ML Assignment 4.ipynb

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    "# LP3 Group B Assignment 4\n",
    "## Implement Gradient Descent Algorithm to find the local minima of a function. \n",
    "### For example, find the local minima of the function y=(x+3)² starting from the point x=2 ."
   ]
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   "id": "2ce43769",
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    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'matplotlib'",
     "output_type": "error",
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      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Cell \u001b[1;32mIn [6], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mnumpy\u001b[39;00m \u001b[39mas\u001b[39;00m \u001b[39mnp\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mmatplotlib\u001b[39;00m\u001b[39m.\u001b[39;00m\u001b[39mpyplot\u001b[39;00m \u001b[39mas\u001b[39;00m \u001b[39mplt\u001b[39;00m\n\u001b[0;32m      4\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mmean_squared_error\u001b[39m(y_true, y_predicted):\n\u001b[0;32m      5\u001b[0m     cost \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39msum((y_true\u001b[39m-\u001b[39my_predicted)\u001b[39m*\u001b[39m\u001b[39m*\u001b[39m\u001b[39m2\u001b[39m) \u001b[39m/\u001b[39m \u001b[39mlen\u001b[39m(y_true) \u001b[39m#Calculating the loss or cost\u001b[39;00m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "def mean_squared_error(y_true, y_predicted):\n",
    "    cost = np.sum((y_true-y_predicted)**2) / len(y_true) #Calculating the loss or cost\n",
    "    return cost\n",
    " \n",
    "def gradient_descent(x, y, iterations = 1000, learning_rate = 0.0001, stopping_threshold = 1e-6): #Gradient Descent Function\n",
    "    #Initializing weight, bias, learning rate and iterations\n",
    "    current_weight = 0.1\n",
    "    current_bias = 0.01\n",
    "    iterations = iterations\n",
    "    learning_rate = learning_rate\n",
    "    n = float(len(x))\n",
    "    costs = []\n",
    "    weights = []\n",
    "    previous_cost = None\n",
    "    \n",
    "    for i in range(iterations): #Estimation of optimal parameters\n",
    "        y_predicted = (current_weight * x) + current_bias #Making predictions\n",
    "        current_cost = mean_squared_error(y, y_predicted) #Calculationg the current cost\n",
    "        #If the change in cost is less than or equal to stopping_threshold we stop the gradient descent\n",
    "        if previous_cost and abs(previous_cost-current_cost)<=stopping_threshold:\n",
    "            break\n",
    "        previous_cost = current_cost\n",
    "        costs.append(current_cost)\n",
    "        weights.append(current_weight)\n",
    "        #Calculating the gradients\n",
    "        weight_derivative = -(2/n) * sum(x * (y-y_predicted))  \n",
    "        bias_derivative = -(2/n) * sum(y-y_predicted)\n",
    "        #Updating weights and bias\n",
    "        current_weight = current_weight - (learning_rate * weight_derivative)\n",
    "        current_bias = current_bias - (learning_rate * bias_derivative)        \n",
    "        #Printing the parameters for each 1000th iteration\n",
    "        print(f\"Iteration{i+1}:Cost{current_cost},Weight\\{current_weight},Bias{current_bias}\")\n",
    "    #Visualizing the weights and cost at for all iterations\n",
    "    plt.figure(figsize = (8,6))\n",
    "    plt.plot(weights, costs)\n",
    "    plt.scatter(weights, costs, marker='o', color='red')\n",
    "    plt.title(\"Cost vs Weights\")\n",
    "    plt.ylabel(\"Cost\")\n",
    "    plt.xlabel(\"Weight\")\n",
    "    plt.show()\n",
    "    return current_weight, current_bias\n",
    "\n",
    "#Data\n",
    "X = np.array([32.50234527, 53.42680403, 61.53035803, 47.47563963, 59.81320787,\n",
    "           55.14218841, 52.21179669, 39.29956669, 48.10504169, 52.55001444,\n",
    "           45.41973014, 54.35163488, 44.1640495 , 58.16847072, 56.72720806,\n",
    "           48.95588857, 44.68719623, 60.29732685, 45.61864377, 38.81681754])\n",
    "Y = np.array([31.70700585, 68.77759598, 62.5623823 , 71.54663223, 87.23092513,\n",
    "           78.21151827, 79.64197305, 59.17148932, 75.3312423 , 71.30087989,\n",
    "           55.16567715, 82.47884676, 62.00892325, 75.39287043, 81.43619216,\n",
    "           60.72360244, 82.89250373, 97.37989686, 48.84715332, 56.87721319])\n",
    " \n",
    "#Estimating weight and bias using gradient descent\n",
    "estimated_weight, eatimated_bias = gradient_descent(X, Y, iterations=2000)\n",
    "print(f\"Estimated Weight: {estimated_weight}\\nEstimated Bias: {eatimated_bias}\")\n",
    "Y_pred = estimated_weight*X + eatimated_bias #Making predictions using estimated parameters\n",
    "#Plotting the regression line\n",
    "plt.figure(figsize = (8,6))\n",
    "plt.scatter(X, Y, marker='o', color='red')\n",
    "plt.plot([min(X), max(X)], [min(Y_pred), max(Y_pred)], color='blue',markerfacecolor='red',markersize=10,linestyle='dashed')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()"
   ]
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   "cell_type": "code",
   "execution_count": 7,
   "id": "ee083f1e",
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    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'matplotlib'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Cell \u001b[1;32mIn [7], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mmatplotlib\u001b[39;00m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
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   "source": [
    "import matplotlib "
   ]
  }
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