neural-net.ipynb

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   "display_name": "Python 3.9.5 64-bit ('nn-test': conda)"
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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "input = np.array([1.54, 1.32])\n",
    "weights = np.array([1.56, -0.45])\n",
    "bias = np.array([0.0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))\n",
    "\n",
    "\n",
    "def make_prediction(input, weights, bias):\n",
    "    # simple two layer network\n",
    "    layer1 = np.dot(input, weights) + bias\n",
    "    layer2 = sigmoid(layer1)\n",
    "    return layer2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The prediction is [0.85916839]\n"
     ]
    }
   ],
   "source": [
    "prediction = make_prediction(input, weights, bias)\n",
    "print(f'The prediction is {prediction}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The derivative is [1.71833678]\nThe new prediction is [0.04285867]\n"
     ]
    }
   ],
   "source": [
    "# basic gradient descent\n",
    "target = 0\n",
    "MSE = (prediction - target)**2\n",
    "derivative = 2 * (prediction - target)\n",
    "print(f'The derivative is {derivative}')\n",
    "\n",
    "weights = weights - derivative\n",
    "prediction = make_prediction(input, weights, bias)\n",
    "MSE = (prediction - target)**2\n",
    "print(f'The new prediction is {prediction}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([0.00351628])"
      ]
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "source": [
    "# getting derivative of error function with respect to bias using backpropagation\n",
    "d_error_wrt_prediction = 2*(prediction - target)\n",
    "layer1_result = np.dot(input, weights) + bias \n",
    "d_prediction_wrt_layer1 = sigmoid(layer1_result) * (1 - sigmoid(layer1_result))     # derivative of sigmoid fn\n",
    "d_layer1_wrt_bias = 1   # independent variable, so d(x)/dx = 1\n",
    "d_error_wrt_bias = d_layer1_wrt_bias * d_prediction_wrt_layer1 * d_error_wrt_prediction  # chain rule\n",
    "d_error_wrt_bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralNetwork:\n",
    "    def __init__(self, learning_rate):\n",
    "        # learning_rate determines the magnitude by which we update params based on gradients\n",
    "        self.learning_rate = learning_rate  \n",
    "\n",
    "        # weights and bias randomly chosen\n",
    "        self.weights = np.array([np.random.randn(), np.random.randn()])\n",
    "        self.bias = np.random.randn()\n",
    "\n",
    "    def sigmoid(self, x):\n",
    "        return 1/(1+np.exp(-x))\n",
    "\n",
    "    def predict(self, input):\n",
    "        layer1 = np.dot(input, self.weights) + self.bias\n",
    "        layer2 = self.sigmoid(layer1)\n",
    "        return layer2 \n",
    "\n",
    "    def sigmoid_derivative(self, x):\n",
    "        return self.sigmoid(x) * (1-self.sigmoid(x))\n",
    "\n",
    "    def compute_gradients(self, input, target):\n",
    "        layer1 = np.dot(input, self.weights) + self.bias \n",
    "        layer2 = self.sigmoid(layer1)\n",
    "        prediction = layer2 \n",
    "\n",
    "        d_error_wrt_prediction = 2*(prediction - target)\n",
    "        d_prediction_wrt_layer1 = self.sigmoid_derivative(layer1)\n",
    "        d_layer1_wrt_bias = 1\n",
    "        d_error_wrt_bias = d_layer1_wrt_bias * d_prediction_wrt_layer1 * d_error_wrt_prediction\n",
    "        \n",
    "        d_layer1_wrt_weights = (input*1) + (self.weights*0)     # derivative of dot product\n",
    "        d_error_wrt_weights = d_layer1_wrt_weights * d_prediction_wrt_layer1 * d_error_wrt_prediction\n",
    "        return d_error_wrt_weights, d_error_wrt_bias\n",
    "\n",
    "    def update_params(self, d_error_wrt_weights, d_error_wrt_bias):\n",
    "        # modify params based on gradients observed\n",
    "        self.bias = self.bias - (d_error_wrt_bias * self.learning_rate)\n",
    "        self.weights = self.weights - (d_error_wrt_weights * self.learning_rate)\n",
    "\n",
    "    def train(self, inputs, targets, iterations):\n",
    "        cumulative_errors = []\n",
    "        for i in range(iterations):\n",
    "            # we train by picking a random data instance\n",
    "            random_data_index = np.random.randint(len(input_vectors))\n",
    "            input_vector = inputs[random_data_index]\n",
    "            target = targets[random_data_index]\n",
    "\n",
    "            # perfom gradient descent\n",
    "            d_error_wrt_weights, d_error_wrt_bias = self.compute_gradients(\n",
    "                input_vector, target\n",
    "            )\n",
    "            self.update_params(d_error_wrt_weights, d_error_wrt_bias)\n",
    "\n",
    "            # calculate the error acroos data points every 100 iterations to get the trend of improvement\n",
    "            if i % 100 == 0:\n",
    "                cumulative_error = 0\n",
    "                # Loop through all the instances to measure the error\n",
    "                for data_instance_index in range(len(input_vectors)):\n",
    "                    data_point = inputs[data_instance_index]\n",
    "                    target = targets[data_instance_index]\n",
    "\n",
    "                    prediction = self.predict(data_point)\n",
    "                    error = np.square(prediction - target)  # MSE\n",
    "                    cumulative_error = cumulative_error + error\n",
    "                cumulative_errors.append(cumulative_error)\n",
    "        return cumulative_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Error for all training instances')"
      ]
     },
     "metadata": {},
     "execution_count": 21
    },
    {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# random input and targets\n",
    "input_vectors = np.array(\n",
    "    [\n",
    "        [3, 1.5],\n",
    "        [2, 1],\n",
    "        [4, 1.5],\n",
    "        [3, 4],\n",
    "        [3.5, 0.5],\n",
    "        [2, 0.5],\n",
    "        [5.5, 1],\n",
    "        [1, 1],\n",
    "    ]\n",
    ")\n",
    "targets = np.array([0, 1, 0, 1, 0, 1, 1, 0])\n",
    "learning_rate = 0.1\n",
    "\n",
    "neural_network = NeuralNetwork(learning_rate)\n",
    "training_error = neural_network.train(input_vectors, targets, 10000)\n",
    "\n",
    "plt.plot(training_error)\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Error for all training instances\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Error for all training instances')"
      ]
     },
     "metadata": {},
     "execution_count": 26
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "learning_rate = 0.01\n",
    "neural_network = NeuralNetwork(learning_rate)\n",
    "training_error = neural_network.train(input_vectors, targets, 10000)\n",
    "\n",
    "plt.plot(training_error)\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Error for all training instances\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Error for all training instances')"
      ]
     },
     "metadata": {},
     "execution_count": 25
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "learning_rate = 0.1\n",
    "neural_network = NeuralNetwork(learning_rate)\n",
    "training_error = neural_network.train(input_vectors, targets, 50000)\n",
    "\n",
    "plt.plot(training_error)\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Error for all training instances\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Error for all training instances')"
      ]
     },
     "metadata": {},
     "execution_count": 27
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "learning_rate = 0.01\n",
    "neural_network = NeuralNetwork(learning_rate)\n",
    "training_error = neural_network.train(input_vectors, targets, 50000)\n",
    "\n",
    "plt.plot(training_error)\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Error for all training instances\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}