07. Loss (Cost) Function.ipynb

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   "cell_type": "code",
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   "metadata": {},
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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": [
    "# Loss/Cost Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Intuition\n",
    "In the previous example, we have used the variable `pull` with the value `1` or `-1` to define whether our network parameters (weights and biases) should be pulled towards the positive or the negative direction depending on the label of the current data point. We have seen that over the course of the training, the network gradually improves in classifying our data set. However, this \"pull up or down depending on the label\" approach does not provide us with a concrete measure that we can use to evaluate how the training is improving. For this reason machine learning uses an additional layer called a *loss function* (also named *cost* function)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A Single Data Point\n",
    "Let's first consider what would be the loss of a neural network which is trained on a single data point: Here, the neural network takes this single data point, for example `[1.2, 0.7]`, all the weights and biases of the neural network, and computes the output. In our case, let's say that the output of the network is `0.63`. A loss function then compares this output with the desired output, defined by the label of that data point. In our case, let's say that the label for this data point is `1`. The difference between these two values `(1.0 - 0.63) = 0.37` defined as *loss* or *cost* shows how good or bad the networks is performing in classifying our data. If the difference between the actual and the desired output is large, the network is performing bad. If this distance is close to zero, (for example if the output was `0.98`, then `(1.0 - 0.98) = 0.02`), the network is performing well. To bring this distance towards zero, we use the backpropagation algorithm just like before, with the additional step of computing the derivative of the loss function itself. <br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple data points\n",
    "In praxis, to efficiently train a neural network requires a lot of data, not a single data point. In this case we need to compute the *total loss* of a neural network, which means that we need to sum all of the single losses (of all (or some) data points) into a single number, whose value we need to minimize. The goal is to bring this number close to zero __for all__ data points. <br> \n",
    "The obstacle to do this is that in the process of backpropagation, we can only compute partial derivatives for a single data point. In order to compute the partial derivatives for all data points, the best we can do is to compute the partials for all the single data points, and then average them into a single _gradient_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The quadratic cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the basic types of loss/cost functions is the __quadratic cost function__. It is also sometimes known as the mean squared error or just MSE. It squares the difference between the label and the output, which makes the loss always a positive value. In our prevous example the quadratic loss would be <br>`(1.0 - 0.63)*(1.0 - 0.63) = 0.1369`. The general form of this function in a neural network would be:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{eqnarray}  C(w,b) \\equiv\n",
    "  \\frac{1}{n} \\sum_x \\| y(x) - a\\|^2.\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, $w$ denotes the collection of all weights in the network, $b$ all the biases, $n$ is the total number of training inputs, a\n",
    "$a$ is the vector of outputs from the network when $x$ is input, and the sum is over all training inputs, $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting from the previous example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_23.png\" alt=\"drawing\" width=\"550\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will implement the same neural network architecture with the added quadratic loss function added at the end. This is how the diagram looks like now:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img/neural_networks_25.png\" alt=\"drawing\" width=\"750\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only thing that changes with respect to the previous example, is a single additional step in computing a feedforward pass, and a single additional step in computing the derivative $\\frac{\\partial C}{\\partial S}$ of the cost function $C$ in respect to the network's output $S$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By applying the general formula, the cost of a single training example $(\\mathbf{X},\\mathbf{Y})$ is "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*} \n",
    "C_x = (label-S)^2.\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the derivative $\\frac{\\partial C_x}{\\partial S}$ is simply:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}  \n",
    "\\frac{\\partial C_x}{\\partial S} &= 2*(label - S)\\\\\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's implement the algorithm with the same data set. First we will load the display and helper methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [
     0,
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    ]
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   "outputs": [],
   "source": [
    "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 = circuit_forward(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 = circuit_forward(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()\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 sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def circuit_forward(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\n",
    "\n",
    "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": "markdown",
   "metadata": {},
   "source": [
    "We will use the same data and labels as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = 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": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = np.array([ 1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                    -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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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(data, labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the training algorithm, much simplified and not-optimised for readability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def train_neural_network(data, labels, step_size, epochs, iter_info):\n",
    "\n",
    "    # first we initialise all the weights and biases as normally distributed random numbers\n",
    "    rnd = np.random.normal(size=9)\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",
    "    # in each epoch, we will go through all the data points once\n",
    "    for i in range(epochs):\n",
    "        # total cost must be restarted in every epoch\n",
    "        total_cost = 0.0\n",
    "        ddA1, ddA2, ddA3, ddB1, ddB2, ddB3, ddC1, ddC2, ddC3 = 0,0,0,0,0,0,0,0,0\n",
    "        # here we loop trough all the data points, and get X, Y and the corresponding label\n",
    "        for index, ((X,Y), label) in enumerate(zip(data, labels)): \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",
    "            # This is the implementation of the quadratic cost for the single data point\n",
    "            cost = (label-S)**2\n",
    "            # This value is then accumulated into total_cost variable, so that the cost is expressed\n",
    "            # for all the data points\n",
    "            total_cost += cost\n",
    "\n",
    "            # backpropagating through the network\n",
    "            # here we compute the derivative of the cost C in respect to the network output S\n",
    "            dS = 2*(label-S)\n",
    "            # output layer weights and biases are multiplied by dS by using the chain rule\n",
    "            dA3, dB3, dC3 = dS*N1, dS*N2, dS*1\n",
    "            \n",
    "            # The rest of the derivative computation is the same as before:\n",
    "            \n",
    "            #second layer activations\n",
    "            dN1, dN2 = dS*A3, dS*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",
    "            # since we have multiple data points, and we can compute only a single partial derivative at the time\n",
    "            # we accumulate their values in the variables ddA1...ddC3\n",
    "            \n",
    "            ddA1 += dA1\n",
    "            ddA2 += dA2\n",
    "            ddA3 += dA3\n",
    "            ddB1 += dB1\n",
    "            ddB2 += dB2\n",
    "            ddB3 += dB3\n",
    "            ddC1 += dC1\n",
    "            ddC2 += dC2\n",
    "            ddC3 += dC3\n",
    "        \n",
    "        # Now we make an average of all the accumulated derivatives by dividing with the number of data points\n",
    "        datalen = len(data)\n",
    "        ddA1 /= datalen\n",
    "        ddA2 /= datalen\n",
    "        ddA3 /= datalen\n",
    "        ddB1 /= datalen\n",
    "        ddB2 /= datalen\n",
    "        ddB3 /= datalen\n",
    "        ddC1 /= datalen\n",
    "        ddC2 /= datalen\n",
    "        ddC3 /= datalen\n",
    "\n",
    "        # finally, we do the parameter update with the averaged values ddA1...ddC3\n",
    "        A1 += step_size * ddA1; \n",
    "        B1 += step_size * ddB1; \n",
    "        C1 += step_size * ddC1;\n",
    "        A2 += step_size * ddA2; \n",
    "        B2 += step_size * ddB2;\n",
    "        C2 += step_size * ddC2;\n",
    "        A3 += step_size * ddA3; \n",
    "        B3 += step_size * ddB3; \n",
    "        C3 += step_size * ddC3;\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",
    "            print (f'total cost: {round(total_cost,4)}\\n')\n",
    "        \n",
    "    return (A1, A2, A3, B1, B2, B3, C1, C2, C3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 7.9801\n",
      "\n"
     ]
    },
    {
     "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.9602\n",
      "\n"
     ]
    },
    {
     "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.3639\n",
      "\n"
     ]
    },
    {
     "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.2028\n",
      "\n"
     ]
    }
   ],
   "source": [
    "train = train_neural_network(data, labels, 0.5, 1501, 500)"
   ]
  }
 ],
 "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
}