{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " Loading BokehJS ...\n", "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "(function(global) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " var force = true;\n", "\n", " if (typeof (window._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n", " window._bokeh_onload_callbacks = [];\n", " window._bokeh_is_loading = undefined;\n", " }\n", "\n", "\n", " \n", " if (typeof (window._bokeh_timeout) === \"undefined\" || force === true) {\n", " window._bokeh_timeout = Date.now() + 5000;\n", " window._bokeh_failed_load = false;\n", " }\n", "\n", " var NB_LOAD_WARNING = {'data': {'text/html':\n", " \"
\\n\"+\n", " \"

\\n\"+\n", " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", " \"

\\n\"+\n", " \"\\n\"+\n", " \"\\n\"+\n", " \"from bokeh.resources import INLINE\\n\"+\n", " \"output_notebook(resources=INLINE)\\n\"+\n", " \"\\n\"+\n", " \"
\"}};\n", "\n", " function display_loaded() {\n", " if (window.Bokeh !== undefined) {\n", " var el = document.getElementById(\"ee49779f-d563-4fcb-ae28-e997a06043fd\");\n", " el.textContent = \"BokehJS \" + Bokeh.version + \" successfully loaded.\";\n", " } else if (Date.now() < window._bokeh_timeout) {\n", " setTimeout(display_loaded, 100)\n", " }\n", " }\n", "\n", " function run_callbacks() {\n", " window._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n", " delete window._bokeh_onload_callbacks\n", " console.info(\"Bokeh: all callbacks have finished\");\n", " }\n", "\n", " function load_libs(js_urls, callback) {\n", " window._bokeh_onload_callbacks.push(callback);\n", " if (window._bokeh_is_loading > 0) {\n", " console.log(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n", " return null;\n", " }\n", " if (js_urls == null || js_urls.length === 0) {\n", " run_callbacks();\n", " return null;\n", " }\n", " console.log(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n", " window._bokeh_is_loading = js_urls.length;\n", " for (var i = 0; i < js_urls.length; i++) {\n", " var url = js_urls[i];\n", " var s = document.createElement('script');\n", " s.src = url;\n", " s.async = false;\n", " s.onreadystatechange = s.onload = function() {\n", " window._bokeh_is_loading--;\n", " if (window._bokeh_is_loading === 0) {\n", " console.log(\"Bokeh: all BokehJS libraries loaded\");\n", " run_callbacks()\n", " }\n", " };\n", " s.onerror = function() {\n", " console.warn(\"failed to load library \" + url);\n", " };\n", " console.log(\"Bokeh: injecting script tag for BokehJS library: \", url);\n", " document.getElementsByTagName(\"head\")[0].appendChild(s);\n", " }\n", " };var element = document.getElementById(\"ee49779f-d563-4fcb-ae28-e997a06043fd\");\n", " if (element == null) {\n", " console.log(\"Bokeh: ERROR: autoload.js configured with elementid 'ee49779f-d563-4fcb-ae28-e997a06043fd' but no matching script tag was found. \")\n", " return false;\n", " }\n", "\n", " var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.5.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.5.min.js\"];\n", "\n", " var inline_js = [\n", " function(Bokeh) {\n", " Bokeh.set_log_level(\"info\");\n", " },\n", " \n", " function(Bokeh) {\n", " \n", " },\n", " \n", " function(Bokeh) {\n", " \n", " document.getElementById(\"ee49779f-d563-4fcb-ae28-e997a06043fd\").textContent = \"BokehJS is loading...\";\n", " },\n", " function(Bokeh) {\n", " console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.5.min.css\");\n", " Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.5.min.css\");\n", " console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.5.min.css\");\n", " Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.5.min.css\");\n", " }\n", " ];\n", "\n", " function run_inline_js() {\n", " \n", " if ((window.Bokeh !== undefined) || (force === true)) {\n", " for (var i = 0; i < inline_js.length; i++) {\n", " inline_js[i](window.Bokeh);\n", " }if (force === true) {\n", " display_loaded();\n", " }} else if (Date.now() < window._bokeh_timeout) {\n", " setTimeout(run_inline_js, 100);\n", " } else if (!window._bokeh_failed_load) {\n", " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n", " window._bokeh_failed_load = true;\n", " } else if (force !== true) {\n", " var cell = $(document.getElementById(\"ee49779f-d563-4fcb-ae28-e997a06043fd\")).parents('.cell').data().cell;\n", " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n", " }\n", "\n", " }\n", "\n", " if (window._bokeh_is_loading === 0) {\n", " console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n", " run_inline_js();\n", " } else {\n", " load_libs(js_urls, function() {\n", " console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n", " run_inline_js();\n", " });\n", " }\n", "}(this));" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from ipywidgets import interact\n", "from bokeh.plotting import figure, show, output_notebook\n", "from bokeh.layouts import gridplot\n", "from bokeh.io import push_notebook\n", "\n", "output_notebook()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## algorithm" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def local_regression(x0, X, Y, tau):\n", " # add bias term\n", " x0 = np.r_[1, x0]\n", " X = np.c_[np.ones(len(X)), X]\n", " \n", " # fit model: normal equations with kernel\n", " xw = X.T * radial_kernel(x0, X, tau)\n", " beta = np.linalg.pinv(xw @ X) @ xw @ Y\n", " \n", " # predict value\n", " return x0 @ beta" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def radial_kernel(x0, X, tau):\n", " return np.exp(np.sum((X - x0) ** 2, axis=1) / (-2 * tau * tau))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## data" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 1000\n", "\n", "# generate dataset\n", "X = np.linspace(-3, 3, num=n)\n", "Y = np.log(np.abs(X ** 2 - 1) + .5)\n", "\n", "# jitter X\n", "X += np.random.normal(scale=.1, size=n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## fit & plot models" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_lwr(tau):\n", " # prediction\n", " domain = np.linspace(-3, 3, num=300)\n", " prediction = [local_regression(x0, X, Y, tau) for x0 in domain]\n", "\n", " plot = figure(plot_width=400, plot_height=400)\n", " plot.title.text = 'tau=%g' % tau\n", " plot.scatter(X, Y, alpha=.3)\n", " plot.line(domain, prediction, line_width=2, color='red')\n", " \n", " return plot" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
\n", "
\n", "
\n", "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(gridplot([\n", " [plot_lwr(10.), plot_lwr(1.)],\n", " [plot_lwr(0.1), plot_lwr(0.01)]\n", "]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## interactive model" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
\n", "
\n", "
\n", "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "

<Bokeh Notebook handle for In[7]>

" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def interactive_update(tau):\n", " model.data_source.data['y'] = [local_regression(x0, X, Y, tau) for x0 in domain]\n", " push_notebook()\n", "\n", "domain = np.linspace(-3, 3, num=100)\n", "prediction = [local_regression(x0, X, Y, 1.) for x0 in domain]\n", "\n", "plot = figure()\n", "plot.scatter(X, Y, alpha=.3)\n", "model = plot.line(domain, prediction, line_width=2, color='red')\n", "show(plot, notebook_handle=True)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e142749d1ac44704bcf81ddd6742be8c" } }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "interact(interactive_update, tau=(0.01, 3., 0.01))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "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": "3.6.1" }, "widgets": { "state": { "a40d45b883bd45e6853fbf2102edc08a": { "views": [ { "cell_index": 12 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 2 }