{ "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": 3, "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": 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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"white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Figure 1: Visualizing the generated data" }, "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": [ "# 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": 21, "metadata": {}, "outputs": [], "source": [ "kernel_x = np.arange(-2, 2, 0.01)\n", "bw_manual = 3\n", "\n", "def epanechnikov_one(h, ker_x, xi): \n", " \"\"\"\n", " Returns the epanechnikov function value.\n", " \"\"\"\n", " value = 0.75*(1-np.square((xi-ker_x)/h))\n", " if (value < 0):\n", " value = 0\n", " return value\n", "\n", "def epanechnikov_list(h, ker_x, xi): \n", " \"\"\"\n", " Returns the epanechnikov function value.\n", " \"\"\"\n", " value = 0.75*(1-np.square((xi-ker_x)/h))\n", " value = [0 if i < 0 else i for i in value]\n", " return value\n", "\n", "\n", "def weights_epanechnikov(bw_manual, input_x, all_input_values ): \n", " w_row = []\n", " for x_i in all_input_values: \n", " ki = epanechnikov_one(bw_manual, x_i, input_x)\n", " ki_sum = np.sum(epanechnikov_list(bw_manual, all_input_values, input_x))\n", " w_row.append(ki/ki_sum)\n", " return w_row\n", "\n", "def single_y_pred_epanechnikov(bw_manual, input_x, x_values, y_values): \n", " w = weights_epanechnikov(bw_manual, input_x, x_values)\n", " y_single = np.sum(np.dot(y_values,w))\n", " return y_single\n", "\n", "# We are selecting a single point and calculating the Kernel value\n", "input_x = 0\n", "col1 = KernelRegression.gauss_const(bw_manual)\n", "col2= KernelRegression.gauss_exp(kernel_x, input_x, bw_manual)\n", "col3 = epanechnikov_list(1, kernel_x, input_x)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "x=%{x}
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