Gradient Descent for Linear Regression.ipynb

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   "source": [
    "# Gradient Descent for Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Needed Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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     "end_time": "2019-03-02T05:00:39.024039Z",
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    "%matplotlib notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# plotting library (completely optional)\n",
    "from matplotlib.pyplot import (\n",
    "    legend, # to show line names in graph\n",
    "    plot, # to plot line graph\n",
    "    scatter, # to plot dotted graph\n",
    "    show # to show plotted graph\n",
    ")\n",
    "\n",
    "# for numeric operations. just to make code easy\n",
    "from numpy import (\n",
    "    array, # to make matrix operations easy\n",
    "    mean, # to calculate average of a list of numbers\n",
    "    sqrt, # to find square root\n",
    "    square, # to find square of a number\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Data Processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:40.698945Z",
     "start_time": "2019-03-02T05:00:40.692329Z"
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   "source": [
    "# dataset with independent (x) & dependent (y) values\n",
    "\n",
    "data_set = array([\n",
    "    [32,31], [53,68], [60,62], [47,71], [59,87],\n",
    "    [55,78], [52,79], [39,59], [48,75], [52,71],\n",
    "    [45,55], [54,82], [44,62], [58,75], [56,81],\n",
    "    [48,60], [44,82], [60,97], [45,48], [38,56],\n",
    "    [66,83], [65,11], [47,57], [41,51], [51,75]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:41.406399Z",
     "start_time": "2019-03-02T05:00:41.403564Z"
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    "hidden": true
   },
   "outputs": [],
   "source": [
    "# seperating x & y from dataset\n",
    "\n",
    "x_list = data_set[:, 0]\n",
    "y_list = data_set[:, 1]"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "scatter(x_list, y_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Linear Model's Weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:42.884529Z",
     "start_time": "2019-03-02T05:00:42.881876Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# initial model's parameters (for line equation)\n",
    "# with these values, we get a horizontal straight line\n",
    "\n",
    "intercept = 0\n",
    "slope = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Model's Hyper Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:44.399559Z",
     "start_time": "2019-03-02T05:00:44.396818Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# training rate & iteration cycle count\n",
    "# depends on increasing accuracy and time for each cycle\n",
    "\n",
    "learning_rate = 0.0001\n",
    "iteration_cycles = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:45.090953Z",
     "start_time": "2019-03-02T05:00:45.088079Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "count = len(x_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Prediction function (Line Equation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:46.323153Z",
     "start_time": "2019-03-02T05:00:46.320023Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# formula to find a (y) coordinate given its x-axis coordinate in a straight line\n",
    "\n",
    "def line_equation(x):\n",
    "    return slope * x + intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Training (Gradiant Descent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:47.692157Z",
     "start_time": "2019-03-02T05:00:47.653620Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# training for 1000 runs. rate of increase in accuracy decreases with each iteration\n",
    "for _ in range(iteration_cycles):\n",
    "\n",
    "    # getting new y-axis coordinates for all actual x-axis coordinates using line equation\n",
    "    new_y = list(map(line_equation, x_list))\n",
    "\n",
    "    # differencfe between actual coordinare & the one with the new one\n",
    "    y_difference = y_list - new_y\n",
    "\n",
    "    # calculating gradiant using tangent of loss function\n",
    "    intercept_gradient = sum(-2 / count * y_difference)\n",
    "    slope_gradient = sum(-2 / count * y_difference * x_list)\n",
    "\n",
    "    # updating intercept & slope \n",
    "    intercept -= learning_rate * intercept_gradient\n",
    "    slope -= learning_rate * slope_gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(1.293533304562727, 0.3327273175126918)"
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "slope, intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Prediciton with Training-Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:48.772954Z",
     "start_time": "2019-03-02T05:00:48.767694Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# finding new y-axis coordinates with slope & intercept after 1000 corrections\n",
    "predicted_y = list(map(line_equation, x_list))\n",
    "\n",
    "# error function (there are a lot. we can choose any function)\n",
    "# RMSE maximizes errors which are lesser than 1 and minimizes errors which are greater than 1. so choose wisely\n",
    "rmse = sqrt(mean(square(y_list - predicted_y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:49.340807Z",
     "start_time": "2019-03-02T05:00:49.334069Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "intercept = 0.3327273175126918\nslope = 1.293533304562727\nrmse = 17.728288850706324\n"
     ]
    }
   ],
   "source": [
    "# printing new values\n",
    "print(\"intercept =\", intercept)\n",
    "print(\"slope =\", slope)\n",
    "print(\"rmse =\", rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Prediciton with Testing-Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:50.571267Z",
     "start_time": "2019-03-02T05:00:50.568061Z"
    },
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# finding y-axis coordinates for new x-axis coordinates\n",
    "test_x = [44, 32, 63, 100]\n",
    "test_y = list(map(line_equation, test_x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## Visualizing Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-03-02T05:00:51.895315Z",
     "start_time": "2019-03-02T05:00:51.849711Z"
    },
    "hidden": true
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# plotting actual points, new predictions & line of best fit for actual points\n",
    "scatter(x_list, y_list, label='original')\n",
    "scatter(test_x, test_y, label='prediction')\n",
    "plot(x_list, predicted_y, label='line of best fit')\n",
    "legend()\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.9.2 64-bit"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "interpreter": {
   "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}