kernel_fns = {'kernel_x': kernel_x}\n",
"for input_x in new_x: \n",
" input_string= 'x_value_{}'.format(np.round(input_x,2)) \n",
" kernel_fns[input_string] = KernelRegression.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=[-5,20])"
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"source": [
"def weights(bw_manual, input_x, all_input_values ): \n",
" w_row = []\n",
" for x_i in all_input_values: \n",
" ki = kernel_function(bw_manual, x_i, input_x)\n",
" ki_sum = np.sum(KernelRegression.kernel_function(bw_manual, all_input_values, input_x))\n",
" w_row.append(ki/ki_sum)\n",
" return w_row\n",
"\n",
"def single_y_pred(bw_manual, input_x, iks, igrek): \n",
" w = weights(bw_manual, input_x, iks)\n",
" y_single = np.sum(np.dot(igrek,w))\n",
" return y_single\n",
"\n",
"#ypred_single = single_y_pred(bw_manual, new_x[0], new_x)"
]
},
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"cell_type": "code",
"execution_count": 16,
"metadata": {},
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{
"ename": "TypeError",
"evalue": "single_y_pred() missing 1 required positional argument: 'igrek'",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0minput_x\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnew_x\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mY_single\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msingle_y_pred\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbw_manual\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput_x\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew_x\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0mY_pred\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY_single\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mTypeError\u001b[0m: single_y_pred() missing 1 required positional argument: 'igrek'"
]
}
],
"source": [
"Y_pred = []\n",
"for input_x in new_x: \n",
" w = []\n",
" Y_single = single_y_pred(bw_manual, input_x, new_x)\n",
" Y_pred.append(Y_single)"
]
},
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"cell_type": "code",
"execution_count": 34,
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"data= {'x': new_x, 'y': fun_y(new_x), 'y_manual': np.array(y_all)}\n",
"fig = px.scatter(x=new_x,y=fun_y(x))\n",
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},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
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]
},
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"cell_type": "code",
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"standoff": 15
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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",
"## 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] = KernelRegression.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",
"\n",
"Y_pred = []\n",
"for input_x in XXX: \n",
" w = []\n",
" Y_single = KernelRegression.single_y_pred(bw_manual, input_x, XXX, YYY)\n",
" Y_pred.append(Y_single)\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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