gradient_descent_logistic_regression.ipynb

{
 "cells":[
  {
   "cell_type":"markdown",
   "source":[
    "**This notebook covers gradient descent for logistic regression**"
   ],
   "attachments":{
    
   },
   "metadata":{
    "datalore":{
     "node_id":"RQCb6gpYUVnpEVk6Vdve7Y",
     "type":"MD",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's import the required set of libraries\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math, copy\n"
   ],
   "execution_count":1,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"3NY0JqPGmJTjMlYmxOX9I1",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's define our training data set\n",
    "\n",
    "X_train = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",
    "y_train = np.array([0, 0, 0, 1, 1, 1])"
   ],
   "execution_count":2,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"KWbcMYFzpyYGkBcqhAj2tf",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's plot the training data set \n",
    "\n",
    "# Define custom colors for classes (0 and 1)\n",
    "colors = ['red' if label == 0 else 'blue' for label in y_train]\n",
    "\n",
    "# Create a scatter plot with custom marker colors\n",
    "plt.scatter(X_train[:,0], X_train[:,1], c=colors, marker='x', s=100)  # Adjust marker and size as needed\n",
    "\n",
    "plt.xlabel(\"training data feature 1\")\n",
    "plt.ylabel(\"training data feature 2\")\n",
    "plt.title(\"Decision boundary graph\")\n",
    "plt.show()"
   ],
   "execution_count":3,
   "outputs":[
    {
     "data":{
      "image\/png":[
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\n"
      ]
     },
     "metadata":{
      "image\/png":{
       
      }
     },
     "output_type":"display_data"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"xyIwZtybWxgbzbwWXJxHH0",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# now let's define the sigmoid function\n",
    "\n",
    "def sig_fn(z):\n",
    "    g = 1\/(1+np.exp(-z))\n",
    "    return g"
   ],
   "execution_count":4,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"kDD2XUdbmOBAt4r6pGiaZd",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# now let's define the compute gradient function\n",
    "\n",
    "def compute_gradient_logistic(x,y,w,b):\n",
    "\n",
    "    size_x = x.shape[0]\n",
    "    features_x = x.shape[1]\n",
    "    der_db = 0\n",
    "    der_dw = np.zeros(w.shape[0])\n",
    "    for i in range(size_x):\n",
    "        pred_y = np.dot(x[i], w) + b\n",
    "        pred_y_sig = sig_fn(pred_y)\n",
    "        diff = pred_y_sig - y[i]\n",
    "        for j in range(features_x):\n",
    "            der_dw[j] += diff * x[i,j]\n",
    "        der_db += diff\n",
    "\n",
    "    der_db = der_db\/size_x\n",
    "    der_dw = der_dw\/size_x\n",
    "\n",
    "    return der_db, der_dw"
   ],
   "execution_count":5,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"35gSsBkYXM16gIpuDt9yTt",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# now let's put our compute gradient logistic function to test\n",
    "\n",
    "X_tmp = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",
    "y_tmp = np.array([0, 0, 0, 1, 1, 1])\n",
    "w_tmp = np.array([2.,3.])\n",
    "b_tmp = 1.\n",
    "dj_db_tmp, dj_dw_tmp = compute_gradient_logistic(X_tmp, y_tmp, w_tmp, b_tmp)\n",
    "print(f\"dj_db: {dj_db_tmp}\" )\n",
    "print(f\"dj_dw: {dj_dw_tmp.tolist()}\" )"
   ],
   "execution_count":6,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "dj_db: 0.49861806546328574\n",
      "dj_dw: [0.498333393278696, 0.49883942983996693]\n"
     ],
     "output_type":"stream"
    }
   ],
   "metadata":{
    "datalore":{
     "node_id":"KTWQ2RIVR0VDudsbWJvQed",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# let's define compute cost logistic function \n",
    "\n",
    "def compute_cost_logistic(x,y,w,b):\n",
    "\n",
    "    size_x = x.shape[0]\n",
    "    #epsilon = 1e-15  # Small positive value to avoid log(0) and log(1)\n",
    "    cost = 0\n",
    "    for i in range(size_x):\n",
    "        pred_y = np.dot(x[i], w) +b\n",
    "        pred_sig_fn = sig_fn(pred_y)\n",
    "        #pred_sig_fn = np.clip(pred_sig_fn, epsilon, 1 - epsilon)\n",
    "        loss = -y[i]*np.log(pred_sig_fn) - (1-y[i])*np.log(1-pred_sig_fn)\n",
    "        cost += loss\n",
    "\n",
    "    cost = cost\/size_x\n",
    "\n",
    "    return cost\n",
    "\n"
   ],
   "execution_count":10,
   "outputs":[
    
   ],
   "metadata":{
    "datalore":{
     "node_id":"tSL0PLm267gpnSsvIxjkLY",
     "type":"CODE",
     "hide_input_from_viewers":true,
     "hide_output_from_viewers":true
    }
   }
  },
  {
   "cell_type":"code",
   "source":[
    "# now let's further write the run gradient descent function \n",
    "\n",
    "def run_gradient_descent(x,y,w,b,iter,alpha):\n",
    "\n",
    "    size_x = x.shape[0]\n",
    "    features_x = x.shape[1]\n",
    "\n",
    "    w_tmp = copy.deepcopy(w)\n",
    "    b_tmp = b\n",
    "\n",
    "    cost_hist = []\n",
    "\n",
    "    for i in range(iter):\n",
    "        dj_db, dj_dw = compute_gradient_logistic(x, y, w_tmp, b_tmp)\n",
    "        w_tmp = w_tmp - alpha * dj_dw\n",
    "        b_tmp = b_tmp - alpha * dj_db\n",
    "\n",
    "        # Save cost J at each iteration\n",
    "        if i<100000:      # prevent resource exhaustion \n",
    "            cost_hist.append( compute_cost_logistic(x,y,w_tmp,b_tmp) )\n",
    "\n",
    "        # Print cost every at intervals 10 times or as many iterations if < 10\n",
    "        if i% math.ceil(iter \/ 10) == 0:\n",
    "            print(f\"Iteration {i:4d}: Cost {cost_hist[-1]}   \")\n",
    "        \n",
    "        if cost_hist[i]>cost_hist[i-1]:\n",
    "            break\n",
    "    \n",
    "    return w_tmp, b_tmp, cost_hist\n"
   ],
   "execution_count":15,
   "outputs":[
    
   ],
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  {
   "cell_type":"code",
   "source":[
    "# now let's put our run gradient descent function to test\n",
    "X_train = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",
    "y_train = np.array([0, 0, 0, 1, 1, 1])\n",
    "w_tmp  = np.zeros_like(X_train[0])\n",
    "b_tmp  = 0.\n",
    "alph = 0.1\n",
    "iters = 10000\n",
    "\n",
    "w_out, b_out, _ = run_gradient_descent(X_train, y_train, w_tmp, b_tmp, iters, alph) \n",
    "print(f\"\\nupdated parameters: w:{w_out}, b:{b_out}\")"
   ],
   "execution_count":16,
   "outputs":[
    {
     "name":"stdout",
     "text":[
      "Iteration    0: Cost 0.684610468560574   \n",
      "Iteration 1000: Cost 0.1590977666870457   \n",
      "Iteration 2000: Cost 0.08460064176930078   \n",
      "Iteration 3000: Cost 0.05705327279402531   \n",
      "Iteration 4000: Cost 0.04290759421682   \n",
      "Iteration 5000: Cost 0.03433847729884557   \n",
      "Iteration 6000: Cost 0.02860379802212006   \n",
      "Iteration 7000: Cost 0.02450156960879306   \n",
      "Iteration 8000: Cost 0.02142370332569295   \n",
      "Iteration 9000: Cost 0.019030137124109114   \n",
      "\n",
      "updated parameters: w:[5.28123029 5.07815608], b:-14.222409982019837\n"
     ],
     "output_type":"stream"
    }
   ],
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