06. Neural Networks.ipynb

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   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=3)\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpreting the linear function as a neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the last example we tried to classify our data into two categories by maximising and minimizing the following function:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "F = f(\\mathbf{X},\\mathbf{Y})=A\\mathbf{X}+B\\mathbf{Y}+C\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where, $\\mathbf{X}$ and $\\mathbf{Y}$ are the input vectors, and $A$, $B$ and $C$ are the parameters that we are trying to learn."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_16.png\" alt=\"drawing\" width=\"400\"/>"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function $f$, we have been using in our last example was not an arbitrary choice. This type of function is very common in machine learning, and it is used to model an element of a neural network called a neuron or a unit."
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "#### Origins of neural networks: Perceptrons"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Perceptron networks are the precursor of the contemporary neural networks we use today. Let's see how they work. A __perceptron__ is a small computational unit that takes several binary inputs, $X_1, X_2,…$, and produces a single binary output. The image below illustrates a perceptron with 3 binary inputs, although the number of inputs is not restricted. "
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_19.png\" alt=\"drawing\" width=\"350\"/>"
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   "cell_type": "markdown",
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   "source": [
    "How can we use perceptrons to do something useful? Let's say that we are trying to formally decide whether to do something or not. For example, we might want to decide whether to go and see a movie, or not. We could for example think of three aspects that are relevant to the decision, and define them as questions. For example: is the weather nice or not, do your friends like it or not, do you like the main actor/actress or not. The answers to these questions could only be yes or no, or in computer terms 1 or 0. Such yes (1) or no (0) answers that are relevant to decide what the output will be are taken as inputs $X_1, X_2,…$ of the perceptron. The perceptron's binary output should evaluate the inputs and tell us whether to go to the movies (1) or not (0)."
   ]
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   "source": [
    "Certain aspects of our decision making might be more or less important than the others. For example, an aspect reflected in the input $X_1$ could be more important to you than the aspect $X_2$. You could, for example, think that what your friends think of the movie is twice as important than how the weather is. To implement this in the perceptron model, each input is multiplied by a real number that reflects its importance. If an aspect $X_1$ is more important then the aspect $X_2$, then $X_2$  should be multiplied by a larger number than $X_1$. The number with which we multiply an input is called a _weight_. "
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, to decide whether the decision will be positive or negative, the weighted sum of all the inputs must be compared to some value which will be the final decision factor. We can temporarily call this value a _threshold_. Let's say that our threshold is the number `3.5`. Once we sum our decisions multiplied by their respective weights, we get a real number value. If the value is less or equal to `3.5`, the perceptron outputs `0`, which indicates we shouldn't do the thing. If the value is larger than `3.5`, the perceptron outputs `1` which indicates we should do the thing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_20.png\" alt=\"drawing\" width=\"400\"/>"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can represent the output of a neuron algebraically:"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{eqnarray}\n",
    "  \\mbox{output} & = & \\left\\{ \\begin{array}{ll}\n",
    "      0 & \\mbox{if } \\sum_j W_j X_j \\leq \\text{ threshold} \\\\\n",
    "      1 & \\mbox{if } \\sum_j W_j X_j > \\text{ threshold}\n",
    "      \\end{array} \\right.\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's simplify the way we describe perceptrons, by making two notational changes. The first change is to write $\\sum_j W_j X_j$ in terms of vectors as a dot product, $w \\cdot x \\equiv \\sum_j w_j x_j$, where $w$ and $x$ are vectors whose components are the weights and inputs, respectively. The second change is to move the threshold to the other side of the inequality and to replace it by what's known as the perceptron's __bias__, $B \\equiv\n",
    "-\\mbox{threshold}$. Using the bias instead of the threshold, the perceptron rule can be rewritten:"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{eqnarray}\n",
    "  \\mbox{output} = \\left\\{ \n",
    "    \\begin{array}{ll} \n",
    "      0 & \\mbox{if } W\\cdot X + B \\leq 0 \\\\\n",
    "      1 & \\mbox{if } W\\cdot X + B > 0\n",
    "    \\end{array}\n",
    "  \\right.\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This change is reflected in the following diagram."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_21.png\" alt=\"drawing\" width=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can think of the bias as a measure of how easy it is to get the perceptron to output 1. For a perceptron with a really big positive bias, it's extremely easy for the perceptron to output 1, as the weighted sum plus a large positive value, easily gets larger than 0. But if the bias is very negative, then it's difficult for the perceptron to output a 1, as the large negative value will pull the output to be less than 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we would like to use perceptrons for classification like we did before, we run into a problem. To minimise or maximise a function of multiple inputs we need partial derivatives. The derivative shows us how the output of the function changes in terms of inputs if we slightly nudge one of the inputs. The problem with perceptrons is that their binary decision making aspect make them intrinsically insensitive to the small changes of inputs. To differentiate a function, after all, it needs to be smooth and continuous, not discreete. A tiny change of one of our inputs can cause the output of a neuron to abruptly change from 0 to 1 or vice versa. That will then spawn over the entire network of neurons and cause unpredictable changes."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can overcome this problem by changing the architecture of our neural network. Instead of binary inputs, and outputs, we can now think of all the values within the neuron as *real numbers*. Instead of thinking of the criteria for going to the movies in terms of simple yes or no, we can refine think of it in terms of probabilities, where 0 is the least probable, and 1 is the most probable, but there are also values in between to choose from. This also applies to the output which no longer can be expressed in binary terms. This part we replace with the so called _activation function_, which maps its input smoothly to an output in between 0 and 1.  With this change, the small changes in the neuron's weights and bias cause only a small change in the neuron's output. That's the crucial fact which will allow a network of neurons to learn."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_22.png\" alt=\"drawing\" width=\"400\"/>"
   ]
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   "source": [
    "### Classification by using a two-layer Neural Network"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our classification taks, we used the function  $F = f(\\mathbf{X},\\mathbf{Y})=A\\mathbf{X}+B\\mathbf{Y}+C$. Now you can see that this function is a simplified neuron without the activation function. Its inputs are $\\mathbf{X}$ and $\\mathbf{Y}$, their corresponding weights are $A$ and $B$, and $C$ represents the bias. "
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A neural network works by connecting multiple neurons in a network. Unlike a single neuron, a network of neurons is capable of creating smoother, non-linear decision boundaries between data points belonging to different categories we are interested to predict. Our network will contain 4 neurons, distributed in 3 layers. The first layer contains the inputs, and is called the __input layer__. The second layer, called a __hidden layer__, comprises of 2 identical neurons, $n_1$, and $n_2$, each multiplying our input data points $\\mathbf{X}$ and $\\mathbf{Y}$ by a different set of parameters $A_i, B_i, C_i$, where $i=1,2$. The third layer, called the __output layer__ contains a single neuron $s$ that multiplies the outputs $N_1$, and $N_2$ of the previous neurons  by a new set of parameters $A_3$, $B_3$, and $C_3$, and outputs the result $S$, like shown on the following diagram."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_23.png\" alt=\"drawing\" width=\"650\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In machine learning this scheme is usually simplified as following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_24.png\" alt=\"drawing\" width=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "As an activation function we will again be using sigmoid function $\\sigma(x)$ defined as:"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "$$\n",
    "\\sigma = \\frac{1}{1+e^{-x}}\\\\\n",
    "$$"
   ]
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   "metadata": {},
   "source": [
    "and defined in code as:"
   ]
  },
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   "execution_count": 2,
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   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us construct a new dataset containing 2D points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 = np.array([[ 1.2, 0.7],\n",
    "                 [-0.3,-0.5],\n",
    "                 [ 3.0, 0.1],\n",
    "                 [-0.1,-1.0],\n",
    "                 [-0.0, 1.1],\n",
    "                 [ 2.1,-1.3],\n",
    "                 [ 3.1,-1.8],\n",
    "                 [ 1.1,-0.1],\n",
    "                 [ 1.5,-2.2],\n",
    "                 [ 4.0,-1.0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With each point, there is a label `1` or `-1` is associated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels2 = np.array([ 1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                    -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot this data by using the function `plot_data`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "code_folding": [
     0
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   "outputs": [],
   "source": [
    "def plot_data(data, labels):\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.scatter(data[:,0], data[:,1], c=labels, s=50,  cmap=plt.cm.bwr,zorder=50)\n",
    "    nudge = 0.08\n",
    "    for i in range(data.shape[0]):\n",
    "        d = data[i]\n",
    "        ax.annotate(f'{i}',(d[0]+nudge,d[1]+nudge))\n",
    "    ax.set_aspect('equal', 'datalim')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 304,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(data2, labels2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the data is structured such that a linear classifier wouldn't be able to apropriately classify it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's initialise the parameters of the network. This be done very efficiently with matrices, but here for the sake of clarifying the procedure we will initialise them manually with separate variables that take normally distributed random values between 0 and 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7566485514420692 0.002725779569172881 0.4076987155211042 0.10770685308094682 -0.8309211754969811 0.17043072781064242 -2.0621777482806545 0.620219798994706 1.43868497651903\n"
     ]
    }
   ],
   "source": [
    "# generating a random data set\n",
    "rnd = np.random.normal(size=9)\n",
    "\n",
    "# hidden layer neuron 1\n",
    "A1 = rnd[0] #weight for X\n",
    "B1 = rnd[1] #weight for Y\n",
    "C1 = rnd[2] #bias\n",
    "\n",
    "# hidden layer neuron 2\n",
    "A2 = rnd[3] #weight for X\n",
    "B2 = rnd[4] #weight for Y\n",
    "C2 = rnd[5] #bias\n",
    "\n",
    "# output layer neuron\n",
    "A3 = rnd[6] #weight for n1\n",
    "B3 = rnd[7] #weight for n2\n",
    "C3 = rnd[8] # bias\n",
    "\n",
    "print (A1, B1, C1, A2, B2, C2, A3, B3, C3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Computing the forward pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the given weights, biases and data points, we need to compute the final output (activation) of the function  $S = s(\\mathbf{X},\\mathbf{Y})$. We can accomplish that manually or by evaluating a function `forward_pass`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def forward_pass(A1,A2,A3,B1,B2,B3,C1,C2,C3,X,Y):\n",
    "    N1 = sigmoid(A1*X + B1*Y + C1) # 1st neuron\n",
    "    N2 = sigmoid(A2*X + B2*Y + C2) # 2nd neuron\n",
    "    S = A3*N1 + B3*N2 + C3 # final activation\n",
    "    return S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do it manually first:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we take the first data point `[ 1.2, 0.7]`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.2, 0.7)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, Y = data2[0]\n",
    "X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "z1 = A1*X + B1*Y + C1\n",
    "z2 = A2*X + B2*Y + C2\n",
    "N1 = sigmoid(z1) # 1st neuron\n",
    "N2 = sigmoid(z2) # 2nd neuron\n",
    "S = A3*N1 + B3*N2 + C3 # final activation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the output will be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07875823603547283"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We should get the same result by evaluating the function `forward_pass`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07875823603547283"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forward_pass(A1,A2,A3,B1,B2,B3,C1,C2,C3,X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Computing the backward pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By analysing the image, let's compute the derivatives:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_23.png\" alt=\"drawing\" width=\"650\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simplest to compute are the derivatives in respect to the weights $A_3$, $B_3$, and the bias $C_3$, $\\frac{\\partial S}{\\partial A_3}$, $\\frac{\\partial S}{\\partial B_3}$ and $\\frac{\\partial S}{\\partial C_3}$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial S}{\\partial A_3} &=N_1; &\\frac{\\partial S}{\\partial B_3} &=N2; &\\frac{\\partial S}{\\partial C_3}&=1;\\\\\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dA3: 0.78877963667698\n",
      "dB3: 0.4299718825501192\n",
      "dC3: 1\n"
     ]
    }
   ],
   "source": [
    "dA3, dB3, dC3 = N1, N2, 1\n",
    "print (f'dA3: {dA3}\\ndB3: {dB3}\\ndC3: {dC3}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to proceed to the weights and biases in the first layer, we need to compute derivatives in respect to the activations $N_1$ and $N_2$: $\\frac{\\partial S}{\\partial N_1}$ and $\\frac{\\partial S}{\\partial N_2}$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial S}{\\partial N_1} &=A_3 &\\frac{\\partial S}{\\partial N_2} &=B_3\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dN1: -2.0621777482806545\n",
      "dN2: 0.620219798994706\n"
     ]
    }
   ],
   "source": [
    "dN1, dN2 = A3, B3\n",
    "print (f'dN1: {dN1}\\ndN2: {dN2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To determine the derivatives in respect to the bias $C_1$ and the weights $A_1$ and $B_1$ we need to use chain rule as before:  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial S}{\\partial C_1} &=\\frac{\\partial S}{\\partial N_1}*\\frac{\\partial N_1}{\\partial z_1}*1\n",
    "&\\frac{\\partial S}{\\partial A_1} &=\\frac{\\partial S}{\\partial N_1}*\\frac{\\partial N_1}{\\partial z_1}*1*\\mathbf{X}; &\\frac{\\partial S}{\\partial B_1} &=\\frac{\\partial S}{\\partial N_1}*\\frac{\\partial N_1}{\\partial z_1}*1*\\mathbf{Y};\\\\\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial S}{\\partial C_1} &=\\frac{\\partial S}{\\partial N_1}*N_1*(1-N_1);\n",
    "&\\frac{\\partial S}{\\partial A_1} &=\\frac{\\partial S}{\\partial N_1}*N_1*(1-N_1)*\\mathbf{X}; &\\frac{\\partial S}{\\partial B_1} &=\\frac{\\partial S}{\\partial N_1}*N_1*(1-N_1)*\\mathbf{Y};\\\\\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the term $\\frac{\\partial S}{\\partial N_1}*N_1*(1-N_1)$ figures in all three partial derivatives, we can take that as an advantage and make it into a common variable `dZ1`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.3435718487979292"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dZ1 = dN1 * N1*(1-N1)\n",
    "dZ1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This makes it east to compute the derivatives $\\frac{\\partial S}{\\partial C_1}$, $\\frac{\\partial S}{\\partial A_1}$, and $\\frac{\\partial S}{\\partial B_1}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dA1: -0.412286218557515\n",
      "dB1: -0.2405002941585504\n",
      "dC1: -0.3435718487979292\n"
     ]
    }
   ],
   "source": [
    "dA1 = dZ1*X\n",
    "dB1 = dZ1*Y\n",
    "dC1 = dZ1*1\n",
    "print (f'dA1: {dA1}\\ndB1: {dB1}\\ndC1: {dC1}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in the previous case, to determine the derivatives in respect to the bias $C_2$ and the weights $A_2$ and $B_2$ we need to use chain rule:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial S}{\\partial C_2} &=\\frac{\\partial S}{\\partial N_2}*\\frac{\\partial N_2}{\\partial z_2}*1;\n",
    "&\\frac{\\partial S}{\\partial A_2} &=\\frac{\\partial S}{\\partial N_2}*\\frac{\\partial N_2}{\\partial z_2}*1*\\mathbf{X}; &\\frac{\\partial S}{\\partial B_2} &=\\frac{\\partial S}{\\partial N_2}*\\frac{\\partial N_2}{\\partial z_2}*1*\\mathbf{Y};\\\\\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\frac{\\partial S}{\\partial C_2} &=\\frac{\\partial S}{\\partial N_2}*N_2*(1-N_2);\n",
    "&\\frac{\\partial S}{\\partial A_2} &=\\frac{\\partial S}{\\partial N_2}*N_2*(1-N_2)*\\mathbf{X}; &\\frac{\\partial S}{\\partial B_2} &=\\frac{\\partial S}{\\partial N_2}*N_1*(1-N_2)*\\mathbf{Y};\\\\\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the term $\\frac{\\partial S}{\\partial N_2}*N_2*(1-N_2)$ figures in all three partial derivatives, we can take that as an advantage and make it into a common variable `dZ2`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15201343078338642"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dZ2 = dN2 * N2*(1-N2)\n",
    "dZ2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This makes it east to compute the derivatives $\\frac{\\partial S}{\\partial C_2}$, $\\frac{\\partial S}{\\partial A_2}$, and $\\frac{\\partial S}{\\partial B_2}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dA2: 0.18241611694006368\n",
      "dB2: 0.10640940154837049\n",
      "dC2: 0.15201343078338642\n"
     ]
    }
   ],
   "source": [
    "dA2 = dZ2*X\n",
    "dB2 = dZ2*Y\n",
    "dC2 = dZ2*1\n",
    "print (f'dA2: {dA2}\\ndB2: {dB2}\\ndC2: {dC2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the given label, we will need to multiply our derivatives `dA1`, `dB1`, `dC1`, `dA2`, `dB2`, `dC2`, `dA3`, `dB3` and `dC3` with either `-1` or `+1` depending on the given situation. In the algorithm, we will introduce a new variable `pull` that can be set to  `1` or `-1`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's test if we are able to successfully increase the function $S=s(\\mathbf{X},\\mathbf{Y})$. Our original score was:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07875823603547283"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forward_pass(A1,A2,A3,B1,B2,B3,C1,C2,C3,X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to gradually maximize the function $s$ towards our desired result, we need to update all of our  parameters (weights and biases). This is done by adding to the parameter's value the value of its partial derivative. To achieve this gradually in small steps, we multiply the value of the partial derivative by a a small number (step)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "step_size = 0.01\n",
    "A1 = A1 + dA1 * step_size\n",
    "B1 = B1 + dB1 * step_size\n",
    "C1 = C1 + dC1 * step_size\n",
    "A2 = A2 + dA2 * step_size\n",
    "B2 = B2 + dB2 * step_size\n",
    "C2 = C2 + dC2 * step_size\n",
    "A3 = A3 + dA3 * step_size\n",
    "B3 = B3 + dB3 * step_size\n",
    "C3 = C3 + dC3 * step_size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we now evaluate the function $f(\\mathbf{X},\\mathbf{Y})$, with the updated parameters $A$, $B$, and $C$, we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10096610562552"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forward_pass(A1,A2,A3,B1,B2,B3,C1,C2,C3,X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result should better then the original result!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A simple neural network algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can put these elements together in a working algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "code_folding": [
     80,
     87,
     102
    ],
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def train_linear_classifier(data, labels, step_size, reg_strength, no_loops, iter_info):\n",
    "    rnd = np.random.normal(size=9)\n",
    "\n",
    "    # hidden layer neuron 1\n",
    "    A1 = rnd[0] #weight for X\n",
    "    B1 = rnd[1] #weight for Y\n",
    "    C1 = rnd[2] #bias\n",
    "\n",
    "    # hidden layer neuron 2\n",
    "    A2 = rnd[3] #weight for X\n",
    "    B2 = rnd[4] #weight for Y\n",
    "    C2 = rnd[5] #bias\n",
    "\n",
    "    # output layer neuron\n",
    "    A3 = rnd[6] #weight for n1\n",
    "    B3 = rnd[7] #weight for n2\n",
    "    C3 = rnd[8] # bias\n",
    "    \n",
    "    grid = create_meshgrid(data)\n",
    "\n",
    "    for i in range(no_loops):\n",
    "        # get a single random data point\n",
    "        index = np.random.randint(data.shape[0])\n",
    "        # get X, Y of that data point and its label\n",
    "        X,Y = data[index]\n",
    "        label = labels[index]\n",
    "\n",
    "        # forward pass\n",
    "        N1 = sigmoid(A1*X + B1*Y + C1) # 1st neuron\n",
    "        N2 = sigmoid(A2*X + B2*Y + C2) # 2nd neuron\n",
    "        S = A3*N1 + B3*N2 + C3 # final activation\n",
    "\n",
    "        pull = 0.0\n",
    "        if (label == 1 and S < 1):\n",
    "            pull = 1.0\n",
    "        if (label ==-1 and S > -1):\n",
    "            pull = -1.0\n",
    "\n",
    "        # backpropagating through the network\n",
    "        # output layer weights and biases\n",
    "        dA3, dB3, dC3 = pull*N1, pull*N2, pull*1\n",
    "\n",
    "        #second layer activations\n",
    "        dN1, dN2 = pull*A3, pull*B3\n",
    "\n",
    "        # intermediate values\n",
    "        dz1 = dN1 * N1 * (1 - N1)\n",
    "        dz2 = dN2 * N2 * (1 - N2)\n",
    "\n",
    "        # second layer neuron 1\n",
    "        dA1 = dz1*X\n",
    "        dB1 = dz1*Y\n",
    "        dC1 = dz1*1\n",
    "\n",
    "        # second layer neuron 2\n",
    "        dA2 = dz2*X\n",
    "        dB2 = dz2*Y\n",
    "        dC2 = dz2*1\n",
    "\n",
    "        #regularization\n",
    "        dA1 += -A1*reg_strength; dA2 += -A2*reg_strength; dA3 += -A3*reg_strength;\n",
    "        dB1 += -B1*reg_strength; dB2 += -B2*reg_strength; dB3 += -B3*reg_strength;\n",
    "\n",
    "        # finally, do the parameter update\n",
    "        A1 += step_size * dA1; \n",
    "        B1 += step_size * dB1; \n",
    "        C1 += step_size * dC1;\n",
    "        A2 += step_size * dA2; \n",
    "        B2 += step_size * dB2;\n",
    "        C2 += step_size * dC2;\n",
    "        A3 += step_size * dA3; \n",
    "        B3 += step_size * dB3; \n",
    "        C3 += step_size * dC3;\n",
    "\n",
    "        if (i%iter_info==0):\n",
    "            accuracy = eval_accuracy_neural((A1,A2,A3,B1,B2,B3,C1,C2,C3),data,labels)\n",
    "            plot_neural_simple((A1,A2,A3,B1,B2,B3,C1,C2,C3),grid, data, labels, i, accuracy)\n",
    "        \n",
    "    return (A1, A2, A3, B1, B2, B3, C1, C2, C3)\n",
    "            \n",
    "def create_meshgrid(data):\n",
    "    h = 0.02\n",
    "    x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1\n",
    "    y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "    return (xx,yy,np.ones(xx.shape))\n",
    "\n",
    "def eval_accuracy_neural(params, data, labels):\n",
    "    A1, A2, A3, B1, B2, B3, C1, C2, C3 = params\n",
    "    num_correct = 0;\n",
    "    data_len = data.shape[0]\n",
    "    \n",
    "    for i in range(data_len):\n",
    "        X,Y = data[i]\n",
    "        true_label = labels[i]\n",
    "        score = forward_pass(A1, A2, A3, B1, B2, B3, C1, C2, C3, X, Y)\n",
    "        predicted_label = 1 if score > 0 else -1\n",
    "        \n",
    "        if (predicted_label == true_label):\n",
    "            num_correct += 1\n",
    "    return num_correct / data_len\n",
    "\n",
    "def plot_neural_simple(params, grid,data, labels, iteration, accuracy):\n",
    "    nudge = 0.06\n",
    "    A1, A2, A3, B1, B2, B3, C1, C2, C3 = params\n",
    "    xx,yy,Z = grid\n",
    "    \n",
    "    for i in range(xx.shape[0]): # row\n",
    "        for j in range(yy.shape[1]): #column\n",
    "            X, Y = xx[i][j],yy[i][j]\n",
    "            score = forward_pass(A1, A2, A3, B1, B2, B3, C1, C2, C3, X, Y) \n",
    "            score = 1 if score > 0 else -1\n",
    "            Z[i][j] = score\n",
    "\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.title(f'accuracy at the iteration {iteration}: {accuracy}')\n",
    "    ax.contourf(xx, yy, Z, cmap=plt.cm.binary, alpha=0.1, zorder=15)\n",
    "    ax.scatter(data[:, 0], data[:, 1], c=labels, s=50,  cmap=plt.cm.bwr,zorder=50)\n",
    "    ax.set_aspect('equal')\n",
    "    for i in range(data.shape[0]):\n",
    "        d = data[i]\n",
    "        ax.annotate(f'{i}',(d[0]+nudge,d[1]+nudge))\n",
    "    plt.xlim(xx.min(), xx.max())\n",
    "    plt.ylim(yy.min(), yy.max())\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_2 = train_linear_classifier(data2, labels2, 0.1, 0.001, 4001, 800)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "data point 0: real label : 1, pred. label: 1, True\n",
      "data point 1: real label : -1, pred. label: -1, True\n",
      "data point 2: real label : 1, pred. label: 1, True\n",
      "data point 3: real label : -1, pred. label: -1, True\n",
      "data point 4: real label : -1, pred. label: -1, True\n",
      "data point 5: real label : 1, pred. label: 1, True\n",
      "data point 6: real label : -1, pred. label: -1, True\n",
      "data point 7: real label : 1, pred. label: 1, True\n",
      "data point 8: real label : -1, pred. label: -1, True\n",
      "data point 9: real label : -1, pred. label: -1, True\n"
     ]
    }
   ],
   "source": [
    "a1,a2,a3,b1,b2,b3,c1,c2,c3 = train_2\n",
    "for i, ((x,y), label) in enumerate(zip(data2, labels2)):\n",
    "    s = forward_pass(a1,a2,a3,b1,b2,b3,c1,c2,c3,x,y)\n",
    "    s = 1 if s > 0 else -1\n",
    "    print (f'data point {i}: real label : {label}, pred. label: {s}, {(s==label)}')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}