TensorFlow_Minimal_Least_squares_DL.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We must always import the relevant libraries for our problem at hand. NumPy and TensorFlow are required for this example.\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation\n",
    "\n",
    "We generate data using the exact same logic and code as the example from the previous notebook. The only difference now is that we save it to an npz file. Npz is numpy's file type which allows you to save numpy arrays into a single .npz file. We introduce this change because in machine learning most often: \n",
    "\n",
    "* you are given some data (csv, database, etc.)\n",
    "* you preprocess it into a desired format (later on we will see methods for preprocesing)\n",
    "* you save it into npz files (if you're working in Python) to access later\n",
    "\n",
    "This is literally saving your NumPy arrays into a file that you can later access, nothing more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First, we should declare a variable containing the size of the training set we want to generate.\n",
    "observations = 1000\n",
    "\n",
    "# We will work with two variables as inputs. \n",
    "# We have picked x and z, since it is easier to differentiate them.\n",
    "# We generate them randomly, drawing from an uniform distribution. There are 3 arguments of this method (low, high, size).\n",
    "# The size of xs and zs is observations x 1. In this case: 1000 x 1.\n",
    "xs = np.random.uniform(low=-10, high=10, size=(observations,1))\n",
    "zs = np.random.uniform(-10, 10, (observations,1))\n",
    "\n",
    "# Combine the two dimensions of the input into one input matrix. \n",
    "# This is the X matrix from the linear model y = x*w + b.\n",
    "# column_stack is a Numpy method, which combines two matrices (vectors) into one.\n",
    "generated_inputs = np.column_stack((xs,zs))\n",
    "\n",
    "# We add a random small noise to the function i.e. f(x,z) = 2x - 3z + 5 + <small noise>\n",
    "noise = np.random.uniform(-1, 1, (observations,1))\n",
    "\n",
    "# Produce the targets according to our f(x,z) = 2x - 3z + 5 + noise definition.\n",
    "# In this way, we are basically saying: the weights should be 2 and -3, while the bias is 5.\n",
    "generated_targets = 2*xs - 3*zs + 5 + noise\n",
    "\n",
    "# save into an npz file called \"TF_intro\"\n",
    "np.savez('TF_intro', inputs=generated_inputs, targets=generated_targets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving with TensorFlow\n",
    "\n",
    "<i/>Note: This intro is just the basics of TensorFlow which has way more capabilities and depth than that.<i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the training data from the NPZ\n",
    "training_data = np.load('TF_intro.npz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/100\n",
      "1000/1000 - 0s - loss: 24.5755\n",
      "Epoch 2/100\n",
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      "Epoch 3/100\n",
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      "Epoch 4/100\n",
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      "Epoch 6/100\n",
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      "Epoch 7/100\n",
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      "Epoch 8/100\n",
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      "Epoch 9/100\n",
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      "Epoch 10/100\n",
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      "Epoch 11/100\n",
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      "Epoch 12/100\n",
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      "Epoch 13/100\n",
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      "Epoch 14/100\n",
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      "Epoch 15/100\n",
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      "Epoch 16/100\n",
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      "Epoch 19/100\n",
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      "Epoch 20/100\n",
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      "Epoch 32/100\n",
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      "Epoch 34/100\n",
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      "Epoch 35/100\n",
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      "Epoch 40/100\n",
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      "Epoch 41/100\n",
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      "Epoch 42/100\n",
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      "Epoch 80/100\n",
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      "Epoch 81/100\n",
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      "Epoch 82/100\n",
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      "Epoch 83/100\n",
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      "Epoch 84/100\n",
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      "Epoch 85/100\n",
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      "Epoch 86/100\n",
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      "Epoch 87/100\n",
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      "Epoch 88/100\n",
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      "Epoch 89/100\n",
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      "Epoch 90/100\n",
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      "Epoch 91/100\n",
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      "Epoch 92/100\n",
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      "Epoch 93/100\n",
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      "Epoch 94/100\n",
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      "Epoch 95/100\n",
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      "Epoch 96/100\n",
      "1000/1000 - 0s - loss: 0.3699\n",
      "Epoch 97/100\n",
      "1000/1000 - 0s - loss: 0.3666\n",
      "Epoch 98/100\n",
      "1000/1000 - 0s - loss: 0.3667\n",
      "Epoch 99/100\n",
      "1000/1000 - 0s - loss: 0.4198\n",
      "Epoch 100/100\n",
      "1000/1000 - 0s - loss: 0.3667\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x212be2c1550>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Declare a variable where we will store the input size of our model\n",
    "# It should be equal to the number of variables you have\n",
    "input_size = 2\n",
    "# Declare the output size of the model\n",
    "# It should be equal to the number of outputs you've got (for regressions that's usually 1)\n",
    "output_size = 1\n",
    "\n",
    "# Outline the model\n",
    "# We lay out the model in 'Sequential'\n",
    "# Note that there are no calculations involved - we are just describing our network\n",
    "model = tf.keras.Sequential([\n",
    "                            # Each 'layer' is listed here\n",
    "                            # The method 'Dense' indicates, our mathematical operation to be (xw + b)\n",
    "                            tf.keras.layers.Dense(output_size,\n",
    "                                                 # there are extra arguments you can include to customize your model\n",
    "                                                 # in our case we are just trying to create a solution that is \n",
    "                                                 # as close as possible to our NumPy model\n",
    "                                                 kernel_initializer=tf.random_uniform_initializer(minval=-0.1, maxval=0.1),\n",
    "                                                 bias_initializer=tf.random_uniform_initializer(minval=-0.1, maxval=0.1)\n",
    "                                                 )\n",
    "                            ])\n",
    "\n",
    "# We can also define a custom optimizer, where we can specify the learning rate\n",
    "custom_optimizer = tf.keras.optimizers.SGD(learning_rate=0.02)\n",
    "# Note that sometimes you may also need a custom loss function \n",
    "# That's much harder to implement and won't be covered in this course though\n",
    "\n",
    "# 'compile' is the place where you select and indicate the optimizers and the loss\n",
    "model.compile(optimizer=custom_optimizer, loss='mean_squared_error')\n",
    "\n",
    "# finally we fit the model, indicating the inputs and targets\n",
    "# if they are not otherwise specified the number of epochs will be 1 (a single epoch of training), \n",
    "# so the number of epochs is 'kind of' mandatory, too\n",
    "# we can play around with verbose; we prefer verbose=2\n",
    "model.fit(training_data['inputs'], training_data['targets'], epochs=100, verbose=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract the weights and bias\n",
    "Extracting the weight(s) and bias(es) of a model is not an essential step for the machine learning process. In fact, usually they would not tell us much in a deep learning context. However, this simple example was set up in a way, which allows us to verify if the answers we get are correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[ 1.9776261],\n",
       "        [-2.9764102]], dtype=float32), array([4.975083], dtype=float32)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extracting the weights and biases is achieved quite easily\n",
    "model.layers[0].get_weights()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.9776261],\n",
       "       [-2.9764102]], dtype=float32)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can save the weights and biases in separate variables for easier examination\n",
    "# Note that there can be hundreds or thousands of them!\n",
    "weights = model.layers[0].get_weights()[0]\n",
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.975083], dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can save the weights and biases in separate variables for easier examination\n",
    "# Note that there can be hundreds or thousands of them!\n",
    "bias = model.layers[0].get_weights()[1]\n",
    "bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract the outputs (make predictions)\n",
    "Once more, this is not an essential step, however, we usually want to be able to make predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "       [ 39.5]], dtype=float32)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can predict new values in order to actually make use of the model\n",
    "# Sometimes it is useful to round the values to be able to read the output\n",
    "# Usually we use this method on NEW DATA, rather than our original training data\n",
    "model.predict_on_batch(training_data['inputs']).round(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "       [-12.2],\n",
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       "       [-11.4],\n",
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       "       [  2.8],\n",
       "       [ 13.8],\n",
       "       [-24.5],\n",
       "       [ -4.7],\n",
       "       [-29.6],\n",
       "       [ 29.8],\n",
       "       [ 29.5],\n",
       "       [-25.3],\n",
       "       [  1.1],\n",
       "       [  9.2],\n",
       "       [ -8.2],\n",
       "       [ 15.8],\n",
       "       [  6.9],\n",
       "       [ -1.2],\n",
       "       [ 17.2],\n",
       "       [ -2.3],\n",
       "       [-13.7],\n",
       "       [ 22.4],\n",
       "       [ 10.2],\n",
       "       [ 21.1],\n",
       "       [ 22.2],\n",
       "       [ -4.3],\n",
       "       [  7.9],\n",
       "       [ 22.8],\n",
       "       [  4.9],\n",
       "       [ 28.7],\n",
       "       [-18.8],\n",
       "       [  1.6],\n",
       "       [ 39.9]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If we display our targets (actual observed values), we can manually compare the outputs and the targets\n",
    "training_data['targets'].round(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The model is optimized, so the outputs are calculated based on the last form of the model\n",
    "\n",
    "# We have to np.squeeze the arrays in order to fit them to what the plot function expects.\n",
    "# Doesn't change anything as we cut dimensions of size 1 - just a technicality.\n",
    "plt.plot(np.squeeze(model.predict_on_batch(training_data['inputs'])), np.squeeze(training_data['targets']))\n",
    "plt.xlabel('outputs')\n",
    "plt.ylabel('targets')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:root] *",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}