6_gradient_descent/6_gradient_descent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style=\"color:green\" align=\"center\">Implement Gradient Descent For Neural Network (or Logistic Regression)</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4 style=\"color:blue\">Predicting if a person would buy life insurnace based on his age using logistic regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above is a binary logistic regression problem as there are only two possible outcomes (i.e. if person buys insurance or he/she doesn't). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>affordibility</th>\n",
       "      <th>bought_insurance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>25</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>52</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>46</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  affordibility  bought_insurance\n",
       "0   22              1                 0\n",
       "1   25              0                 0\n",
       "2   47              1                 1\n",
       "3   52              0                 0\n",
       "4   46              1                 1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"insurance_data.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Split train and test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(df[['age','affordibility']],df.bought_insurance,test_size=0.2, random_state=25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Preprocessing: Scale the data so that both age and affordibility are in same scaling range**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_scaled = X_train.copy()\n",
    "X_train_scaled['age'] = X_train_scaled['age'] / 100\n",
    "\n",
    "X_test_scaled = X_test.copy()\n",
    "X_test_scaled['age'] = X_test_scaled['age'] / 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Model Building: First build a model in keras/tensorflow and see what weights and bias values it comes up with. We will than try to reproduce same weights and bias in our plain python implementation of gradient descent. Below is the architecture of our simple neural network**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"nn.png\" height=800 width=800/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/5000\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 0s/step - loss: 0.6832 - accuracy: 0.5000\n",
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     ]
    },
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    },
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     ]
    },
    {
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     ]
    },
    {
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     ]
    },
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    },
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    },
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    },
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    },
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     ]
    },
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     ]
    },
    {
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     ]
    },
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    },
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     ]
    },
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    },
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      "1/1 [==============================] - 0s 1ms/step - loss: 0.4642 - accuracy: 0.9091\n",
      "Epoch 4943/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4642 - accuracy: 0.9091\n",
      "Epoch 4944/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4641 - accuracy: 0.9091\n",
      "Epoch 4945/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4641 - accuracy: 0.9091\n",
      "Epoch 4946/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4641 - accuracy: 0.9091\n",
      "Epoch 4947/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4641 - accuracy: 0.9091\n",
      "Epoch 4948/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4641 - accuracy: 0.9091\n",
      "Epoch 4949/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4640 - accuracy: 0.9091\n",
      "Epoch 4950/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4640 - accuracy: 0.9091\n",
      "Epoch 4951/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4640 - accuracy: 0.9091\n",
      "Epoch 4952/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4640 - accuracy: 0.9091\n",
      "Epoch 4953/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4640 - accuracy: 0.9091\n",
      "Epoch 4954/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4639 - accuracy: 0.9091\n",
      "Epoch 4955/5000\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4639 - accuracy: 0.9091\n",
      "Epoch 4956/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4639 - accuracy: 0.9091\n",
      "Epoch 4957/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4639 - accuracy: 0.9091\n",
      "Epoch 4958/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4639 - accuracy: 0.9091\n",
      "Epoch 4959/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4639 - accuracy: 0.9091\n",
      "Epoch 4960/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4638 - accuracy: 0.9091\n",
      "Epoch 4961/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4638 - accuracy: 0.9091\n",
      "Epoch 4962/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4638 - accuracy: 0.9091\n",
      "Epoch 4963/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4638 - accuracy: 0.9091\n",
      "Epoch 4964/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4638 - accuracy: 0.9091\n",
      "Epoch 4965/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4637 - accuracy: 0.9091\n",
      "Epoch 4966/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4637 - accuracy: 0.9091\n",
      "Epoch 4967/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4637 - accuracy: 0.9091\n",
      "Epoch 4968/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4637 - accuracy: 0.9091\n",
      "Epoch 4969/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4637 - accuracy: 0.9091\n",
      "Epoch 4970/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4636 - accuracy: 0.9091\n",
      "Epoch 4971/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4636 - accuracy: 0.9091\n",
      "Epoch 4972/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4636 - accuracy: 0.9091\n",
      "Epoch 4973/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4636 - accuracy: 0.9091\n",
      "Epoch 4974/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4636 - accuracy: 0.9091\n",
      "Epoch 4975/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4635 - accuracy: 0.9091\n",
      "Epoch 4976/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4635 - accuracy: 0.9091\n",
      "Epoch 4977/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4635 - accuracy: 0.9091\n",
      "Epoch 4978/5000\n",
      "1/1 [==============================] - 0s 2ms/step - loss: 0.4635 - accuracy: 0.9091\n",
      "Epoch 4979/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4635 - accuracy: 0.9091\n",
      "Epoch 4980/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4635 - accuracy: 0.9091\n",
      "Epoch 4981/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4634 - accuracy: 0.9091\n",
      "Epoch 4982/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4634 - accuracy: 0.9091\n",
      "Epoch 4983/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4634 - accuracy: 0.9091\n",
      "Epoch 4984/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4634 - accuracy: 0.9091\n",
      "Epoch 4985/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4634 - accuracy: 0.9091\n",
      "Epoch 4986/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4633 - accuracy: 0.9091\n",
      "Epoch 4987/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4633 - accuracy: 0.9091\n",
      "Epoch 4988/5000\n",
      "1/1 [==============================] - 0s 999us/step - loss: 0.4633 - accuracy: 0.9091\n",
      "Epoch 4989/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4633 - accuracy: 0.9091\n",
      "Epoch 4990/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4633 - accuracy: 0.9091\n",
      "Epoch 4991/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4632 - accuracy: 0.9091\n",
      "Epoch 4992/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4632 - accuracy: 0.9091\n",
      "Epoch 4993/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4632 - accuracy: 0.9091\n",
      "Epoch 4994/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4632 - accuracy: 0.9091\n",
      "Epoch 4995/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4632 - accuracy: 0.9091\n",
      "Epoch 4996/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4631 - accuracy: 0.9091\n",
      "Epoch 4997/5000\n",
      "1/1 [==============================] - 0s 1ms/step - loss: 0.4631 - accuracy: 0.9091\n",
      "Epoch 4998/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4631 - accuracy: 0.9091\n",
      "Epoch 4999/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4631 - accuracy: 0.9091\n",
      "Epoch 5000/5000\n",
      "1/1 [==============================] - 0s 0s/step - loss: 0.4631 - accuracy: 0.9091\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x22933758d30>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = keras.Sequential([\n",
    "    keras.layers.Dense(1, input_shape=(2,), activation='sigmoid', kernel_initializer='ones', bias_initializer='zeros')\n",
    "])\n",
    "\n",
    "model.compile(optimizer='adam',\n",
    "              loss='binary_crossentropy',\n",
    "              metrics=['accuracy'])\n",
    "\n",
    "model.fit(X_train_scaled, y_train, epochs=5000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Evaluate the model on test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1/1 [==============================] - 0s 1ms/step - loss: 0.3550 - accuracy: 1.0000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.35497748851776123, 1.0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.evaluate(X_test_scaled,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.7054848 ],\n",
       "       [0.35569546],\n",
       "       [0.16827849],\n",
       "       [0.47801173],\n",
       "       [0.7260697 ],\n",
       "       [0.8294984 ]], dtype=float32)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(X_test_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2     1\n",
       "10    0\n",
       "21    0\n",
       "11    0\n",
       "14    1\n",
       "9     1\n",
       "Name: bought_insurance, dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Now get the value of weights and bias from the model**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "coef, intercept = model.get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[5.060867 ],\n",
       "        [1.4086502]], dtype=float32),\n",
       " array([-2.9137027], dtype=float32))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef, intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This means w1=5.060867, w2=1.4086502, bias =-2.9137027**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999847700205"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sigmoid(x):\n",
    "        import math\n",
    "        return 1 / (1 + math.exp(-x))\n",
    "sigmoid(18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>affordibility</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>18</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>49</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>61</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age  affordibility\n",
       "2    47              1\n",
       "10   18              1\n",
       "21   26              0\n",
       "11   28              1\n",
       "14   49              1\n",
       "9    61              1"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Instead of model.predict, write our own prediction function that uses w1,w2 and bias**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7054848693136117"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def prediction_function(age, affordibility):\n",
    "    weighted_sum = coef[0]*age + coef[1]*affordibility + intercept\n",
    "    return sigmoid(weighted_sum)\n",
    "\n",
    "prediction_function(.47, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.35569549781937626"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_function(.18, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Now we start implementing gradient descent in plain python. Again the goal is to come up with same w1, w2 and bias that keras model calculated. We want to show how keras/tensorflow would have computed these values internally using gradient descent**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**First write couple of helper routines such as sigmoid and log_loss**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.99999386, 0.5       , 0.73105858])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sigmoid_numpy(X):\n",
    "   return 1/(1+np.exp(-X))\n",
    "\n",
    "sigmoid_numpy(np.array([12,0,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def log_loss(y_true, y_predicted):\n",
    "    epsilon = 1e-15\n",
    "    y_predicted_new = [max(i,epsilon) for i in y_predicted]\n",
    "    y_predicted_new = [min(i,1-epsilon) for i in y_predicted_new]\n",
    "    y_predicted_new = np.array(y_predicted_new)\n",
    "    return -np.mean(y_true*np.log(y_predicted_new)+(1-y_true)*np.log(1-y_predicted_new))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**All right now comes the time to implement our final gradient descent function !! yay !!!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(age, affordability, y_true, epochs, loss_thresold):\n",
    "    w1 = w2 = 1\n",
    "    bias = 0\n",
    "    rate = 0.5\n",
    "    n = len(age)\n",
    "    for i in range(epochs):\n",
    "        weighted_sum = w1 * age + w2 * affordability + bias\n",
    "        y_predicted = sigmoid_numpy(weighted_sum)\n",
    "        loss = log_loss(y_true, y_predicted)\n",
    "\n",
    "        w1d = (1/n)*np.dot(np.transpose(age),(y_predicted-y_true)) \n",
    "        w2d = (1/n)*np.dot(np.transpose(affordability),(y_predicted-y_true)) \n",
    "\n",
    "        bias_d = np.mean(y_predicted-y_true)\n",
    "        w1 = w1 - rate * w1d\n",
    "        w2 = w2 - rate * w2d\n",
    "        bias = bias - rate * bias_d\n",
    "\n",
    "        print (f'Epoch:{i}, w1:{w1}, w2:{w2}, bias:{bias}, loss:{loss}')\n",
    "\n",
    "        if loss<=loss_thresold:\n",
    "            break\n",
    "\n",
    "    return w1, w2, bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:0, w1:0.974907633470177, w2:0.948348125394529, bias:-0.11341867736368583, loss:0.7113403233723417\n",
      "Epoch:1, w1:0.9556229728273669, w2:0.9058873696677865, bias:-0.2122349122718517, loss:0.681264778737757\n",
      "Epoch:2, w1:0.9416488476693794, w2:0.8719790823960313, bias:-0.2977578997796538, loss:0.6591474252715025\n",
      "Epoch:3, w1:0.9323916996249162, w2:0.8457541517722915, bias:-0.3715094724003511, loss:0.6431523291301917\n",
      "Epoch:4, w1:0.9272267472726993, w2:0.8262362885332687, bias:-0.43506643026891584, loss:0.6316873063379158\n",
      "Epoch:5, w1:0.9255469396815343, w2:0.8124402814952774, bias:-0.48994490058938817, loss:0.623471707997592\n",
      "Epoch:6, w1:0.9267936114129968, w2:0.8034375029757677, bias:-0.5375299543522853, loss:0.6175321183044205\n",
      "Epoch:7, w1:0.93047170420295, w2:0.7983920007454487, bias:-0.5790424270894963, loss:0.6131591858705934\n",
      "Epoch:8, w1:0.9361540784567942, w2:0.7965748796787705, bias:-0.6155315088627655, loss:0.6098518179750948\n",
      "Epoch:9, w1:0.9434791243557357, w2:0.7973647616854131, bias:-0.6478828179413606, loss:0.6072639970231438\n",
      "Epoch:10, w1:0.9521448361628082, w2:0.8002404280558159, bias:-0.6768343869109611, loss:0.6051606942838051\n",
      "Epoch:11, w1:0.9619014360798376, w2:0.8047697991276092, bias:-0.7029956527236098, loss:0.6033841405177724\n",
      "Epoch:12, w1:0.9725437902239876, w2:0.8105978078160995, bias:-0.7268665798879941, loss:0.6018292976282692\n",
      "Epoch:13, w1:0.9839042828641819, w2:0.8174345999952901, bias:-0.7488554155033402, loss:0.6004266142491015\n",
      "Epoch:14, w1:0.9958464546516588, w2:0.8250447751055391, bias:-0.769294418817745, loss:0.5991301804031037\n",
      "Epoch:15, w1:1.0082595007242081, w2:0.8332379503132499, bias:-0.7884533918133878, loss:0.5979097221992564\n",
      "Epoch:16, w1:1.0210536111133566, w2:0.8418606908070436, bias:-0.8065510935633605, loss:0.5967452540340851\n",
      "Epoch:17, w1:1.034156080666481, w2:0.8507897246509063, bias:-0.8237647415878959, loss:0.5956235357679642\n",
      "Epoch:18, w1:1.0475080939682688, w2:0.8599263049589658, bias:-0.8402378469114854, loss:0.5945357398126384\n",
      "Epoch:19, w1:1.0610620872868053, w2:0.8691915649552581, bias:-0.8560866317233403, loss:0.5934759216594547\n",
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     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Epoch:363, w1:5.026262488012782, w2:1.456149647855258, bias:-2.94881136056773, loss:0.4634291480718573\n",
      "Epoch:364, w1:5.0345395499882475, w2:1.456426118261257, bias:-2.952431584207713, loss:0.46326531361545026\n",
      "Epoch:365, w1:5.042801249636176, w2:1.4567027197201048, bias:-2.956045609784402, loss:0.46310207876795667\n",
      "Epoch:366, w1:5.051047623653049, w2:1.4569794548473887, bias:-2.9596534546250037, loss:0.46293944095888917\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(5.051047623653049, 1.4569794548473887, -2.9596534546250037)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient_descent(X_train_scaled['age'],X_train_scaled['affordibility'],y_train,1000, 0.4631)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[5.060867 ],\n",
       "        [1.4086502]], dtype=float32),\n",
       " array([-2.9137027], dtype=float32))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef, intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This shows that in the end we were able to come up with same value of w1,w2 and bias using a plain python implementation of gradient descent function**"
   ]
  }
 ],
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