{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Models Regularization" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import addutils.toc ; addutils.toc.js(ipy_notebook=True)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "from addutils import css_notebook\n", "from sklearn.datasets.samples_generator import make_regression\n", "from sklearn import linear_model\n", "from sklearn import metrics\n", "css_notebook()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " Loading BokehJS ...\n", "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " var force = true;\n", "\n", " if (typeof (root._bokeh_onload_callbacks) === \"undefined\" || force === true) {\n", " root._bokeh_onload_callbacks = [];\n", " root._bokeh_is_loading = undefined;\n", " }\n", "\n", " var JS_MIME_TYPE = 'application/javascript';\n", " var HTML_MIME_TYPE = 'text/html';\n", " var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", " var CLASS_NAME = 'output_bokeh rendered_html';\n", "\n", " /**\n", " * Render data to the DOM node\n", " */\n", " function render(props, node) {\n", " var script = document.createElement(\"script\");\n", " node.appendChild(script);\n", " }\n", "\n", " /**\n", " * Handle when an output is cleared or removed\n", " */\n", " function handleClearOutput(event, handle) {\n", " var cell = handle.cell;\n", "\n", " var id = cell.output_area._bokeh_element_id;\n", " var server_id = cell.output_area._bokeh_server_id;\n", " // Clean up Bokeh references\n", " if (id !== undefined) {\n", " Bokeh.index[id].model.document.clear();\n", " delete Bokeh.index[id];\n", " }\n", "\n", " if (server_id !== undefined) {\n", " // Clean up Bokeh references\n", " var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n", " cell.notebook.kernel.execute(cmd, {\n", " iopub: {\n", " output: function(msg) {\n", " var element_id = msg.content.text.trim();\n", " Bokeh.index[element_id].model.document.clear();\n", " delete Bokeh.index[element_id];\n", " }\n", " }\n", " });\n", " // Destroy server and session\n", " var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n", " cell.notebook.kernel.execute(cmd);\n", " }\n", " }\n", "\n", " /**\n", " * Handle when a new output is added\n", " */\n", " function handleAddOutput(event, handle) {\n", " var output_area = handle.output_area;\n", " var output = handle.output;\n", "\n", " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n", " if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n", " return\n", " }\n", "\n", " var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n", "\n", " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n", " toinsert[0].firstChild.textContent = output.data[JS_MIME_TYPE];\n", " // store reference to embed id on output_area\n", " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", " }\n", " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n", " var bk_div = document.createElement(\"div\");\n", " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n", " var script_attrs = bk_div.children[0].attributes;\n", " for (var i = 0; i < script_attrs.length; i++) {\n", " toinsert[0].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n", " }\n", " // store reference to server id on output_area\n", " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n", " }\n", " }\n", "\n", " function register_renderer(events, OutputArea) {\n", "\n", " function append_mime(data, metadata, element) {\n", " // create a DOM node to render to\n", " var toinsert = this.create_output_subarea(\n", " metadata,\n", " CLASS_NAME,\n", " EXEC_MIME_TYPE\n", " );\n", " this.keyboard_manager.register_events(toinsert);\n", " // Render to node\n", " var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", " render(props, toinsert[0]);\n", " element.append(toinsert);\n", " return toinsert\n", " }\n", "\n", " /* Handle when an output is cleared or removed */\n", " events.on('clear_output.CodeCell', handleClearOutput);\n", " events.on('delete.Cell', handleClearOutput);\n", "\n", " /* Handle when a new output is added */\n", " events.on('output_added.OutputArea', handleAddOutput);\n", "\n", " /**\n", " * Register the mime type and append_mime function with output_area\n", " */\n", " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", " /* Is output safe? */\n", " safe: true,\n", " /* Index of renderer in `output_area.display_order` */\n", " index: 0\n", " });\n", " }\n", "\n", " // register the mime type if in Jupyter Notebook environment and previously unregistered\n", " if (root.Jupyter !== undefined) {\n", " var events = require('base/js/events');\n", " var OutputArea = require('notebook/js/outputarea').OutputArea;\n", "\n", " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n", " register_renderer(events, OutputArea);\n", " }\n", " }\n", "\n", " \n", " if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n", " root._bokeh_timeout = Date.now() + 5000;\n", " root._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", " \"
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  • re-rerun `output_notebook()` to attempt to load from CDN again, or
    • \\n\"+\n", " \"
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\\n\"+\n", " \"\\n\"+\n", " \"from bokeh.resources import INLINE\\n\"+\n", " \"output_notebook(resources=INLINE)\\n\"+\n", " \"\\n\"+\n", " \"
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\\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 \"
  • re-rerun `output_notebook()` to attempt to load from CDN again, or
    • \\n\"+\n \"
  • use INLINE resources instead, as so:
    • \\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 var el = document.getElementById(\"726bfcf0-fddb-4fa8-b26b-5cd3fa9b72d3\");\n if (el != null) {\n el.textContent = \"BokehJS is loading...\";\n }\n if (root.Bokeh !== undefined) {\n if (el != null) {\n el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(display_loaded, 100)\n }\n }\n\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) { callback() });\n }\n finally {\n delete root._bokeh_onload_callbacks\n }\n console.info(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(js_urls, callback) {\n root._bokeh_onload_callbacks.push(callback);\n if (root._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 root._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 root._bokeh_is_loading--;\n if (root._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(\"726bfcf0-fddb-4fa8-b26b-5cd3fa9b72d3\");\n if (element == null) {\n console.log(\"Bokeh: ERROR: autoload.js configured with elementid '726bfcf0-fddb-4fa8-b26b-5cd3fa9b72d3' but no matching script tag was found. \")\n return false;\n }\n\n var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-0.12.13.min.js\"];\n\n var inline_js = [\n function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\n \n function(Bokeh) {\n \n },\n function(Bokeh) {\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.13.min.css\");\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-widgets-0.12.13.min.css\");\n console.log(\"Bokeh: injecting CSS: https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-tables-0.12.13.min.css\");\n }\n ];\n\n function run_inline_js() {\n \n if ((root.Bokeh !== undefined) || (force === true)) {\n for (var i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n var cell = $(document.getElementById(\"726bfcf0-fddb-4fa8-b26b-5cd3fa9b72d3\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n\n }\n\n if (root._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}(window));" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import bokeh.plotting as bk\n", "from bokeh import palettes\n", "from bokeh.layouts import gridplot\n", "bk.output_notebook()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1 Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We talked about linear models, but we know from real life situations that it is not always the case. How can we transform linear models to be able to cope with nonlinearity?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 Going beyond linearity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I have simulated a sine curve (between 60° and 300°) and added some random noise using the following code:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", "
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np.array([i*np.pi/180 for i in range(60,300,4)])\n", "np.random.seed(10) #Setting seed for reproducability\n", "y = np.sin(x) + np.random.normal(0,0.15,len(x))\n", "data = pd.DataFrame(np.column_stack([x,y]),columns=['x','y'])\n", "fig = bk.figure(plot_width=630, plot_height=300, title=None)\n", "fig.circle(data['x'], data['y'],)\n", "bk.show(fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This resembles a sine curve but not exactly because of the noise. We’ll use this as an example to test different scenarios in this article. Lets try to estimate the sine function using polynomial regression with powers of x form 1 to 15. Lets add a column for each power upto 15 in our dataframe. This can be accomplished using the following code:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y x_2 x_3 x_4 x_5 x_6 \\\n", "0 1.047198 1.065763 1.096623 1.148381 1.202581 1.259340 1.318778 \n", "1 1.117011 1.006086 1.247713 1.393709 1.556788 1.738948 1.942424 \n", "2 1.186824 0.695374 1.408551 1.671702 1.984016 2.354677 2.794587 \n", "3 1.256637 0.949799 1.579137 1.984402 2.493673 3.133642 3.937850 \n", "4 1.326450 1.063496 1.759470 2.333850 3.095735 4.106339 5.446854 \n", "\n", " x_7 x_8 x_9 x_10 x_11 x_12 x_13 \\\n", "0 1.381021 1.446202 1.514459 1.585938 1.660790 1.739176 1.821260 \n", "1 2.169709 2.423588 2.707173 3.023942 3.377775 3.773011 4.214494 \n", "2 3.316683 3.936319 4.671717 5.544505 6.580351 7.809718 9.268760 \n", "3 4.948448 6.218404 7.814277 9.819710 12.339811 15.506664 19.486248 \n", "4 7.224981 9.583578 12.712139 16.862020 22.366630 29.668222 39.353420 \n", "\n", " x_14 x_15 \n", "0 1.907219 1.997235 \n", "1 4.707635 5.258479 \n", "2 11.000386 13.055521 \n", "3 24.487142 30.771450 \n", "4 52.200353 69.241170 \n" ] } ], "source": [ "for i in range(2,16): #power of 1 is already there\n", " data['x_{}'.format(i)] = data['x']**i\n", "print(data.head())" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def linear_power_model(model, data, power):\n", " #initialize predictors:\n", " predictors=['x']\n", " if power >= 2:\n", " predictors += ['x_{}'.format(i) for i in range(2,power+1)]\n", " \n", " #Fit the model\n", " model.fit(data[predictors],data['y'])\n", " y_pred = model.predict(data[predictors])\n", " \n", " #Return the result in pre-defined format\n", " rss = sum((y_pred-data['y'])**2)\n", " ret = [rss]\n", " ret.extend([model.intercept_])\n", " ret.extend(model.coef_)\n", " return ret, y_pred" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "results = {}\n", "regr = linear_model.LinearRegression(normalize=True)\n", "for i in range(1,16):\n", " results[i] = linear_power_model(regr, data, i)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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"grid = []\n", "for m in [1, 3, 6, 9, 12, 15]:\n", " p = bk.figure(plot_width=230, plot_height=300, title='Plot for power {}'.format(m))\n", " p.circle(data['x'], data['y'],)\n", " p.line(data['x'], results[m][1], color='firebrick')\n", " grid.append(p)\n", "bk.show(gridplot(grid, ncols=3))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n", "ind = ['model_pow_%d'%i for i in range(1,16)]\n", "coef_matrix_simple = pd.DataFrame(index=ind, columns=col)\n", "for i in range(1,16):\n", " coef_matrix_simple.iloc[i-1,0:i+2] = results[i][0]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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rssinterceptcoef_x_1coef_x_2coef_x_3coef_x_4coef_x_5coef_x_6coef_x_7coef_x_8coef_x_9coef_x_10coef_x_11coef_x_12coef_x_13coef_x_14coef_x_15
model_pow_13.32-0.62NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_23.31.9-0.58-0.006NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_31.1-1.13-1.30.14NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_41.1-0.271.7-0.53-0.0360.014NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_513-5.14.7-1.90.33-0.021NaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_60.99-2.89.5-9.75.2-1.60.23-0.014NaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_70.9319-5669-4517-3.50.4-0.019NaNNaNNaNNaNNaNNaNNaNNaN
model_pow_80.9243-1.4e+021.8e+02-1.3e+0258-152.4-0.210.0077NaNNaNNaNNaNNaNNaNNaN
model_pow_90.871.7e+02-6.1e+029.6e+02-8.5e+024.6e+02-1.6e+0237-5.20.42-0.015NaNNaNNaNNaNNaNNaN
model_pow_100.871.4e+02-4.9e+027.3e+02-6e+022.9e+02-8715-0.81-0.140.026-0.0013NaNNaNNaNNaNNaN
model_pow_110.87-755.1e+02-1.3e+031.9e+03-1.6e+039.1e+02-3.5e+0291-161.8-0.120.0034NaNNaNNaNNaN
model_pow_120.87-3.4e+021.9e+03-4.4e+036e+03-5.2e+033.1e+03-1.3e+033.8e+02-8012-1.10.062-0.0016NaNNaNNaN
model_pow_130.863.2e+03-1.8e+044.5e+04-6.7e+046.6e+04-4.6e+042.3e+04-8.5e+032.3e+03-4.5e+0262-5.70.31-0.0078NaNNaN
model_pow_140.792.4e+04-1.4e+053.8e+05-6.1e+056.6e+05-5e+052.8e+05-1.2e+053.7e+04-8.5e+031.5e+03-1.8e+0215-0.730.017NaN
model_pow_150.7-3.6e+042.4e+05-7.5e+051.4e+06-1.7e+061.5e+06-1e+065e+05-1.9e+055.4e+04-1.2e+041.9e+03-2.2e+0217-0.810.018
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" ], "text/plain": [ " rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5 \\\n", "model_pow_1 3.3 2 -0.62 NaN NaN NaN NaN \n", "model_pow_2 3.3 1.9 -0.58 -0.006 NaN NaN NaN \n", "model_pow_3 1.1 -1.1 3 -1.3 0.14 NaN NaN \n", "model_pow_4 1.1 -0.27 1.7 -0.53 -0.036 0.014 NaN \n", "model_pow_5 1 3 -5.1 4.7 -1.9 0.33 -0.021 \n", "model_pow_6 0.99 -2.8 9.5 -9.7 5.2 -1.6 0.23 \n", "model_pow_7 0.93 19 -56 69 -45 17 -3.5 \n", "model_pow_8 0.92 43 -1.4e+02 1.8e+02 -1.3e+02 58 -15 \n", "model_pow_9 0.87 1.7e+02 -6.1e+02 9.6e+02 -8.5e+02 4.6e+02 -1.6e+02 \n", "model_pow_10 0.87 1.4e+02 -4.9e+02 7.3e+02 -6e+02 2.9e+02 -87 \n", "model_pow_11 0.87 -75 5.1e+02 -1.3e+03 1.9e+03 -1.6e+03 9.1e+02 \n", "model_pow_12 0.87 -3.4e+02 1.9e+03 -4.4e+03 6e+03 -5.2e+03 3.1e+03 \n", "model_pow_13 0.86 3.2e+03 -1.8e+04 4.5e+04 -6.7e+04 6.6e+04 -4.6e+04 \n", "model_pow_14 0.79 2.4e+04 -1.4e+05 3.8e+05 -6.1e+05 6.6e+05 -5e+05 \n", "model_pow_15 0.7 -3.6e+04 2.4e+05 -7.5e+05 1.4e+06 -1.7e+06 1.5e+06 \n", "\n", " coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11 \\\n", "model_pow_1 NaN NaN NaN NaN NaN NaN \n", "model_pow_2 NaN NaN NaN NaN NaN NaN \n", "model_pow_3 NaN NaN NaN NaN NaN NaN \n", "model_pow_4 NaN NaN NaN NaN NaN NaN \n", "model_pow_5 NaN NaN NaN NaN NaN NaN \n", "model_pow_6 -0.014 NaN NaN NaN NaN NaN \n", "model_pow_7 0.4 -0.019 NaN NaN NaN NaN \n", "model_pow_8 2.4 -0.21 0.0077 NaN NaN NaN \n", "model_pow_9 37 -5.2 0.42 -0.015 NaN NaN \n", "model_pow_10 15 -0.81 -0.14 0.026 -0.0013 NaN \n", "model_pow_11 -3.5e+02 91 -16 1.8 -0.12 0.0034 \n", "model_pow_12 -1.3e+03 3.8e+02 -80 12 -1.1 0.062 \n", "model_pow_13 2.3e+04 -8.5e+03 2.3e+03 -4.5e+02 62 -5.7 \n", "model_pow_14 2.8e+05 -1.2e+05 3.7e+04 -8.5e+03 1.5e+03 -1.8e+02 \n", "model_pow_15 -1e+06 5e+05 -1.9e+05 5.4e+04 -1.2e+04 1.9e+03 \n", "\n", " coef_x_12 coef_x_13 coef_x_14 coef_x_15 \n", "model_pow_1 NaN NaN NaN NaN \n", "model_pow_2 NaN NaN NaN NaN \n", "model_pow_3 NaN NaN NaN NaN \n", "model_pow_4 NaN NaN NaN NaN \n", "model_pow_5 NaN NaN NaN NaN \n", "model_pow_6 NaN NaN NaN NaN \n", "model_pow_7 NaN NaN NaN NaN \n", "model_pow_8 NaN NaN NaN NaN \n", "model_pow_9 NaN NaN NaN NaN \n", "model_pow_10 NaN NaN NaN NaN \n", "model_pow_11 NaN NaN NaN NaN \n", "model_pow_12 -0.0016 NaN NaN NaN \n", "model_pow_13 0.31 -0.0078 NaN NaN \n", "model_pow_14 15 -0.73 0.017 NaN \n", "model_pow_15 -2.2e+02 17 -0.81 0.018 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.options.display.float_format = '{:,.2g}'.format\n", "coef_matrix_simple" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is clearly evident that the size of coefficients increase exponentially with increase in model complexity. I hope this gives some intuition into why putting a constraint on the magnitude of coefficients can be a good idea to reduce model complexity.\n", "\n", "Lets try to understand this even better.\n", "\n", "What does a large coefficient signify? It means that we’re putting a lot of emphasis on that feature, i.e. the particular feature is a good predictor for the outcome. When it becomes too large, the algorithm starts modelling intricate relations to estimate the output and ends up overfitting to the particular training data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2 Ridge Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear Regression rely on the independence of the model terms. When terms are correlated and the columns of the design matrix $X$; have an approximate linear dependence, the matrix $(X^TX)^{-1}$ becomes\n", "close to singular. As a result, the least-squares estimate becomes highly sensitive to random errors in the observed response *y*, producing a large variance. This situation of multicollinearity can arise, for example, when data are collected without an experimental design.\n", "\n", "The ridge coefficients minimize a penalized residual sum of squares:\n", "\n", "$$ \\underset{w}{min} \\|Xw -y\\|_2^2 + \\alpha \\|w\\|_2^2$$\n", "\n", "Here, positive $\\alpha \\geq 0 \\hspace{2 pt}$ is a complexity parameter that controls the amount of shrinkage: the larger the value of $\\alpha$, the greater the amount of shrinkage and thus the coefficients become more robust to collinearity.\n", "\n", "One thing is for sure that any non-zero value would give values less than that of simple linear regression. By how much? We’ll find out soon. Lets see ridge regression in action on the same problem as above." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "alpha_ridge = [1e-15, 1e-10, 1e-8, 1e-4, 1e-3,1e-2, 1, 5, 10, 20]\n", "results = {}\n", "for alpha in alpha_ridge:\n", " ridgereg = linear_model.Ridge(alpha=alpha,normalize=True)\n", " results[alpha] = linear_power_model(ridgereg, data, 15)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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"grid = []\n", "for m in [1e-15, 1e-10, 1e-3, 1e-2, 1, 5]:\n", " p = bk.figure(plot_width=230, plot_height=300, title='Plot for alpha {}'.format(m))\n", " p.circle(data['x'], data['y'],)\n", " p.line(data['x'], results[m][1], color='firebrick')\n", " grid.append(p)\n", "bk.show(gridplot(grid, ncols=3))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n", "ind = ['alpha_%.2g'%alpha_ridge[i] for i in range(0,10)]\n", "coef_matrix_ridge = pd.DataFrame(index=ind, columns=col)\n", "\n", "for i,e in enumerate(alpha_ridge):\n", " coef_matrix_ridge.iloc[i,] = results[e][0]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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rssinterceptcoef_x_1coef_x_2coef_x_3coef_x_4coef_x_5coef_x_6coef_x_7coef_x_8coef_x_9coef_x_10coef_x_11coef_x_12coef_x_13coef_x_14coef_x_15
model_pow_13.32-0.62NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_23.31.9-0.58-0.006NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_31.1-1.13-1.30.14NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_41.1-0.271.7-0.53-0.0360.014NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_513-5.14.7-1.90.33-0.021NaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_60.99-2.89.5-9.75.2-1.60.23-0.014NaNNaNNaNNaNNaNNaNNaNNaNNaN
model_pow_70.9319-5669-4517-3.50.4-0.019NaNNaNNaNNaNNaNNaNNaNNaN
model_pow_80.9243-1.4e+021.8e+02-1.3e+0258-152.4-0.210.0077NaNNaNNaNNaNNaNNaNNaN
model_pow_90.871.7e+02-6.1e+029.6e+02-8.5e+024.6e+02-1.6e+0237-5.20.42-0.015NaNNaNNaNNaNNaNNaN
model_pow_100.871.4e+02-4.9e+027.3e+02-6e+022.9e+02-8715-0.81-0.140.026-0.0013NaNNaNNaNNaNNaN
model_pow_110.87-755.1e+02-1.3e+031.9e+03-1.6e+039.1e+02-3.5e+0291-161.8-0.120.0034NaNNaNNaNNaN
model_pow_120.87-3.4e+021.9e+03-4.4e+036e+03-5.2e+033.1e+03-1.3e+033.8e+02-8012-1.10.062-0.0016NaNNaNNaN
model_pow_130.863.2e+03-1.8e+044.5e+04-6.7e+046.6e+04-4.6e+042.3e+04-8.5e+032.3e+03-4.5e+0262-5.70.31-0.0078NaNNaN
model_pow_140.792.4e+04-1.4e+053.8e+05-6.1e+056.6e+05-5e+052.8e+05-1.2e+053.7e+04-8.5e+031.5e+03-1.8e+0215-0.730.017NaN
model_pow_150.7-3.6e+042.4e+05-7.5e+051.4e+06-1.7e+061.5e+06-1e+065e+05-1.9e+055.4e+04-1.2e+041.9e+03-2.2e+0217-0.810.018
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" ], "text/plain": [ " rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5 \\\n", "model_pow_1 3.3 2 -0.62 NaN NaN NaN NaN \n", "model_pow_2 3.3 1.9 -0.58 -0.006 NaN NaN NaN \n", "model_pow_3 1.1 -1.1 3 -1.3 0.14 NaN NaN \n", "model_pow_4 1.1 -0.27 1.7 -0.53 -0.036 0.014 NaN \n", "model_pow_5 1 3 -5.1 4.7 -1.9 0.33 -0.021 \n", "model_pow_6 0.99 -2.8 9.5 -9.7 5.2 -1.6 0.23 \n", "model_pow_7 0.93 19 -56 69 -45 17 -3.5 \n", "model_pow_8 0.92 43 -1.4e+02 1.8e+02 -1.3e+02 58 -15 \n", "model_pow_9 0.87 1.7e+02 -6.1e+02 9.6e+02 -8.5e+02 4.6e+02 -1.6e+02 \n", "model_pow_10 0.87 1.4e+02 -4.9e+02 7.3e+02 -6e+02 2.9e+02 -87 \n", "model_pow_11 0.87 -75 5.1e+02 -1.3e+03 1.9e+03 -1.6e+03 9.1e+02 \n", "model_pow_12 0.87 -3.4e+02 1.9e+03 -4.4e+03 6e+03 -5.2e+03 3.1e+03 \n", "model_pow_13 0.86 3.2e+03 -1.8e+04 4.5e+04 -6.7e+04 6.6e+04 -4.6e+04 \n", "model_pow_14 0.79 2.4e+04 -1.4e+05 3.8e+05 -6.1e+05 6.6e+05 -5e+05 \n", "model_pow_15 0.7 -3.6e+04 2.4e+05 -7.5e+05 1.4e+06 -1.7e+06 1.5e+06 \n", "\n", " coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11 \\\n", "model_pow_1 NaN NaN NaN NaN NaN NaN \n", "model_pow_2 NaN NaN NaN NaN NaN NaN \n", "model_pow_3 NaN NaN NaN NaN NaN NaN \n", "model_pow_4 NaN NaN NaN NaN NaN NaN \n", "model_pow_5 NaN NaN NaN NaN NaN NaN \n", "model_pow_6 -0.014 NaN NaN NaN NaN NaN \n", "model_pow_7 0.4 -0.019 NaN NaN NaN NaN \n", "model_pow_8 2.4 -0.21 0.0077 NaN NaN NaN \n", "model_pow_9 37 -5.2 0.42 -0.015 NaN NaN \n", "model_pow_10 15 -0.81 -0.14 0.026 -0.0013 NaN \n", "model_pow_11 -3.5e+02 91 -16 1.8 -0.12 0.0034 \n", "model_pow_12 -1.3e+03 3.8e+02 -80 12 -1.1 0.062 \n", "model_pow_13 2.3e+04 -8.5e+03 2.3e+03 -4.5e+02 62 -5.7 \n", "model_pow_14 2.8e+05 -1.2e+05 3.7e+04 -8.5e+03 1.5e+03 -1.8e+02 \n", "model_pow_15 -1e+06 5e+05 -1.9e+05 5.4e+04 -1.2e+04 1.9e+03 \n", "\n", " coef_x_12 coef_x_13 coef_x_14 coef_x_15 \n", "model_pow_1 NaN NaN NaN NaN \n", "model_pow_2 NaN NaN NaN NaN \n", "model_pow_3 NaN NaN NaN NaN \n", "model_pow_4 NaN NaN NaN NaN \n", "model_pow_5 NaN NaN NaN NaN \n", "model_pow_6 NaN NaN NaN NaN \n", "model_pow_7 NaN NaN NaN NaN \n", "model_pow_8 NaN NaN NaN NaN \n", "model_pow_9 NaN NaN NaN NaN \n", "model_pow_10 NaN NaN NaN NaN \n", "model_pow_11 NaN NaN NaN NaN \n", "model_pow_12 -0.0016 NaN NaN NaN \n", "model_pow_13 0.31 -0.0078 NaN NaN \n", "model_pow_14 15 -0.73 0.017 NaN \n", "model_pow_15 -2.2e+02 17 -0.81 0.018 " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.options.display.float_format = '{:,.2g}'.format\n", "coef_matrix_simple" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This straight away gives us the following inferences:\n", "\n", "* The RSS increases with increase in alpha, this model complexity reduces\n", "* An alpha as small as 1e-15 gives us significant reduction in magnitude of coefficients. How? Compare the coefficients in the first row of this table to the last row of simple linear regression table.\n", "* High alpha values can lead to significant underfitting. Note the rapid increase in RSS for values of alpha greater than 1\n", "* Though the coefficients are very very small, they are NOT zero.\n", "\n", "The first 3 are very intuitive. But #4 is also a crucial observation. Let’s reconfirm the same by determining the number of zeros in each row of the coefficients data set:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alpha_1e-15 0\n", "alpha_1e-10 0\n", "alpha_1e-08 0\n", "alpha_0.0001 0\n", "alpha_0.001 0\n", "alpha_0.01 0\n", "alpha_1 0\n", "alpha_5 0\n", "alpha_10 0\n", "alpha_20 0\n", "dtype: int64" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coef_matrix_ridge.apply(lambda x: sum(x.values==0),axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This confirms that all the 15 coefficients are greater than zero in magnitude (can be +ve or -ve). Remember this observation and have a look again until its clear. This will play an important role in later while comparing ridge with lasso regression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3 LASSO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Lasso is a linear model that estimates sparse coefficients. It is useful in some contexts due to its tendency to prefer solutions with fewer parameter values, effectively reducing the number of variables upon which the given solution is dependent. For this reason, the Lasso and its variants are fundamental to the field of compressed sensing. Under certain conditions, it can recover the exact set of non-zero weights.\n", "\n", "Mathematically, it consists of a linear model trained with $\\ell_1$ prior as regularizer. The objective function to minimize is:\n", "\n", "$$\\underset{w}{min\\,} { \\frac{1}{2n_{samples}} ||X w - y||_2 ^ 2 + \\alpha ||w||_1}$$\n", "\n", "The lasso estimate thus solves the minimization of the least-squares penalty with $\\alpha$ $||w||_1$ added, where $\\alpha$ is a constant and $||w||_1$ is the $\\ell_1$-norm of the parameter vector." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "alpha_lasso = [1e-15, 1e-10, 1e-8, 1e-4, 1e-3,1e-2, 1, 5, 10, 20]\n", "results = {}\n", "for alpha in alpha_lasso:\n", " lassoreg = linear_model.Lasso(alpha=alpha, normalize=True)\n", " results[alpha] = linear_power_model(lassoreg, data, 15)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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"grid = []\n", "for m in [1e-15, 1e-10, 1e-3, 1e-4, 1e-2, 1]:\n", " p = bk.figure(plot_width=230, plot_height=300, title='Plot for alpha {}'.format(m))\n", " p.circle(data['x'], data['y'],)\n", " p.line(data['x'], results[m][1], color='firebrick')\n", " grid.append(p)\n", "bk.show(gridplot(grid, ncols=3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This again tells us that the model complexity decreases with increase in the values of alpha. But notice the straight line at alpha=1. Appears a bit strange to me. Let’s explore this further by looking at the coefficients:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n", "ind = ['alpha_%.2g'%alpha_lasso[i] for i in range(0,10)]\n", "coef_matrix_lasso = pd.DataFrame(index=ind, columns=col)\n", "\n", "for i,e in enumerate(alpha_lasso):\n", " coef_matrix_lasso.iloc[i,] = results[e][0]" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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rssinterceptcoef_x_1coef_x_2coef_x_3coef_x_4coef_x_5coef_x_6coef_x_7coef_x_8coef_x_9coef_x_10coef_x_11coef_x_12coef_x_13coef_x_14coef_x_15
alpha_1e-150.970.141.1-0.3-0.024-0.000520.00038.8e-051.7e-052.9e-064.1e-074.7e-082.9e-09-5.3e-10-3e-10-9e-11-2.3e-11
alpha_1e-100.970.141.1-0.3-0.024-0.000520.00038.8e-051.7e-052.9e-064.1e-074.7e-082.9e-09-5.3e-10-3e-10-9e-11-2.3e-11
alpha_1e-080.970.141.1-0.3-0.024-0.000520.00038.8e-051.7e-052.9e-064.1e-074.7e-082.9e-09-5.3e-10-3e-10-9e-11-2.3e-11
alpha_0.000110.610.6-0.19-0.022-0-01.1e-052.4e-053.2e-063.2e-074.4e-0900-0-0-2.9e-11
alpha_0.0011.71.3-0-0.13-0-0-0000001.5e-087.5e-10000
alpha_0.013.61.8-0.55-0.00056-0-0-0-0-0-0-0000000
alpha_1370.038-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0
alpha_5370.038-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0
alpha_10370.038-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0
alpha_20370.038-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0
\n", "
" ], "text/plain": [ " rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5 \\\n", "alpha_1e-15 0.97 0.14 1.1 -0.3 -0.024 -0.00052 0.0003 \n", "alpha_1e-10 0.97 0.14 1.1 -0.3 -0.024 -0.00052 0.0003 \n", "alpha_1e-08 0.97 0.14 1.1 -0.3 -0.024 -0.00052 0.0003 \n", "alpha_0.0001 1 0.61 0.6 -0.19 -0.022 -0 -0 \n", "alpha_0.001 1.7 1.3 -0 -0.13 -0 -0 -0 \n", "alpha_0.01 3.6 1.8 -0.55 -0.00056 -0 -0 -0 \n", "alpha_1 37 0.038 -0 -0 -0 -0 -0 \n", "alpha_5 37 0.038 -0 -0 -0 -0 -0 \n", "alpha_10 37 0.038 -0 -0 -0 -0 -0 \n", "alpha_20 37 0.038 -0 -0 -0 -0 -0 \n", "\n", " coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11 \\\n", "alpha_1e-15 8.8e-05 1.7e-05 2.9e-06 4.1e-07 4.7e-08 2.9e-09 \n", "alpha_1e-10 8.8e-05 1.7e-05 2.9e-06 4.1e-07 4.7e-08 2.9e-09 \n", "alpha_1e-08 8.8e-05 1.7e-05 2.9e-06 4.1e-07 4.7e-08 2.9e-09 \n", "alpha_0.0001 1.1e-05 2.4e-05 3.2e-06 3.2e-07 4.4e-09 0 \n", "alpha_0.001 0 0 0 0 0 1.5e-08 \n", "alpha_0.01 -0 -0 -0 -0 0 0 \n", "alpha_1 -0 -0 -0 -0 -0 -0 \n", "alpha_5 -0 -0 -0 -0 -0 -0 \n", "alpha_10 -0 -0 -0 -0 -0 -0 \n", "alpha_20 -0 -0 -0 -0 -0 -0 \n", "\n", " coef_x_12 coef_x_13 coef_x_14 coef_x_15 \n", "alpha_1e-15 -5.3e-10 -3e-10 -9e-11 -2.3e-11 \n", "alpha_1e-10 -5.3e-10 -3e-10 -9e-11 -2.3e-11 \n", "alpha_1e-08 -5.3e-10 -3e-10 -9e-11 -2.3e-11 \n", "alpha_0.0001 0 -0 -0 -2.9e-11 \n", "alpha_0.001 7.5e-10 0 0 0 \n", "alpha_0.01 0 0 0 0 \n", "alpha_1 -0 -0 -0 -0 \n", "alpha_5 -0 -0 -0 -0 \n", "alpha_10 -0 -0 -0 -0 \n", "alpha_20 -0 -0 -0 -0 " ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.options.display.float_format = '{:,.2g}'.format\n", "coef_matrix_lasso" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apart from the expected inference of higher RSS for higher alphas, we can see the following:\n", "\n", "* For the same values of alpha, the coefficients of lasso regression are much smaller as compared to that of ridge regression (compare row 1 of the 2 tables).\n", "* For the same alpha, lasso has higher RSS (poorer fit) as compared to ridge regression\n", "* Many of the coefficients are zero even for very small values of alpha\n", "\n", "The first two points might not be always true but will hold for many cases. The real difference from ridge is coming out in the last inference. Lets check the number of coefficients which are zero in each model using following code:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "alpha_1e-15 0\n", "alpha_1e-10 0\n", "alpha_1e-08 0\n", "alpha_0.0001 6\n", "alpha_0.001 12\n", "alpha_0.01 13\n", "alpha_1 15\n", "alpha_5 15\n", "alpha_10 15\n", "alpha_20 15\n", "dtype: int64" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coef_matrix_lasso.apply(lambda x: sum(x.values==0),axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can observe that even for a small value of alpha, a significant number of coefficients are zero. This also explains the horizontal line fit for alpha=1 in the lasso plots, its just a baseline model! This phenomenon of most of the coefficients being zero is called \"sparsity\". \n", "\n", "Lasso can perform **feature selection**, especially where sparsity in data is a correct assumption, for example for problems where $p >> n$ such as micro array data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4 Remarks\n", "\n", "1. Key Difference\n", "\n", " * Ridge: It includes all (or none) of the features in the model. Thus, the major advantage of ridge regression is coefficient shrinkage and reducing model complexity.\n", " * Lasso: Along with shrinking coefficients, lasso performs feature selection as well. (Remember the ‘selection‘ in the lasso full-form?) As we observed earlier, some of the coefficients become exactly zero, which is equivalent to the particular feature being excluded from the model.\n", "\n", "2. Typical Use Cases\n", "\n", " * Ridge: It is majorly used to prevent overfitting. Since it includes all the features, it is not very useful in case of exorbitantly high #features, say in millions, as it will pose computational challenges.\n", " * Lasso: Since it provides sparse solutions, it is generally the model of choice (or some variant of this concept) for modelling cases where the #features are in millions or more. In such a case, getting a sparse solution is of great computational advantage as the features with zero coefficients can simply be ignored.\n", "\n", "3. Presence of Highly Correlated Features\n", "\n", " * Ridge: It generally works well even in presence of highly correlated features as it will include all of them in the model but the coefficients will be distributed among them depending on the correlation.\n", " * Lasso: It arbitrarily selects any one feature among the highly correlated ones and reduced the coefficients of the rest to zero. Also, the chosen variable changes randomly with change in model parameters. This generally doesn’t work that well as compared to ridge regression.\n", "\n", "Along with Ridge and Lasso, **Elastic Net** is another useful techniques which combines both L1 and L2 regularization. It can be used to balance out the pros and cons of ridge and lasso regression. I encourage you to explore it further." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5 ElasticNet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ElasticNet is a linear regression model trained with L1 and L2 prior as regularizer. This combination allows for learning a sparse model where few of the weights are non-zero like Lasso, while still maintaining the regularization properties of Ridge. We control the convex combination of L1 and L2 using the l1_ratio parameter.\n", "\n", "Elastic-net is useful when there are multiple features which are correlated with one another. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both.\n", "\n", "A practical advantage of trading-off between Lasso and Ridge is it allows Elastic-Net to inherit some of Ridge’s stability under rotation.\n", "\n", "The objective function to minimize is in this case\n", "\n", "$$\\underset{w}{min\\,} { \\frac{1}{2n_{samples}} ||X w - y||_2 ^ 2 + \\alpha \\rho ||w||_1 + \\frac{\\alpha(1-\\rho)}{2} ||w||_2 ^ 2}$$\n", "\n", "The main difference between Lasso and Ridge is the penalty term they use. Ridge uses L2 penalty term which limits the size of the coefficient vector. Lasso uses L1 penalty which imposes sparsity among the coefficients and thus, makes the fitted model more interpretable. Elasticnet is introduced as a compromise between these two techniques, and has a penalty which is a mix of L1 and L2 norms.\n", "\n", "In the $p<" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from itertools import cycle\n", "\n", "from sklearn.linear_model import lasso_path, enet_path\n", "from sklearn import datasets\n", "\n", "diabetes = datasets.load_diabetes()\n", "X = diabetes.data\n", "y = diabetes.target\n", "\n", "X /= X.std(axis=0) # Standardize data (easier to set the l1_ratio parameter)\n", "\n", "# Compute paths\n", "\n", "eps = 5e-3 # the smaller it is the longer is the path\n", "\n", "print(\"Computing regularization path using the lasso...\")\n", "alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False)\n", "\n", "print(\"Computing regularization path using the positive lasso...\")\n", "alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(\n", " X, y, eps, positive=True, fit_intercept=False)\n", "print(\"Computing regularization path using the elastic net...\")\n", "alphas_enet, coefs_enet, _ = enet_path(\n", " X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)\n", "\n", "print(\"Computing regularization path using the positive elastic net...\")\n", "alphas_positive_enet, coefs_positive_enet, _ = enet_path(\n", " X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)\n", "\n", "# Display results\n", "\n", "plt.figure(1)\n", "ax = plt.gca()\n", "\n", "colors = cycle(['b', 'r', 'g', 'c', 'k'])\n", "neg_log_alphas_lasso = -np.log10(alphas_lasso)\n", "neg_log_alphas_enet = -np.log10(alphas_enet)\n", "for coef_l, coef_e, c in zip(coefs_lasso, coefs_enet, colors):\n", " l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)\n", " l2 = plt.plot(neg_log_alphas_enet, coef_e, linestyle='--', c=c)\n", "\n", "plt.xlabel('-Log(alpha)')\n", "plt.ylabel('coefficients')\n", "plt.title('Lasso and Elastic-Net Paths')\n", "plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')\n", "plt.axis('tight')\n", "\n", "\n", "plt.figure(2)\n", "ax = plt.gca()\n", "neg_log_alphas_positive_lasso = -np.log10(alphas_positive_lasso)\n", "for coef_l, coef_pl, c in zip(coefs_lasso, coefs_positive_lasso, colors):\n", " l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)\n", " l2 = plt.plot(neg_log_alphas_positive_lasso, coef_pl, linestyle='--', c=c)\n", "\n", "plt.xlabel('-Log(alpha)')\n", "plt.ylabel('coefficients')\n", "plt.title('Lasso and positive Lasso')\n", "plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')\n", "plt.axis('tight')\n", "\n", "\n", "plt.figure(3)\n", "ax = plt.gca()\n", "neg_log_alphas_positive_enet = -np.log10(alphas_positive_enet)\n", "for (coef_e, coef_pe, c) in zip(coefs_enet, coefs_positive_enet, colors):\n", " l1 = plt.plot(neg_log_alphas_enet, coef_e, c=c)\n", " l2 = plt.plot(neg_log_alphas_positive_enet, coef_pe, linestyle='--', c=c)\n", "\n", "plt.xlabel('-Log(alpha)')\n", "plt.ylabel('coefficients')\n", "plt.title('Elastic-Net and positive Elastic-Net')\n", "plt.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),\n", " loc='lower left')\n", "plt.axis('tight')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "Visit [www.add-for.com]() for more tutorials and updates.\n", "\n", "This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda env:addfor_tutorials]", "language": "python", "name": "conda-env-addfor_tutorials-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }