ImplementationOfGradientDescent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fea0f074",
   "metadata": {},
   "source": [
    "# Assignment 7: Gradient Descent (Task 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82939f9e",
   "metadata": {},
   "source": [
    "For this assignment, you may `numpy`, `pandas`, and packages from the Python standard library.\n",
    "\n",
    "List your team members (name, matriculation number, course of study) in the following cell:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ada3a2fe",
   "metadata": {},
   "source": [
    "| Name | Matr. Nr. | Study Program |\n",
    "| ---  | ---       | ---           |\n",
    "| Dao Khanh Duy | 3591406 | INFOTECH M.Sc. |\n",
    "| Harshal Sanjay Nandigramwar | 3575008 | INFOTECH M.Sc. |\n",
    "| Xiwen Feng | 3219649 | Natural Language Processing B.Sc. |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa40a608",
   "metadata": {},
   "source": [
    "In this task, you will implement the training of linear regression model by using Mean Squarred Error and Correntropy loss functions. Use gradient descent to optimize the weights of linear regression model. The definition of MSE and Correntropy loss fucntions are given in the Assignment7.pdf file.\n",
    "\n",
    "There will be two linear regression models, one is trained by using MSE loss and the other is trained by Correntropy loss function. \n",
    "\n",
    "In addition, two different learning rates are used for training of each models. The reason is that each loss function has different shape and requires specific learning rate.\n",
    "\n",
    "Implement the MSE and Correntropy loss funcitons in the given function templates. Additionally, compute gradients of MSE and Correntropy loss functions and impement them in the corresponding function templates. The gradient should be computed given particular data sample ($x_i, y_i$).\n",
    "\n",
    "The data is generated by sampling from the linear function $f(x) = 2x$, and the output of the third data sample is contaminated by noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "81b1c65e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "61fbbf93",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Weight initialization\n",
    "w_mse = 0.1\n",
    "w_corr = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "673d01b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#learning rate for MSE and Correntropy loss optimization\n",
    "lr = 0.001\n",
    "lr_corr = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "07f9c957",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define Mean Squared Error Function\n",
    "def mse(y, y_mse):\n",
    "    mse = np.sum(np.square(y_mse - y))\n",
    "    mse /= len(y)\n",
    "    return mse\n",
    "\n",
    "#Define Correntopy Function\n",
    "def corr(y, y_corr):    \n",
    "    corr = np.sum(np.exp(-np.square(y_corr - y)))\n",
    "    corr /= len(y)\n",
    "    return -corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e9b25367",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define Gradient of MSE Function\n",
    "def mse_gradient(w_mse, xi, yi):\n",
    "    N = len(yi)\n",
    "    y_mse = w_mse * xi\n",
    "\n",
    "    # fill here with gradient of MSE\n",
    "    mse_grad = np.sum((y_mse - yi) * xi) # gradient to u=(y_mse - yi)\n",
    "    mse_grad *= (2 / N)\n",
    "    return mse_grad\n",
    "\n",
    "# Define Gradient of Correntropy Function\n",
    "def corr_gradient(w_corr, xi, yi):\n",
    "    N = len(yi)\n",
    "    y_corr = w_corr * xi\n",
    "\n",
    "    # fill here with gradient of Correntropy\n",
    "    corr_grad = np.sum(np.exp(-np.square(y_corr - y)) * (y_corr - yi) * xi)\n",
    "    corr_grad *= (2 / N)\n",
    "    return corr_grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6bab35f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate Data\n",
    "x = np.arange(5)\n",
    "y = 2 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "831d0eb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Impulsive Noide (make one sample contaminated with high noise)\n",
    "y_noise = y.copy()\n",
    "y_noise[2] = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "18170ba2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def training(x, y, y_noise, w_mse, w_corr, use_noise=True):\n",
    "    if use_noise:\n",
    "        y_true = y_noise\n",
    "    else:\n",
    "        y_true = y\n",
    "\n",
    "    for i in range(1000):\n",
    "        ids = np.random.randint(5, size=1)\n",
    "        xi = x[ids]\n",
    "        yi = y_true[ids]\n",
    "\n",
    "        # Update linear regression weights based on MSE \n",
    "        w_mse -= lr * mse_gradient(w_mse, xi, yi)\n",
    "\n",
    "        # Update linear regression weights based on Correntropy\n",
    "        w_corr -= lr_corr * corr_gradient(w_corr, xi, yi)\n",
    "\n",
    "\n",
    "    # Approximation of Output With Linear Function Trained on MSE and Correntropy\n",
    "    y_mse = w_mse * x\n",
    "    y_corr = w_corr * x\n",
    "\n",
    "    # Final Loss Values\n",
    "    err = mse(y_true, y_mse)\n",
    "    coerr = corr(y_true, y_corr)\n",
    "\n",
    "    # Plot the output of linear function trained with MSE and Correntopy\n",
    "    plt.plot(y_mse, label='MSE')\n",
    "    plt.plot(y_corr, label='Correntropy')\n",
    "    plt.plot(y, label='Original')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "    print(f'Final weights:\\nw_mse: {w_mse}\\nw_corr: {w_corr}')\n",
    "    \n",
    "    return err, coerr\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "80509561",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final weights:\n",
      "w_mse: 8.212330650973495\n",
      "w_corr: 33.76252625558979\n",
      "\n",
      "Errors:\n",
      "MSE: 1597.651318707384\n",
      "Correntropy: -0.2\n"
     ]
    }
   ],
   "source": [
    "err, coerr = training(x, y, y_noise, w_mse, w_corr, use_noise=True)\n",
    "print(f'\\nErrors:\\nMSE: {err}\\nCorrentropy: {coerr}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c2664fa",
   "metadata": {},
   "source": [
    "##### Observations\n",
    "\n",
    "* Correntropy is more sensitive to noise and outliers when compared to mse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7806a7b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final weights:\n",
      "w_mse: 1.9999936703360919\n",
      "w_corr: 2.0\n",
      "\n",
      "Errors:\n",
      "MSE: 2.4038787114208843e-10\n",
      "Correntropy: -1.0\n"
     ]
    }
   ],
   "source": [
    "# This is without noise. Proves that things are working correct, \n",
    "# as weights are very close to 2 in both the cases.\n",
    "\n",
    "err, coerr = training(x, y, y_noise, w_mse, w_corr, use_noise=False)\n",
    "print(f'\\nErrors:\\nMSE: {err}\\nCorrentropy: {coerr}')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.12 ('ml')",
   "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": "3.9.12"
  },
  "vscode": {
   "interpreter": {
    "hash": "99c647157295a3fd9bc2246ef38bea300d0f89364b8176408f58ca9cea183f22"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}