06-crossentropy-loss.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config IPCompleter.greedy=True\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn.datasets, sklearn.model_selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-entropy loss\n",
    "\n",
    "So far we used mean squared error (MSE) loss. In this notebook, I would like to show you cross-entropy loss, which is more suited for the classification problems. Mean squared error is preferred loss if we perform regression (we try to predict real number), but for the classification task, when we should predict in which class the example is from, the cross-entropy is much better. We will see why is this way through this notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may take cross-entropy loss into more details, however, I don't think it is necessary. Still, I would like to point out some articles, that should be a good starting point when somebody wants to know deeper, what is really happening.\n",
    "\n",
    "First of all, you may want to know something about entropy itself. This is probably a term you already heard about during statistics, cybersecurity, or information theory in general. It basically describes, how much \"surprise\" is in the data. The article [[1]](#Bibliography) is a good starting point.\n",
    "\n",
    "Then there is cross-entropy. When we have two distributions, cross-entropy in some sense measure difference between these distributions. We may think about the target classes as about one of the distribution and about the model prediction as about the second distribution. Our goal is to align the model prediction distribution as close as possible to the target distribution. Now you may see, why the cross-entropy may be a better idea compared to MSE. YOu may find some more math and in-depth view in [[2]](#Bibliography).\n",
    "\n",
    "Finally, similar to MSE, we may derive cross-entropy as a result of maximum likelihood estimation. So we have ways to show, that the cross-entropy is a good loss function and that it works. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get to math. Cross entropy is defined as follow:\n",
    "$$\n",
    "H(P,Q)=-\\sum_{x\\in X}^{n}p(x)\\log q(x)\n",
    "$$\n",
    "\n",
    "Remember, we are talking about the distributions. Here, the $P$ is the target distribution and $Q$ is the model distribution. As such $p(x)$ and $q(x)$ is not a single number, but a vector - distribution over all the classes. If we want to know, how to compute cross-entropy for a single example, the formulas is following:\n",
    "$$\n",
    "\\mathcal{L}(t, y)=-\\sum_i t_i \\log y_i \n",
    "$$\n",
    "\n",
    "Here, the $t$ is the target distribution and $y$ is the predited distribution. Let's show it on the example. Let's say we have example, where the target should be equal to second class. If we want to express this in the distribution, that would equal to vector $t=(0,1,0,0)$ (I consider only 4 classes). Now, the model predicted $y=(0.2, 0.1, 0.5, 0.2)$. The cross-entropy in this case is following:\n",
    "$$\n",
    "\\mathcal{L} = -(0 \\cdot \\log 0.2 + 1 \\cdot \\log 0.1 + 0 \\cdot \\log 0.5 + 0 \\cdot \\log 0.2) = - 1 \\cdot \\log 0.1 = 2.30259 \n",
    "$$\n",
    "On the other hand, if the correct class would be the third one (that is $t=(0,0,1,0)$), the cross-entropy would change.\n",
    "$$\n",
    "\\mathcal{L} = -(0 \\cdot \\log 0.2 + 0 \\cdot \\log 0.1 + 1 \\cdot \\log 0.5 + 0 \\cdot \\log 0.2) = - 1 \\cdot \\log 0.5 = 0.69314\n",
    "$$\n",
    "\n",
    "As we may see, the closer the prediction is to the target distribution, the lower the loss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary cross-entropy loss\n",
    "\n",
    "Firstly, let's look at the binary cross-entropy. That is a loss, that takes into account only two classes - exactly what we were doing so far. There doesn't matter, we have only one class, as we may compute the probability of the second class as complement $1 - p$. Here comes the final loss:\n",
    "\n",
    "$$\n",
    "\\mathcal{L}_{BCE}(t,y)=-t\\log y - (1-t)\\log (1-y)\n",
    "$$\n",
    "\n",
    "I just expand the sum to both classes and computed the distribution of the second class as a complement to the first one. Now it is simple to get the derivative as well.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial y}= -\\frac{t}{y} + \\frac{1-t}{1-y}\n",
    "$$\n",
    "\n",
    "There is however one problem. What if the prediction is exactly equal to $0$ or $1$? Although that is impossible, when sigmoid is used, the precision of float value may not hold that small value and just round the result to either $0$ or $1$. In that case, the fractions are not defined. Usually some small $\\varepsilon$ is added to the denominator.\n",
    "\n",
    "Now we know enough, so we may check the implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BCELoss:\n",
    "    def __call__(self, target, predicted):\n",
    "        return np.sum(-target * np.log(np.maximum(predicted, 1e-15)) - (1 - target) * np.log(np.maximum(1 - predicted, 1e-15)), axis=0)\n",
    "    def gradient(self, target, predicted):\n",
    "        return - target / (np.maximum(predicted, 1e-15)) + (1 - target) / (np.maximum(1 - predicted, 1e-15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may now compare binary cross-entropy with mean squared error loss. Firstly, let's download the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = sklearn.datasets.fetch_openml('mnist_784', version=1, return_X_y=True)\n",
    "y = y.astype(int)\n",
    "one_or_seven_indices = np.logical_or(y == 4, y == 9)\n",
    "data = X[one_or_seven_indices].reshape(-1, 784)\n",
    "data[data < 128] = 0\n",
    "data[data > 0] = 1\n",
    "data = np.hstack([data, np.ones((data.shape[0],1))])\n",
    "target = y[one_or_seven_indices].reshape(-1)\n",
    "target[target==4] = 0\n",
    "target[target==9] = 1\n",
    "train_data, test_data, train_target, test_target = sklearn.model_selection.train_test_split(data, target, test_size=0.3, random_state=47)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then let's define `MSELoss` the same way as in the previous notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MSELoss:\n",
    "    def __call__(self, target, predicted):\n",
    "        return np.sum((target - predicted) ** 2, axis=0)\n",
    "    def gradient(self, target, predicted):\n",
    "        return -(target - predicted)\n",
    "    \n",
    "class AccuracyMetric:\n",
    "    def __init__(self, name=None):\n",
    "        self.name = name or \"accuracy\"\n",
    "        self.correct = 0\n",
    "        self.num = 0\n",
    "    def __call__(self, target, predicted):\n",
    "        self.correct += np.sum((predicted >= 0.5) & (target == 1)) + np.sum((predicted < 0.5) & (target == 0))\n",
    "        self.num += len(target)\n",
    "    def summary(self):\n",
    "        acc = self.correct / self.num\n",
    "        self.correct = 0\n",
    "        self.num = 0\n",
    "        return acc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we may use the `Neuron` class from the previous notebook and pass different loss to the constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100% (2000 of 2000) |####################| Elapsed Time: 0:01:18 Time:  0:01:18\n"
     ]
    }
   ],
   "source": [
    "from src.neuron_05 import Neuron\n",
    "\n",
    "mse = Neuron(loss=MSELoss(), metrices=[AccuracyMetric()], epochs=2000, learning_rate=0.001, batch_size=128, random_state=42)\n",
    "mse_result = mse.fit(train_data, train_target, test_data, test_target, progress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100% (2000 of 2000) |####################| Elapsed Time: 0:01:24 Time:  0:01:24\n"
     ]
    }
   ],
   "source": [
    "from src.neuron_05 import Neuron\n",
    "\n",
    "bce = Neuron(loss=BCELoss(), metrices=[AccuracyMetric()], epochs=2000, learning_rate=0.001, batch_size=128, random_state=42)\n",
    "bce_result = bce.fit(train_data, train_target, test_data, test_target, progress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All we need to do now is to plot the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(mse_result['train_loss'], label=\"MSE train loss\", color='tab:blue')\n",
    "plt.plot(mse_result['test_loss'], label=\"MSE test loss\", color='tab:blue', linestyle='--')\n",
    "plt.plot(bce_result['train_loss'], label=\"BCE train loss\", color='tab:orange')\n",
    "plt.plot(bce_result['test_loss'], label=\"BCE test loss\", color='tab:orange', linestyle='--')\n",
    "plt.yscale('log')\n",
    "ticks = [0.028, 0.04, 0.056, 0.08, 0.112, 0.16, 0.225, 0.32, 0.45, 0.64, 0.9, 1.28]\n",
    "plt.yticks(ticks=ticks, labels=ticks)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(mse_result['train_accuracy'], label=\"MSE train accuracy\", color='tab:blue')\n",
    "plt.plot(mse_result['test_accuracy'], label=\"MSE test accuracy\", color='tab:blue', linestyle='--')\n",
    "plt.plot(bce_result['train_accuracy'], label=\"BCE train accuracy\", color='tab:orange')\n",
    "plt.plot(bce_result['test_accuracy'], label=\"BCE test accuracy\", color='tab:orange', linestyle='--')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is interesting. Although BCE loss is much higher compared to MSE, accuracy is better for binary cross-entropy loss. Loss values can't be directly compared when different loss, architecture, or regularization is used. The performance of the network should be determined by some metric, now we see why."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why is binary cross-entropy loss better than MSE loss\n",
    "\n",
    "We may notice something much more interesting. BCE accuracy increased much faster in comparison to MSE loss, although the model is the same. Why is it? This fact is connected to the sigmoid activation function and binary cross-entropy. If you remember the sigmoid graph and it's derivative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sig(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "x = np.arange(-6, 6, 0.1)\n",
    "plt.figure(figsize=(12,4))\n",
    "plt.plot(x, sig(x), label=\"function\")\n",
    "plt.plot(x, sig(x)*(1-sig(x)), label=\"derivative\")\n",
    "plt.title(\"Sigmoid\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may notice, that values far away from zero have derivatives almost 0. When MSE loss is used, the derivative of MSE won't be greater than 1. The derivative of the sigmoid is lower than $0.25$ - probably less when the misclassified example is too far. As a result, the gradient of weights is too small and it takes some time to \"shift\" the example to the correct side of the sigmoid.\n",
    "\n",
    "On the other hand, when binary cross-entropy loss is in use, the derivative is $\\frac{t}{y}=\\frac{1}{y}$ for the correct class. When the example is misclassified too much ($y$ is very small), the higher is the resulting derivative. As such, for very wrongly misclassified examples, the weights are updated more compared to MSE and it balances the sigmoid.\n",
    "\n",
    "We may look at it from the other view. Sigmoid is an exponential function and binary cross-entropy is a logarithmic function. When we put this together, they balance each other and we may think about the resulting gradient in \"linear scale\".\n",
    "\n",
    "As a result of better gradient propagation, a model with binary cross-entropy learns faster from the beginning.\n",
    "\n",
    "I will talk about similar topics later on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiclass cross-entropy\n",
    "\n",
    "It is easy to generalize our loss to more classes. Remember, how the cross-entropy looked like.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(t, y)=-\\sum_i t_i \\log y_i \n",
    "$$\n",
    "\n",
    "We may directly implement it, we are going to call it `CategoricalCrossEntropyLoss`. Let's expand the sum, so we can better see what is happening.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(t, y)=-t_0 \\log y_0 - t_1 \\log y_1 - t_2 \\log y_2 - \\cdots - t_9 \\log y_9 \n",
    "$$\n",
    "\n",
    "Notice, that the target distribution $\\pmb{t}$ is one-hot encoded, that is, the vector $\\pmb{t}$ would be something like $(0,0,0,1,0,0,\\dots,0)$. As the zeros remove corresponding classes from the loss, we end up with a simplified version.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(t, y)=-t_r \\log y_r \n",
    "$$\n",
    "\n",
    "where $r$ is the index of the correct class. Moreover, $t_r$, in this case, is $1$, so the loss is even simpler.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}(t, y)=-\\log y_r \n",
    "$$\n",
    "\n",
    "This is something, you may know as a negative log-likelihood, I will talk about it in a moment. Finally, the derivative of the loss is very simple.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial y_r} = -\\frac{1}{y_r} \\\\\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial y_{i \\neq r}} = 0\n",
    "$$\n",
    "\n",
    "So, here is the resulting code, that reflects these changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CategoricalCrossEntropyLoss:\n",
    "    def __call__(self, target, predicted):\n",
    "        indices = np.arange(len(target))\n",
    "        return -np.log(np.maximum(predicted[indices,target], 1e-15))\n",
    "    \n",
    "    def gradient(self, target, predicted):\n",
    "        grad = np.zeros((len(target), 10))\n",
    "        indices = np.arange(len(target))\n",
    "        grad[indices,target] = -1 / np.maximum(predicted[indices,target], 1e-15)\n",
    "        return grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are not going to use this loss yet, but we will see it in action in the following notebook. The `np.maximum` calls are there only for stability, in case the value is $0$ and the division would be undefined.\n",
    "\n",
    "Note that the `predicted` parameter is expected to have shape `(examples,classes)`, whereas the `target` parameter is expected to be in shape `(examples)` with values up to the number of classes.\n",
    "\n",
    "Also note that the loss is interested in only one output. For each example, the loss is computed only on the correct class (if the model predicted other classes with higher probability, the loss doesn't care about it) as well as the gradient updates only one input. The cross-entropy expects, that each class would justify itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross-entropy and negative log-likelihood\n",
    "\n",
    "There is sometimes confusion about cross-entropy loss and negative log-likelihood loss. Probably because of Pytorch, which has both of these losses. The fact is, that there are the same.\n",
    "\n",
    "Although I didn't want to dive deeper into the math behind, it is best to do it for the negative log-likelihood.\n",
    "\n",
    "Firstly, let's start with maximum-likelihood. That is, we want to find parameters, that best explain the data.\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\max}\\ p_{model}(\\pmb{X}_{examples}; \\theta)\n",
    "$$\n",
    "\n",
    "As examples are independent of each other, we may rewrite that.\n",
    "\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\max}\\ \\prod_{i} p_{model}(x_i; \\theta)\n",
    "$$\n",
    "\n",
    "Mathematicians usually don't like multiplication, so we wanna get rid of it. Luckily, the multiplication of numbers is the same (in the sense of optimization) as the sum of logarithms.\n",
    "\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\max}\\ \\sum_{i} \\log p_{model}(x_i; \\theta)\n",
    "$$\n",
    "\n",
    "Finally, the maximization of $x$ is equal to the minimalization of $-x$.\n",
    "\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\min}\\ \\sum_{i} - \\log p_{model}(x_i; \\theta)\n",
    "$$\n",
    "\n",
    "Here we see, why we call it **negative log-likelihood** loss. \n",
    "\n",
    "However, we are still not there. This is still something different than what I showed as cross-entropy. What we may do is divide the sum by the number of examples, as the scaling of the values doesn't affect the optimization process.\n",
    "\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\min}\\ \\sum_{i}^{n} - \\frac{1}{n} \\log p_{model}(x_i; \\theta)\n",
    "$$\n",
    "\n",
    "But that is the definition of expectation value (what would be the expected outcome for all the data). In other words, what would be the expected output if we sample the data from the examples. We may express is as the following formula.\n",
    "\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\min}\\ \\mathbb{E}_{x \\sim p_{example}(x)} \\log p_{model}(x; \\theta)\n",
    "$$\n",
    "\n",
    "We are almost there. We can now see two probability distributions - there is $p_{example}(x)$ distribution (i will denote $p_t(x)$ as it is our target distribution) and $p_{model}(x)$ distribution (i will denote as $p_y(x)$ as it is the model prediction distribution). Now I just make these changes.\n",
    "\n",
    "$$\n",
    "\\theta_{ML} = \\underset{\\theta}{\\arg\\min}\\ \\mathbb{E}_{x \\sim p_t(x)} \\log p_y(x; \\theta)\n",
    "$$\n",
    "\n",
    "This is the exact definition of cross-entropy.\n",
    "\n",
    "Last step to get our loss is to rewrite the expected value by definition. For one example, where $t$ are individual classes:\n",
    "\n",
    "$$\n",
    "\\mathbb{E}_{x \\sim p_t(x)} \\log p_y(x; \\theta) = \\sum_k p_t(k) \\log p_y(k)\n",
    "$$\n",
    "\n",
    "And that's exactly, where we wanted to end up - the cross-entropy alias the negative log-likelihood (**NLL**) loss. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, that was a lot of math. You don't need to remember it, I just wanted to point out, that you may encounter negative log-likelihood loss and that it is, in fact, the same thing as cross-entropy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bibliography\n",
    "\n",
    " - \\[1\\] Entropy in machine learning, Francesco Gadaleta, 6 May 2019, [online](https://amethix.com/entropy-in-machine-learning/)\n",
    " - \\[2\\] A Gentle Introduction to Cross-Entropy for Machine Learning, Jason Brownlee, 21 October 2019, [onlin](https://machinelearningmastery.com/cross-entropy-for-machine-learning/)\n",
    " - \\[3\\] Cross-entropy and Maximum Likelihood Estimation, Roan Gylberth, 16 February 2019, [online](https://medium.com/konvergen/cross-entropy-and-maximum-likelihood-estimation-58942b52517a)."
   ]
  }
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