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ml-data-analysis/linear-reg/Linear Regression with Grad...

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linear regression with Gradient Descent
7 years ago
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Applying Gradient Descent on 1d feature set\n",
"\n",
"### Data:\n",
"**Math Scores and Drug Concentrations** from http://www.stat.ufl.edu/~winner/datasets.html\n",
"\n",
"[link to data](http://www.stat.ufl.edu/~winner/data/lsd.dat)\n",
"\n",
"\n",
"### Goal\n",
"Fit a linear regression to predict future math scores based on drug concentration using Gradient Descent Algorithm"
]
},
{
"cell_type": "code",
"execution_count": 218,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Library imports and dependencies\n",
"%matplotlib notebook\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import time\n",
"\n",
"from matplotlib import animation, rc\n",
"from IPython.display import HTML\n",
"\n",
"\n",
"#rc('animation', html='html5')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Gradient descent algorithm"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
fix error
7 years ago
"execution_count": 235,
linear regression with Gradient Descent
7 years ago
"metadata": {
"collapsed": false
},
"outputs": [
{
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"\n",
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"};\n",
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"\n",
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"\n",
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" comm.on_msg(function(msg) {\n",
" //console.log('receiving', msg['content']['data'], msg);\n",
" // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
" ws.onmessage(msg['content']['data'])\n",
" });\n",
" return ws;\n",
"}\n",
"\n",
"mpl.mpl_figure_comm = function(comm, msg) {\n",
" // This is the function which gets called when the mpl process\n",
" // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
"\n",
" var id = msg.content.data.id;\n",
" // Get hold of the div created by the display call when the Comm\n",
" // socket was opened in Python.\n",
" var element = $(\"#\" + id);\n",
" var ws_proxy = comm_websocket_adapter(comm)\n",
"\n",
" function ondownload(figure, format) {\n",
" window.open(figure.imageObj.src);\n",
" }\n",
"\n",
" var fig = new mpl.figure(id, ws_proxy,\n",
" ondownload,\n",
" element.get(0));\n",
"\n",
" // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
" // web socket which is closed, not our websocket->open comm proxy.\n",
" ws_proxy.onopen();\n",
"\n",
" fig.parent_element = element.get(0);\n",
" fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
" if (!fig.cell_info) {\n",
" console.error(\"Failed to find cell for figure\", id, fig);\n",
" return;\n",
" }\n",
"\n",
" var output_index = fig.cell_info[2]\n",
" var cell = fig.cell_info[0];\n",
"\n",
"};\n",
"\n",
"mpl.figure.prototype.handle_close = function(fig, msg) {\n",
" fig.root.unbind('remove')\n",
"\n",
" // Update the output cell to use the data from the current canvas.\n",
" fig.push_to_output();\n",
" var dataURL = fig.canvas.toDataURL();\n",
" // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
" // the notebook keyboard shortcuts fail.\n",
" IPython.keyboard_manager.enable()\n",
" $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
" fig.close_ws(fig, msg);\n",
"}\n",
"\n",
"mpl.figure.prototype.close_ws = function(fig, msg){\n",
" fig.send_message('closing', msg);\n",
" // fig.ws.close()\n",
"}\n",
"\n",
"mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
" // Turn the data on the canvas into data in the output cell.\n",
" var dataURL = this.canvas.toDataURL();\n",
" this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
"}\n",
"\n",
"mpl.figure.prototype.updated_canvas_event = function() {\n",
" // Tell IPython that the notebook contents must change.\n",
" IPython.notebook.set_dirty(true);\n",
" this.send_message(\"ack\", {});\n",
" var fig = this;\n",
" // Wait a second, then push the new image to the DOM so\n",
" // that it is saved nicely (might be nice to debounce this).\n",
" setTimeout(function () { fig.push_to_output() }, 1000);\n",
"}\n",
"\n",
"mpl.figure.prototype._init_toolbar = function() {\n",
" var fig = this;\n",
"\n",
" var nav_element = $('<div/>')\n",
" nav_element.attr('style', 'width: 100%');\n",
" this.root.append(nav_element);\n",
"\n",
" // Define a callback function for later on.\n",
" function toolbar_event(event) {\n",
" return fig.toolbar_button_onclick(event['data']);\n",
" }\n",
" function toolbar_mouse_event(event) {\n",
" return fig.toolbar_button_onmouseover(event['data']);\n",
" }\n",
"\n",
" for(var toolbar_ind in mpl.toolbar_items){\n",
" var name = mpl.toolbar_items[toolbar_ind][0];\n",
" var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
" var image = mpl.toolbar_items[toolbar_ind][2];\n",
" var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
"\n",
" if (!name) { continue; };\n",
"\n",
" var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
" button.click(method_name, toolbar_event);\n",
" button.mouseover(tooltip, toolbar_mouse_event);\n",
" nav_element.append(button);\n",
" }\n",
"\n",
" // Add the status bar.\n",
" var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
" nav_element.append(status_bar);\n",
" this.message = status_bar[0];\n",
"\n",
" // Add the close button to the window.\n",
" var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
" var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
" button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
" button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
" buttongrp.append(button);\n",
" var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
" titlebar.prepend(buttongrp);\n",
"}\n",
"\n",
"mpl.figure.prototype._root_extra_style = function(el){\n",
" var fig = this\n",
" el.on(\"remove\", function(){\n",
"\tfig.close_ws(fig, {});\n",
" });\n",
"}\n",
"\n",
"mpl.figure.prototype._canvas_extra_style = function(el){\n",
" // this is important to make the div 'focusable\n",
" el.attr('tabindex', 0)\n",
" // reach out to IPython and tell the keyboard manager to turn it's self\n",
" // off when our div gets focus\n",
"\n",
" // location in version 3\n",
" if (IPython.notebook.keyboard_manager) {\n",
" IPython.notebook.keyboard_manager.register_events(el);\n",
" }\n",
" else {\n",
" // location in version 2\n",
" IPython.keyboard_manager.register_events(el);\n",
" }\n",
"\n",
"}\n",
"\n",
"mpl.figure.prototype._key_event_extra = function(event, name) {\n",
" var manager = IPython.notebook.keyboard_manager;\n",
" if (!manager)\n",
" manager = IPython.keyboard_manager;\n",
"\n",
" // Check for shift+enter\n",
" if (event.shiftKey && event.which == 13) {\n",
" this.canvas_div.blur();\n",
" // select the cell after this one\n",
" var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
" IPython.notebook.select(index + 1);\n",
" }\n",
"}\n",
"\n",
"mpl.figure.prototype.handle_save = function(fig, msg) {\n",
" fig.ondownload(fig, null);\n",
"}\n",
"\n",
"\n",
"mpl.find_output_cell = function(html_output) {\n",
" // Return the cell and output element which can be found *uniquely* in the notebook.\n",
" // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
" // IPython event is triggered only after the cells have been serialised, which for\n",
" // our purposes (turning an active figure into a static one), is too late.\n",
" var cells = IPython.notebook.get_cells();\n",
" var ncells = cells.length;\n",
" for (var i=0; i<ncells; i++) {\n",
" var cell = cells[i];\n",
" if (cell.cell_type === 'code'){\n",
" for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
" var data = cell.output_area.outputs[j];\n",
" if (data.data) {\n",
" // IPython >= 3 moved mimebundle to data attribute of output\n",
" data = data.data;\n",
" }\n",
" if (data['text/html'] == html_output) {\n",
" return [cell, data, j];\n",
" }\n",
" }\n",
" }\n",
" }\n",
"}\n",
"\n",
"// Register the function which deals with the matplotlib target/channel.\n",
"// The kernel may be null if the page has been refreshed.\n",
"if (IPython.notebook.kernel != null) {\n",
" IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
"}\n"
],
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fix error
7 years ago
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linear regression with Gradient Descent
7 years ago
],
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"metadata": {},
"output_type": "display_data"
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{
"ename": "KeyboardInterrupt",
"evalue": "",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
fix error
7 years ago
"\u001b[0;32m<ipython-input-235-b20746d8c1e7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 104\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 105\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 106\u001b[0;31m \u001b[0mgradient_descent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.07\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 107\u001b[0m \u001b[0;31m#for i in range(40):\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 108\u001b[0m \u001b[0;31m# w, b = 1, i\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m<ipython-input-235-b20746d8c1e7>\u001b[0m in \u001b[0;36mgradient_descent\u001b[0;34m(alpha, iterations)\u001b[0m\n\u001b[1;32m 94\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 95\u001b[0m \u001b[0max_loss\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mautoscale_view\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 96\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\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 97\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msleep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mfps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 98\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
linear regression with Gradient Descent
7 years ago
"\u001b[0;32m/home/spike/.pyenv/versions/3.5.1/lib/python3.5/site-packages/matplotlib/backends/backend_webagg_core.py\u001b[0m in \u001b[0;36mdraw\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 181\u001b[0m \u001b[0mbackend_agg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mRendererAgg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlock\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrelease\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 182\u001b[0m \u001b[0;31m# Swap the frames\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 183\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmanager\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrefresh_all\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 184\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 185\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdraw_idle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/home/spike/.pyenv/versions/3.5.1/lib/python3.5/site-packages/matplotlib/backends/backend_webagg_core.py\u001b[0m in \u001b[0;36mrefresh_all\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 472\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrefresh_all\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 473\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mweb_sockets\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 474\u001b[0;31m \u001b[0mdiff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcanvas\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_diff_image\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 475\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mweb_sockets\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 476\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msend_binary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdiff\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/home/spike/.pyenv/versions/3.5.1/lib/python3.5/site-packages/matplotlib/backends/backend_webagg_core.py\u001b[0m in \u001b[0;36mget_diff_image\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 238\u001b[0m _png.write_png(\n\u001b[1;32m 239\u001b[0m \u001b[0moutput\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mview\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0muint8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m4\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--> 240\u001b[0;31m self._png_buffer)\n\u001b[0m\u001b[1;32m 241\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 242\u001b[0m \u001b[0;31m# Swap the renderer frames\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
]
}
],
"source": [
"df = pd.read_csv('lsd.dat.txt', '\\s+', header=None, names=['Drug', 'MathScore'])\n",
"\n",
"\n",
"x = df['Drug']\n",
"y = df['MathScore']\n",
"\n",
"_y = y/(y.max() - y.min())\n",
"_x = x/(x.max() - x.min())\n",
"\n",
"\n",
"fig = plt.figure(figsize=(12, 4))\n",
"ax1 = fig.add_subplot(1,2,1)\n",
"\n",
"\n",
"ax1.set_xlim(0, x.max() + 1)\n",
"\n",
"ax1.scatter(x, y, label='')\n",
"ax1.set_xlabel('Drug Concentration')\n",
"ax1.set_ylabel('Math Score')\n",
"ax1.set_title('Linear Regression')\n",
"\n",
"\n",
"ax_loss = fig.add_subplot(1,2,2)\n",
"ax_loss.set_xlabel('Iterations')\n",
"ax_loss.set_ylabel('Loss')\n",
"\n",
"\n",
"\n",
"## Helper Functions\n",
"def hypothesis(w, b, x):\n",
" return w*x + b\n",
" \n",
"def get_loss(w, b):\n",
" mean_squares = []\n",
" for (xi,yi) in zip(x,y):\n",
" mean_squares.append((hypothesis(w, b, xi) - yi)**2)\n",
" loss = sum(mean_squares) / 2*len(mean_squares)\n",
" return loss\n",
"\n",
"def draw_line(weight, bias):\n",
" xx = np.linspace(1, x.max())\n",
" ax1.plot(xx , xx*weight+bias, color='red', label='Loss = {}'.format(np.floor(loss(weight, bias))))\n",
" ax1.legend() \n",
"\n",
"def init_hyp_line():\n",
" line.set_data([], [])\n",
"\n",
"def setup_hypothesis(): \n",
" line, = ax1.plot([],[], color='red')\n",
" #print(line)\n",
" return line\n",
"\n",
"fps = 60\n",
"\n",
"def draw_hyp(weight, bias, line, loss):\n",
" weight, bias\n",
" xx = np.linspace(1, x.max())\n",
" yy = xx*weight+bias\n",
" line.set_data(xx,yy)\n",
" #line.set_label('Loss = {}'.format(np.floor(loss)))\n",
" #ax1.legend()\n",
" \n",
" #ax1.relim()\n",
" #ax1.autoscale_view(True,True,True) \n",
" #fig.canvas.draw()\n",
"\n",
"def gradient_descent(alpha, iterations):\n",
" \n",
" ax_loss.set_xlim(0, iterations)\n",
" hypothesis_line = setup_hypothesis()\n",
" \n",
" w, b = 1, 1\n",
" \n",
" \n",
" losses = []\n",
" iters = []\n",
" for i in range(iterations):\n",
" ax_loss.clear()\n",
" \n",
" hxx = hypothesis(w,b,x)\n",
" \n",
" \n",
" b = b - alpha/len(y)* sum([hx - y for hx, y in zip(hxx, y)])\n",
" w = w - alpha/len(y) * sum([(hx - y)*x for hx, y, x in zip(hxx, y, x)])\n",
" \n",
" loss = get_loss(w,b)\n",
" losses.append(loss)\n",
" iters.append(i)\n",
" ax_loss.plot(iters, losses, color='green', label='Loss = {}\\nIter={}'.format(np.floor(loss), i))\n",
" ax_loss.legend()\n",
" ax_loss.relim()\n",
" \n",
" draw_hyp(w,b,hypothesis_line, loss)\n",
" \n",
" ax_loss.autoscale_view(True,True,True)\n",
" fig.canvas.draw()\n",
" time.sleep(1/fps)\n",
"\n",
" \n",
"\n",
"\n",
" \n",
" \n",
" \n",
" \n",
"gradient_descent(0.07, 1000)\n",
"#for i in range(40):\n",
"# w, b = 1, i\n",
"# draw_hyp(w,b,hypothesis_line, loss(w,b))\n",
"# time.sleep(1/fps)\n",
" \n",
" \n",
"\n",
"\n",
"#plt.draw()\n",
"\n",
" \n",
"\n",
"#anim = animation.FuncAnimation(fig, animate, init_func=init_hyp_line, interval=10, frames=10)\n",
"#HTML(anim.to_html5_video())\n",
"#def gradient_descent(learn_rate):\n",
"# for i in range(100):\n",
" \n",
" \n",
" \n",
" \n",
"#test_w = -5\n",
"#test_b = 20\n",
"#draw_line(test_w, test_b)\n",
"#loss(test_w, test_b)\n",
"\n"
]
},
{
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