diff --git a/.ipynb_checkpoints/KernelRegression-checkpoint.ipynb b/.ipynb_checkpoints/KernelRegression-checkpoint.ipynb
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+++ b/.ipynb_checkpoints/KernelRegression-checkpoint.ipynb
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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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+ "np.random.seed(1)# xwidth controls the range of x values.\n",
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+ "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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+ "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",
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+ "# Plot the x and y values \n",
+ "px.scatter(x=new_x,y=fun_y(new_x), title='Figure 1: Visualizing the generated data')"
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+ "cell_type": "code",
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+ "#fig = px.scatter(x=new_x,y=fun_y(new_x), title='Figure 2: Statsmodels fit to generated data')\n",
+ "#fig.add_trace(go.Scatter(x=new_x, y=pred_y, name='Statsmodels fit', mode='lines'))"
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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",
+ "# \"\"\"\n",
+ "# return 1/(h*np.sqrt(np.pi*2))\n",
+ "#\n",
+ "#def gauss_exp(ker_x, xi, h): \n",
+ "# \"\"\"\n",
+ "# #Returns the gaussian function exponent term\n",
+ "# \"\"\"\n",
+ "# num = - 0.5*np.square((xi- ker_x))\n",
+ "# den = h*h\n",
+ "# return num/den\n",
+ "#\n",
+ "#def kernel_function(h, ker_x, xi): \n",
+ "# \"\"\"\n",
+ "# #Returns the gaussian function value. Combines the gauss_const and\n",
+ "# #gauss_exp to get this result\n",
+ "# \"\"\"\n",
+ "# const = gauss_const(h)\n",
+ "# gauss_val = const*np.exp(gauss_exp(ker_x,xi,h))\n",
+ "# return gauss_val\n",
+ "\n",
+ "# We are selecting a single point and calculating the Kernel value\n",
+ "input_x = new_x[0]\n",
+ "col1 = KernelRegression.gauss_const(bw_manual)\n",
+ "col2= KernelRegression.gauss_exp(kernel_x, input_x, bw_manual)\n",
+ "col3 = KernelRegression.kernel_function(bw_manual, kernel_x, input_x)"
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+ "\n",
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+ "execution_count": 10,
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+ "source": [
+ "# 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"
+ ]
+ },
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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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+ "cell_type": "code",
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+ "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)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "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'"
+ ]
+ }
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+ "for input_x in new_x: \n",
+ " w = []\n",
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+ " Y_pred.append(Y_single)"
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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",
+ "#fig.add_trace(go.Scatter(x=new_x, y=pred_y, name='Statsmodel KR', mode='lines'))\n",
+ "fig.add_trace(go.Scatter(x=new_x, y=np.array(Y_pred), name='Manual KR', mode='lines'))"
+ ]
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+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fires_thefts = pd.read_csv('fires_thefts.csv', names=['x','y'])\n"
+ ]
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+ "linecolor": "white",
+ "ticks": "",
+ "title": {
+ "standoff": 15
+ },
+ "zerolinecolor": "white",
+ "zerolinewidth": 2
+ }
+ }
+ },
+ "xaxis": {
+ "anchor": "y",
+ "domain": [
+ 0,
+ 1
+ ],
+ "title": {
+ "text": "x"
+ }
+ },
+ "yaxis": {
+ "anchor": "x",
+ "domain": [
+ 0,
+ 1
+ ],
+ "title": {
+ "text": "y"
+ }
+ }
+ }
+ },
+ "text/html": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "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'))"
+ ]
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Slideshow",
+ "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": "3.8.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/.ipynb_checkpoints/kernel_regression-checkpoint.ipynb b/.ipynb_checkpoints/kernel_regression-checkpoint.ipynb
new file mode 100644
index 0000000..a860370
--- /dev/null
+++ b/.ipynb_checkpoints/kernel_regression-checkpoint.ipynb
@@ -0,0 +1,99 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "50d1198e",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Regresja jÄ…drowa
\n",
+ "\n",
+ "#### Karolina Oparczyk, Tomasz Grzybowski, Jan Nowak\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f792be04",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Regresja jądrowa używana jest jako funkcja wagi do opracowania modelu regresji nieparametrycznej. Nadaje ona niektórym elementom zbioru większą \"wagę\", która ma wpływ na ostateczny wynik. \n",
+ "\n",
+ "Można ją porównać do rysowania krzywej na wykresie punktowym tak, aby była jak najlepiej do nich dopasowana. Jest mniej wrażliwa na wartości odstające, niż na przykład regresja liniowa."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ce35888e",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Właściwości regresji jądrowej:\n",
+ "* symetryczna - wartość maksymalna leży pośrodku krzywej\n",
+ "\n",
+ "* powierzchnia pod krzywÄ… funkcji wynosi 1\n",
+ "* wartość funkcji jądrowej nie jest ujemna"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "dbe6165c",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "Przykłady:\n",
+ "* jÄ…dro Gaussa\n",
+ "\\begin{equation}\n",
+ "K(x) = (2\\pi)^{-\\frac12} \\text{ exp } (-\\frac{{x}^{2}}2) \\text{ lg}(x)\n",
+ "\\end{equation}\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f46e92e5",
+ "metadata": {},
+ "source": [
+ "* jÄ…dro Epanechnikova\n",
+ "\\begin{equation}\n",
+ "K(x) = (\\frac34)(1-x^2)l_{|x|\\leq1}(x)\n",
+ "\\end{equation}\n",
+ ""
+ ]
+ }
+ ],
+ "metadata": {
+ "celltoolbar": "Slideshow",
+ "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": "3.8.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/KernelRegression.ipynb b/KernelRegression.ipynb
index a83c305..39629eb 100644
--- a/KernelRegression.ipynb
+++ b/KernelRegression.ipynb
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
- "execution_count": 76,
+ "execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "-"
@@ -14,12 +14,13 @@
"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 "
+ "import pandas as pd \n",
+ "import KernelRegression"
]
},
{
"cell_type": "code",
- "execution_count": 77,
+ "execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
@@ -35,7 +36,7 @@
},
{
"cell_type": "code",
- "execution_count": 49,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -47,7 +48,7 @@
" 14.78002175, 15.96551436, 16.82442832, 18.00844275, 19.11656304])"
]
},
- "execution_count": 49,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -58,7 +59,7 @@
},
{
"cell_type": "code",
- "execution_count": 78,
+ "execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
@@ -74,9 +75,91 @@
},
{
"cell_type": "code",
- "execution_count": 79,
+ "execution_count": 5,
"metadata": {},
"outputs": [
+ {
+ "data": {
+ "text/html": [
+ " \n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
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"application/vnd.plotly.v1+json": {
@@ -980,9 +1063,9 @@
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"text/html": [
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+ " "
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+ },
+ "metadata": {},
+ "output_type": "display_data"
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@@ -22767,9 +22944,9 @@
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