diff --git a/.ipynb_checkpoints/KernelRegression-checkpoint.ipynb b/.ipynb_checkpoints/KernelRegression-checkpoint.ipynb new file mode 100644 index 0000000..39629eb --- /dev/null +++ b/.ipynb_checkpoints/KernelRegression-checkpoint.ipynb @@ -0,0 +1,23033 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "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" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(1)# xwidth controls the range of x values.\n", + "xwidth = 20\n", + "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" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "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])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "new_x" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "np.random.seed(1)# xwidth controls the range of x values.\n", + "xwidth = 20\n", + "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" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "hovertemplate": "x=%{x}
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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "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", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "#ker_log = KernelReg(new_x, fun_y(new_x), 'c')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "#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'))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "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)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "## 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])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "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)" + ] + }, + { + "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'" + ] + } + ], + "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)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "hovertemplate": "x=%{x}
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" + ] + }, + "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 krzywą funkcji wynosi 1\n", + "* wartość funkcji jądrowej nie jest ujemna" + ] + }, + { + "cell_type": "markdown", + "id": "dbe6165c", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Przykłady:\n", + "* jądro 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": [ + "* jądro 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" + }, { "data": { "application/vnd.plotly.v1+json": { @@ -980,9 +1063,9 @@ } }, "text/html": [ - "
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