05_probabilities_bayesian.ipynb

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    "# Creative Machine Learning - Probabilities and Bayesian inference\n",
    "\n",
    "### Author: Philippe Esling (esling@ircam.fr)\n",
    "\n",
    "In this course we will cover\n",
    "1. A [quick recap](#recap) on simple probability concepts\n",
    "2. An introduction to [probability distributions](#distributions)\n",
    "3. An explanation on how to [sample](#sampling) from distributions ourselves\n",
    "4. An introduction to [Bayesian inference](#bayesian)\n",
    "5. A simple implementation of [Maximum Likelihood](#ml)\n",
    "6. How to optimize [unknown parameters](#)"
   ]
  },
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    "<a id=\"probability\"> </a>\n",
    "## Understanding probability\n",
    "\n",
    "The field of probability aims to model random or uncertain events. We usually refer to random events when we cannot predict the outcome of a phenomenon with absolute certainty. Maybe the simplest and most iconic case of randomness that everyone has encoutered is to _flip a coin_. In that case, we are uncertain of the result, and might see randomness as a way of expressing this uncertainty.\n",
    "\n",
    "Hence, a random variable $X$ denotes a quantity that is uncertain, such as the result of an experiment (flipping a coin) or the measurement of an uncertain property (the weather of tomorrow). However, if we can observe a sufficiently large set of _samples_ $\\{\\mathbf{x}_{i}\\}_{i=1}$, it might take different values on each occasion, but some values may occur more often than others. Hence, we can start reasoning on these random events from a different perspective. If the coin is fair, and do not have access to any external information, we expect the _probability_ of the result to be heads 1 times out of 2, or equivalently 50\\% of the times. Here, the use of percentage informs us on one of the interpretation of probability, as the _relative frequency_ of events. By repeatedly flipping the coin and observing the results, we can count the occurrence of each outcome.\n",
    "\n",
    "To understand these concepts graphically, we will rely on `numpy` and `matplotlib`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from cml.plot import cml_figure_matplotlib as figure"
   ]
  },
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   "metadata": {},
   "source": [
    "## Definitions\n",
    "Let's start with some basic definitions and principles.\n",
    "- An ***experiment*** or ***trial*** is an action with an uncertain outcome, such as tossing a coin.\n",
    "- A ***sample space*** is the set of all possible outcomes of an experiment. In a coin toss, there's a set of two possible oucomes (*heads* and *tails*).\n",
    "- A ***sample point*** is a single possible outcome - for example, *heads*)\n",
    "- An ***event*** is a specific outome of single instance of an experiment - for example, tossing a coin and getting *tails*.\n",
    "- ***Probability*** is a value between 0 and 1 that indicates the likelihood of a particular event, with 0 meaning that the event is impossible, and 1 meaning that the event is inevitable. In general terms, it's calculated like this:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\text{probability of an event} = \\frac{\\text{Number of sample points that produce the event}}{\\text{Total number of sample points in the sample space}} \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "For example, the probability of getting *heads* when tossing as coin is <sup>1</sup>/<sub>2</sub> - there is only one side of the coin that is designated *heads*. and there are two possible outcomes in the sample space (*heads* and *tails*). So the probability of getting *heads* in a single coin toss is 0.5 (or 50% when expressed as a percentage)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on tails\n"
     ]
    }
   ],
   "source": [
    "vals = ['heads', 'tails']\n",
    "trials = 5\n",
    "for t in range(trials):\n",
    "    # Get a random 0 or 1\n",
    "    toss = random.randint(0,1)\n",
    "    # Print the result of our toss\n",
    "    print('Coin is tossed on ' + vals[toss])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run the previous code several times, we will always get different (uncertain) results, showing the underlying randomness. However, if we start simulating (_sampling_) this _experiment_ a certain number of times, we can start to look at the _distribution_ of _events_ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 2500x10000 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(100,25)\n",
    "# loop through 5,10,50,100,1000,10000 trials\n",
    "for t_id, trials in enumerate([5,10,50,100,1000,10000]):\n",
    "    # Keep track\n",
    "    heads_or_tails = [0, 0]\n",
    "    for t in range(trials):\n",
    "        # Get a random 0 or 1\n",
    "        toss = random.randint(0,1)\n",
    "        # Increment the list element corresponding to the toss result\n",
    "        heads_or_tails[toss] = heads_or_tails[toss] + 1\n",
    "    # Show a pie chart of the results\n",
    "    plt.subplot(1, 6, t_id+1)\n",
    "    plt.pie(heads_or_tails, labels=['heads', 'tails'])\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "<a id=\"theory\"> </a>\n",
    "## Probability theory\n",
    "\n",
    "Probability theory defines the mathematical framework that allows to describe and analyze random phenomena, regardless of the interpretation of probability that we prefer. To rely on this framework, we starts by assuming few axioms of probability. We postulate a set of possible events $\\Omega$ called the *sample space* (in our coin toss example, we would have $\\Omega = \\{Heads, Tails\\}$. We can define a _probability measure_ $p(\\omega)$ to an event $\\omega\\in\\Omega$, which gives a value between 0 (very unlikely) and 1 (very probable) that shows how likely the event is. In our previous example, we could write that the probability of throwing a 7 is expressed as\n",
    "\n",
    "$$\n",
    "p(\\omega = 7) = 0.167\n",
    "$$\n",
    "\n",
    "where our sample space is defined as $\\Omega = \\{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\\}$\n",
    "\n",
    "### Axioms of probability\n",
    "The foundation of probability theory is defined in these axioms, on which we can develop tools and techniques to calculate probabilities of different events.\n",
    "\n",
    "- For any event $\\omega\\in\\Omega$, $0\\leq p(\\omega) \\leq 1$.\n",
    "- Probability of the sample space $\\Omega$ is $p(\\Omega)=1$.\n",
    "- For a set of \\textit{disjoint} events $\\omega_1,\\cdots,\\omega_n$ we have $p(\\bigcup_{i=1}^{n} \\omega_i)=\\sum_{i=1}^{n} \\omega_{i}$\n",
    "\n",
    "The first axiom is quite straightforward and states that probability is measured in the interval $[0,1]$. The second axiom states that the probability of the whole sample space is equal to one, as it contains all possible outcomes of our random experiment. For instance, in our coin toss, the outcome will always be either $Heads$ or $Tails$, and therefore will always be contained in $\\Omega$. Finally, the third axioms state that for two disjoint events, the probability of one or the other to happen is the sum of their individual probabilities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"recap\"> </a>\n",
    "\n",
    "## Quick recap on probability\n",
    "\n",
    "The field of probability aims to model random or uncertain events through random variables $X$ denoting a quantity that is uncertain, which take values $\\omega$ in a sample space $\\omega \\in \\Omega$. If we observe several occurrences of this variable $\\{\\mathbf{x}_{i}\\}_{i=1}$, we might try to model the _probability distribution_ $p(\\mathbf{x})$ of that variable. We recall here that the probability of an event $a$ is a real number $p(a)$, with $0 \\leq p(a) \\leq 1$, knowing that $p(\\Omega)=1$ and $p(\\{\\})=0$. The probability of two events occuring simultaneously is defined as $p\\left(a, b \\right)$ (or equivalently as $p\\left(a \\cup b \\right)$). Therefore, the probability of one event **or** the other occuring is defined as\n",
    "$\n",
    "\\begin{equation}\n",
    "p\\left(a \\cap b \\right) = p(a) + p(b) - p\\left(a \\cup b \\right)\n",
    "\\end{equation}\n",
    "$\n",
    "\n",
    "The *conditional probability* of an event $a$ occuring *given* another event $b$ is denoted $p \\left(a \\mid b \\right)$ and is defined as\n",
    "$$\n",
    "\\begin{equation}\n",
    "p \\left(a \\mid b \\right) = \\frac{p \\left(a , b \\right)}{p \\left(b \\right)}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "This can be understood as the probability of event $a$ to occur if we restrict the world of possibilities to event $b$. The *chain rule* defines the probabilities of a set of events to co-occur simultaneously\n",
    "$$\n",
    "\\begin{equation}\n",
    "p \\left(x_{1},...,x_{n} \\right) = \\prod_{i=n}^{1}{p \\left(x_{i}\\mid x_{i-1},..., x_{1} \\right)}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Finally, we say that two events are independent if $p(a\\mid b) = p(a)$.\n",
    "\n",
    "To understand these concepts graphically, we will rely on `PyTorch` and specifically the `distributions` package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.distributions as distribution\n",
    "import torch.distributions.transforms as transform\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"distributions\"> </a>\n",
    "### Probability distributions\n",
    "\n",
    "Let $X$ be a random variable associated with a *probability distribution function* that assigns probabilities to the different outcomes $X$ can take in the sample space. We can divide random variables into three different types:\n",
    "\n",
    "- **$X$ is discrete**: Discrete random variables may only assume values on a specified list. \n",
    "- **$X$ is continuous**: Continuous random variable can take on arbitrarily exact values. \n",
    "- **$X$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, (i.e. a combination of the above two categories). \n",
    "\n",
    "**Expected Value**\n",
    "The expected value $\\mathbb{E}\\left[X\\right]$ for a given probability distribution can be described as _\"the mean expected value for many repeated samples from that distribution.\"_ As the number of repeated observation goes to infinity, the difference between the average outcome and the expected value becomes arbitrarily small. Formally, it is defined for discrete variables as\n",
    "\n",
    "$$\n",
    "\\mathbb{E}\\left[X\\right] = \\sum\\limits_{i}\\mathbf{x}_i p(\\mathbf{x}=\\mathbf{x}_i)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Discrete distributions\n",
    "\n",
    "If $X$ is discrete, then its distribution is called a *probability mass function* (pmf), which measures the probability $X$ takes on the value $x_{i}$, denoted $P(X=x_{i})$. Let $\\mathbf{x}$ be a discrete random variable with range $R_{X}=\\{x_1,\\cdots,x_n\\}$ (finite or countably infinite). The function\n",
    "\n",
    "$$\n",
    "p_{X}(x_{i})=p(X=x_{i}), \\forall i\\in\\{1,\\cdots,n\\}\n",
    "$$\n",
    "\n",
    "is called the probability mass function (PMF) of $X$.\n",
    "\n",
    "Hence, the PMF defines the probabilities of all possible values for a random variable. The above notation allows to express that the PMF is defined for the random variable $X$, so that $p_{X}(1)$ gives the probability that $X=1$. For discrete random variables, the PMF is also called the \\textit{probability distribution}. The PMF is a probability measure, therefore it satisfies all the corresponding properties\n",
    "- $0 \\leq p_{X}(x_i) < 1, \\forall x_i$\n",
    "- $\\sum_{x_i\\in R_{X}} p_{X}(x_i) = 1$\n",
    "- $\\forall A \\subset R_{X}, p(X \\in A)=\\sum_{x_a \\in A}p_{X}(x_a)$\n",
    "\n",
    "A very simple example of discrete distribution is the `Bernoulli` distribution. With this distribution, _we can model a coin flip_, if it has equal probability. More formally, a Bernoulli distribution is defined as\n",
    "\n",
    "$$ \n",
    "Bernoulli(x)= p^x (1-p)^{(1-x)} \n",
    "$$\n",
    "\n",
    "with $p$ controlling the probability of the two classes. Hence, a fair coin should have $p=0.5$, and if we throw the coin a very large number of times, we hope to see on average an equal amount of _heads_ and _tails_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0., 0., 0., 1., 1., 0., 0., 1., 0., 1.])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 48000x64000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bernoulli = distribution.Bernoulli(0.5)\n",
    "samples = bernoulli.sample((10000,))\n",
    "print(samples[:10])\n",
    "figure(640, 480)\n",
    "sns.displot(samples)\n",
    "plt.title(\"Samples from a Bernoulli (coin toss)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we can also _sample_ from the distribution to have individual values of a single throw. In that case, we obtain a series of separate events that _follow_ the distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coin is tossed on tails\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on tails\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on tails\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on tails\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n"
     ]
    }
   ],
   "source": [
    "vals = ['heads', 'tails']\n",
    "samples = bernoulli.sample((10, ))\n",
    "for s in samples:\n",
    "    print('Coin is tossed on ' + vals[int(s)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can mess up our probability to model an unfair (loaded) coin, as shown in the following example (where we use a cheated coin that should give us a lot more of _heads_ than _tails_) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 48000x64000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n",
      "Coin is tossed on heads\n"
     ]
    }
   ],
   "source": [
    "bernoulli = distribution.Bernoulli(0.2)\n",
    "samples = bernoulli.sample((10000,))\n",
    "figure(640, 480); sns.displot(samples)\n",
    "plt.title(\"Samples from an unfair coin\"); plt.show()\n",
    "vals = ['heads', 'tails']\n",
    "samples = bernoulli.sample((10, ))\n",
    "for s in samples:\n",
    "    print('Coin is tossed on ' + vals[int(s)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Poisson distribution\n",
    "\n",
    "Let's introduce one of the (many) useful probability mass functions. We say $Z$ is *Poisson*-distributed if:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "P\\left(Z = k\\right) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k \\in \\mathbb{N^{+}} \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$\\lambda \\in \\mathbb{R}$ is a parameter of the distribution that controls its shape (usually termed the *intensity* of the Poisson distribution). By increasing $\\lambda$, we add more probability to larger values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. If a random variable $Z$ has a Poisson mass distribution, we denote it by\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "Z \\sim \\text{Poi}(\\lambda) \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n",
    "\n",
    "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n",
    "\n",
    "We will plot the probability mass distribution for different $\\lambda$ values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continuous distributions\n",
    "\n",
    "The same ideas apply to _continuous_ random variables, which can model for instance the height of human beings. If we try to guess the height of someone that we do not know, there is a higher probability that this person will be around 1m70, instead of 20cm or 3m. For the rest of this course, we will use the shorthand notation $p(\\mathbf{x})$ for the distribution $p(\\mathbf{x}=x_{i})$,  which expresses for a real-valued random variable $\\mathbf{x}$, evaluated at $x_{i}$, the probability that $\\mathbf{x}$ takes the value $x_i$.\n",
    "\n",
    "One notorious example of such distributions is the Gaussian (or Normal) distribution, which is defined as \n",
    "\\begin{equation}\n",
    "    p(x)=\\mathcal{N}(\\mu,\\sigma)=\\frac{1}{\\sqrt{2\\pi\\sigma^{2}}}e^{-\\frac{(x-\\mu)^{2}}{2\\sigma^{2}}}\n",
    "\\end{equation}\n",
    "\n",
    "Similarly as before, we can observe the behavior of this distribution with the following code (in our height example)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(128.5206)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 48000x64000 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wEGPGjNFZx9BtVhvV+gSAV199FU2aNKlQR6lUol27dtJJfVURGxuLwMBABAYGIiYmRmc91WuorP/r1q3TOS0xMRFA2clc6pdUjh49GgBw7949bNiwQWf7TZs26VyH169fl17Hpk2bdM7D0HURGRmp9fnu3bujZcuWAMreo4WFhVrrKZVKvZ8PxhJCYOrUqdJyly5davDJmtX9vvvtt98MumKmpt6f1b3Oq6LODNuVnZ2NxYsXY/HixfDw8EBISAiCgoLw5JNPonPnzhoDL7Rr1w5RUVGYNm1ahY3/n3/+qTBvNzc3tG7dGj4+Pmjfvj1mzJhhUJ+0zQsASkpKpMeZmZmVzkffWZbHjh3T2/bo0aNo06YNGjRogBYtWuDatWt663fv3l3qo7+/P/z9/XXWVSqVAMo+KNu1a4czZ84AKPtQmj17NurXr4+9e/di37592LlzJ2JiYrR++aopqjP8tXnyyScBlF0eqX6mvTaq1wUAHTt21FqnNta1LtrOPG/cuLG0zfr5+eHFF1+s8nxVDhw4gPT0dHh5eeHxxx9HUlIStmzZgr179+Lw4cO4ceOG0fMGgLy8PCQkJGg8Z2tri5YtW8LHxwetW7dGUFAQnn/++UrndevWLdy+fVvn9Pv370uP69evLz1Wfck8c+aMzrAEgOLiYvz1119aR2orLi6u8DoUCgW8vLyk19GpUye89tprlb4OQPt6Bcq+NKscOXJE7zxOnjxp0LKq6tKlS/jwww+xePFiuLi4YO3atRg8eHCl7ar7fafrb1ReTb0/q3udV0WdCXd1WVlZ2Lp1K7Zu3QoAsLe3R0hICJ5//nmMHz8eTk5OsLGxwapVq7Bnzx7p0jgVV1dXvPrqq+jbty+eeOIJNGzY0Kh+5ObmVlpHfeOqKqVSKV0Op4v6B6+rq2ul4a76Bl6vXj3s37/f4L6oXxoYGhoKd3d3jB8/HkDZt27VN+9bt27h4MGD+PXXX7Ft2za9H6Sm0ve39fLyAlD2hs7Ly9M7n+vXr0uPte21AjW/rivj6OiIGTNm4JlnnkFQUBBcXV2rbd6FhYUYOHAgtm3bBl9fXzRq1AgvvfQSXnrpJQDAxYsXsWfPHmzZssWkMOnWrRsmTpyI3r17o127dkZ90alsXWrTqFEj6chTWlpapfXVtwdtOnTogGnTpqF3794IDAys9NI7XXRtL6q9dqDy/lbWV1MsW7YMo0aNQufOnTFo0CCMGzdO794rUP3vO0PfUzX9/qyudV4VdTLcyysqKsL+/fuxf/9+LFmyBDExMWjVqhUaNGiAUaNGYfXq1VLd4cOH46uvvkLTpk015nHz5k1cunQJJ06cQEpKSqWHlICyb6c1yZDDUcXFxVof62LsFxn1IyNFRUWYMGEC/ve//2Hy5MkYOHCgNB5BkyZNMHr0aIwePRpZWVkYP348Dh48aNQyTeHs7AxA85CzLupvVF13Fazpda3PU089hY0bN6J169Yaz+fk5ODvv//G6dOn8eeff1b6wavPuXPnEBAQgNGjR+P5559Hr169pEAMCAhAQEAA3nrrLezduxdjxoypMEqkPra2tli9ejVeeukljUOWSqUSqamp+Ouvv3Do0CH07NkTo0aN0jsvY9aD+iFTQ75s6guB8PDwCtfSl5aWIiMjA+fOncORI0fQqlUrk/bkqtLfmvxCWVpaihdffBGnT5+GnZ0d/ve//2Hv3r0ah7rLq+73naFq8v1ZG+tcG1n/5h4aGoq4uDjExcUZfEOD5ORkLFu2TPq/+mHnDh064KeffkLTpk1RWFiIpUuXIigoCM7OznB3d0fPnj0xb948XLhwodpfizFU46vro74Hp+9wpYrqN6fMzEwoFAqDS1RUVIV5nTlzBrNmzYKvry9atmyJcePG4dtvv5WONnh4eGDbtm0VvkjVBtXhWdWHjT7qvyeqnwthCdzc3PDbb7+hdevWKC0txZo1a9CrVy+4urrC1dUVQUFBeOONN3D8+HGTl1VcXIwffvgBw4YNg6urK7p06SIFuipEnnnmGaxZs6ZK8124cCFefvll2NjY4NKlS5g+fTr8/f3h4OAAX19fjBw5Ep9//rnO30NNpT5fQ4546Kozffp0hIWFwc7ODmlpaXjjjTfw8MMPw9HREa1atcLgwYOxbNkyk3/GqEp/q/MIjjbnzp3D0qVLAZQN6f3pp5/qrS+X951Kba1zbWQd7vb29njsscfw2GOP6fxNRpt///1X6/MvvfSS9O1r8uTJCA0NxYkTJzR+pwOM37utbk5OTjoPV6moRoK7f/9+pYfwAUiH7d3c3Kr10FJaWho2b96M6dOno0WLFtKJbo0aNcKQIUOqbTmGSk1NBVD2BUPXaIMqjz76qPT43LlzNdqvqho3bhwaN24MAHj33Xfx2muvISYmpsKec3Vvsw8ePMDZs2excuVKPPvsswgMDERGRgYAYOTIkQbfXEShUOCVV14BUPaFMigoCN9++y0uX75cYW+rpt53qlEdgbKRKSuja3RF1Z5ZQUEBnnrqKXz++ee4cOGCdG6KiqmvIzk5WXpcWX+NGQmyqhYtWiSdSzNu3Di9w3rL5X2nUlvrXBtZh/vRo0elx88995zB7Xx9faXH6r9Bt2/fHkDZB9cvv/yis33Xrl2r0s0a9cwzz+ic5u7uLp3AcvToUYMObalO0Klfvz5CQkL01t2wYQPu3LmDjIwM6Uz80aNHS0M+qpZdXnFxsfRtX9XP2qa+Jzts2DC9ddWHATbHTwj6qLZZANI5JtqYss3+/vvvEELg77//1lnnn3/+wZYtWwCUHU41dI+xadOm0hfUffv26fypSaFQ1OhtmlWfJf7+/ggICNBZ74knnkDz5s21TlOti9OnTyMlJUXnPEz9/FA/iW7kyJF666oPc11TlEolpk6dKh29WbNmjcbVM+rk8r5Tqa11ro2swz06OhpJSUkAgKeffhoTJ06stE2TJk3w1ltvSf/fuXOn9Fj1m7SNjY104kd5bdu2xeuvv25Kt6vV/PnzdV7itnTpUumMYNUHb2XULyOaP3++znrdu3eX9hr3798vfXFQDwDVTX20UT/kVtlJfjVh06ZN0ofRu+++W2FcdJUOHTpIX6COHz+OS5cu1VofDaF+HoX6iVbq3NzcsGDBAqOXoVqnfn5+6NChg856qnWal5encZRI/Utl+T16Q/oPALNnz4aPj0/VOl4F6tv9okWLtNZRKBSIiIjQOQ/Va9F3WdjIkSMNui+DPvHx8YiLi5Pm16lTJ631evfuXaXx8E1x5swZfPzxxwDK1qPqqpvy5PK+U6mtda6NrMO9pKQEM2fOlDaWdevW4YsvvtB6+ZarqyumTp2KM2fOoG3btgCAr776SrruFdD8RvzNN99o7FE2atQIM2fOxIkTJ6TDoIBhvx3VpEceeQQ7d+7U+GBs2LAhPvvsM+nyp8uXL2tcM6pPfHw8Nm7cCKDsC9P69es1Dv3b2NhgzJgx+O2331CvXj3k5eXh/fffl6afP39eujTkrbfewuuvv65xyZFCocDAgQOl32Xv3Lkj3Ya3NqWmpkonUrZt2xa7d+9Gu3btNOoEBQUhKioK9evXx4MHD/D222/Xej8ro77NfvbZZxon1Tk6OmLChAk4e/asRjBWdZv96aefAJSt+19++aXC2ASNGzdGWFiYdPRsy5YtGoGufjXKhAkTMGLECOmoUE5OjnQOS+/evfHmm29qnFQXEBCA7777Dh9//LHGPKv7MKfqUk2gbG937dq1Gu/zhx56CJs3b0afPn0qHHJVUa2LNm3aYPny5Ro/a7Vu3RorVqzAjz/+qPE6jP38eOedd/DgwQPY2tpi586dePrppzWmDxo0CD///LPOvtaEsLAwvUd3APm871Rqc51rU6VRiayxjBs3ThoVTSUzM1PExcWJkydPiqSkpAo3MVm3bl2FEYsaNmworly5ItUpKCgQcXFx4tKlS6KwsFAIUTae8rBhw6QxiW/fvi3Onj0rjWykPkLdoEGDtPZXfRhMfaPAqZQfflF9dLn9+/cLIcpuxPL333+L06dPS2NgCyFEdna26NChQ4V56xt+tkGDBuLIkSPS9OLiYnHu3Dlx6tQpjfG5CwoKxLBhwyq079mzp8bNN/Ly8kRcXJw4ffq0xvCdpaWlRt3IxNAR6srfnKR8sbe317hXgBBCJCYmipMnT2qMfS2EELNnz9b6OlV0DaPZrFkzqU75kQbVy9WrV4UQQly6dKlKfwsbGxtpuF/Vujp//rw4f/689J4oKSkR06dPF4mJidL6OH36tNbtQldRjQ6nkp6eLk6ePCkSEhKk94bqb960adMK7dXH1y6/boYMGaLx/rx+/bo4ffq0NNysEELExsaKN998U/r/P//8Iz799NMqr3P17b5Zs2Ya07y8vMS///4rTS8qKhLnzp0TZ8+elV7jyZMnpXmUH62sc+fOGkNh3759W5w+fVpcuXJFen3Jycli4sSJUp1r166JLVu2GLxtqxf1IYXV14lq2y0tLRUzZ86UplfXCHX6Svfu3aX7HKhU9/tOvV/6Pj9r4/1Z2+u8XKnaB6e1lnbt2omNGzdqfNCUV1BQIHbs2KF3I/fx8dF6d6rS0lKxa9cu6aYE5cdtVg2BWNvh7uTkJCIjIyu8oYQoG460ffv2Wudd2V3h7OzsxNKlSzVurKDu8OHDeu/C169fP713lUtMTNT596msVFe4q15nRESEztf577//6hzf2xLCHSgbqlh9uE91x44dk8ZJnzdvnsa0Rx991OBl2NraiiVLlmh8cVRXWloqtm/fLjw9PbW279Klizhx4oQoKCgQeXl5Yu/evRrTx48fL43Rre7OnTviww8/FPb29qJRo0Yad0Dcvn17lde5vnAHym52oz7sqfrr27Rpk2jUqJH03tc2VHC/fv1ERkZGhfZ5eXli9erVwsXFRdjY2Gjc9yEuLs7gbbt8mTRpksYXZpWMjAwxZMgQje2vNsIdgFi5cqVGX6r7fWdJ4W6Oda4qiv97UGc0aNAATzzxBNq1aycdVrtz5w7++ecfnD17tsKZ77o89dRT6Nq1K+rXr4/09HQcOXJEOtMTKLs2d+zYsfD29sa1a9ewefPmWrvWed26dZgyZQoASPcY9vHxQc+ePeHh4YG7d+/i+PHj+Ouvv0xelouLC55++mn4+Pigfv36yMzMxOHDhw0eGapz587o1KkT3NzcoFAocOvWLcTFxeHs2bNah901F2dnZ/Tp0wdt2rSBnZ0dbt68idjYWMTHx5u7awbr1KkTnnrqKTRs2BAZGRk4ceIELl++rFFn+PDhCAgIQFZWFn788UeDrjdW5+zsjO7du6Ndu3ZwdnZGUVERUlNTcfz4cYMGgKls3v3790ebNm2Ql5eHK1eu4MCBAxrDhnp5eeH5559HvXr1EB0djdOnT5u0TF3at2+Pnj17onHjxsjKysKhQ4f0njClzt7eHs888wzat28PpVKJ5ORkHDhwoMIlbOPHj0fDhg1x6tQpk04Yc3BwwLPPPgs/Pz8UFxfj77//xoEDB0y+Nrw2yOF9B9T+OgeAOhfudYG2cCciorpD1ifUERER1UUMdyIiIplhuBMREckMw52IiEhmeEIdERGRzHDPvRaZe7Q6IiKqGxjutcTZ2Rm5ubkMeCIiqnEMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZEb24e7g4IAFCxbg4sWLKCgoQGZmJvbs2YPBgwfXSDsiIiJLIKyh9O3bVyiVSr3l6tWrGm2cnZ3FqVOnhC7Lly/Xuixj2+krzs7OQgghnJ2dzf63ZGFhYWGRfTF7BwwqL7/8ss6wVUlNTdVo8+233wohhMjNzRXjxo0TTk5OwtXVVcydO1eUlJQIIYR4/vnnKyzL2Hb6CsOdhYWFhaUWi9k7YFBZvny5EEKIKVOmGFS/bdu2UhA/99xzFaZ/9NFHQgghrly5IhQKhcntKisMdxYWFhaWWixm74BB5ZdffhFCCNG9e3eD6oeFhQkhhLh8+bLW6a1bt5b2+Hv06GFyu8oKw53FEkt4xBKxav13GiU8YonZ+8XCwmJasZoT6nx9fQEAiYmJBtUPCQkBAPz2229apycnJyM5ORkA0Lt3b5PbEVkjN08PJJTmaxQ3Tw9zd4uITGQ14d6mTRvk5OTg5s2blda1sbFBt27dAACxsbE66124cAEAEBAQYFI7IiIiS2IV4e7u7g5nZ2ckJiZi3LhxiImJwa1bt3D37l2cPXsW8+bNg5OTk0b9hg0bAgBSUlJ0zjctLQ0A4O3tbVI7IiIiS1LP3B0wRJs2bQAAnTt3xg8//KAxrXPnzujcuTMmT56MAQMG4Nq1a2jcuLE0PTs7W+d8c3JyAADOzs4AYHQ7bezs7GBvby/9X19dotoQHrGkwiH3tv7tkHAx3jwdIqIaYxV77qrf221tbbFlyxZ06tQJDg4OaN68OebPn4+ioiJ06NABv//+O+zs7DRCurCwUOd8i4uLAUAKYWPbaRMaGorc3FyppKenV/o6iWqStt/X7fRsw0Rkvawi3AEgOjoaixcvxpgxYxAfH4+ioiJkZmZi2bJlGD16NACgY8eOmDp1KhQKhUHztLOzAwAUFRUBgNHttImIiICLi4tUvLy8DJo3ERGRqazisPwPP/xQ4XC8uqioKBw/fhzdu3fH0KFDcfz4cWmao6OjznYODg4AgNzcXABAXl6eUe20KS4ulvbwiYiIapPV7LlX5sSJEwCA1q1bIyMjQ3re3d1dZxsPj7LfH1NTUwHA6HZERESWRDbhrqJUKpGdnY07d+4AAPz8/HTW9fHxAQAkJCQAgNHtiIiILInFh7ubmxuioqIQFRWl99Kz9u3bAwCSkpIAAMeOHQMABAcHa63v4OCAxx57DABw9OhR6Xlj2xEREVkKiw/327dvo1evXhg8eDCGDBmitY6Pjw/69esHAPjjjz8AANu3bwcAjBgxAo0aNarQ5oUXXoC9vT1u3LiB6Oho6Xlj2xEREVkKiw/3Bw8e4OeffwYAhIWFoWPHjhrTHR0dsXbtWtSvXx/Xr1/Hxo0bAQCbNm1CRkYGGjZsiNWrV2ucCe/n54dly5YBAJYtW4bS0lJpmrHtiIiILIUCZYPMWzQvLy+cPn0anp6eKCwsRFRUFP7++2+4urpi2LBhaNmyJUpKSjBq1Cjs3LlTajd48GDs2LEDNjY2iIuLwx9//AE3NzeMGTMGzs7OOH36NJ566ikolUqN5RnbTh9nZ2fk5ubCxcUF9+7dq7a/DZGhVq3/Dgml+RrPje7UDVvjTmo819HWCa9PmVqbXSOiamYV4Q6UjVL3zTffaL1ZS0pKCmbOnKn1Zi+jR4/Gl19+CVdXV43nd+3ahXHjxuHu3btal2dsO10Y7mRuDHeiusMqrnMHgCtXrqBPnz54+OGHERwcDFdXV+Tk5ODcuXP4888/dR4i37p1K37//XcMHDgQPj4+yMnJwalTp/DXX3/pXZ6x7YiIiMzNasJd5fz58zh//nyV2uTn50u/29dGOyIiInOy+BPqiIiIqGoY7kRERDLDcCciIpIZhjsREZHMMNyJiIhkhuFOREQkMwx3IiIimWG4ExERyQzDnYiISGYY7kRERDLDcCciIpIZhjsREZHMMNyJiIhkhuFOREQkM1Z3y1cisn7hEUvg5umh8Vx2ZhbCQ981U4+I5IXhTkS1zs3TAwml+RrPdSwX9kRkPIY7EWlo7++PVeu/03iOe9VE1oXhTkQabOztDNqr5qF1IsvFcCeSIW3B29a/HRIuxlfbMnhonchyMdyJZEhb8AbY29f4cnlIn8gyMNyJqNoYekifiGoWr3MnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzHD4WSKqUdrGm6/um9gQkSaGOxHVKG3jzdfGTWyI6jIeliciIpIZhjsREZHMMNyJiIhkhuFOREQkMwx3IiIimWG4ExERyQzDnYiISGYY7kRERDLDQWyIrFh4xBK4eXpUeL66R4DjKHNE1oXhTmTF3Dw9Koz+BlT/CHAcZY7IuvCwPBERkcww3ImIiGSG4U5ERCQzDHciIiKZYbgTERHJDMOdiIhIZhjuREREMsNwJyIikhmGOxERkcww3ImIiGSG4U5ERCQzDHciIiKZYbgTERHJDMOdiIhIZqw+3KOioiCEwIcffqh1euPGjbFixQokJSWhsLAQaWlp2LZtG4KDg/XO19h2RERE5mbV4f7cc89h8ODBOqc3b94cZ86cwdtvv402bdrA3t4eXl5eGDFiBKKjozFr1qxqbUdERGQJrDbcXVxc8Omnn+qtExkZCV9fX2RmZmLgwIFwcHCAp6cnPv74Y9ja2mLlypV48sknq60dERGRJbDacI+IiEDz5s11Tu/Tpw/69OmDBw8eYPjw4di9ezeKioqQlZWFOXPm4Oeff4atrS2WLVtWLe2IiIgshVWGe7du3fDKK68gMTERJ06c0Fpn4sSJAICDBw/i1KlTFaavXr0aANCjRw94e3ub3I6IiMhSWF2429ra4quvvoKNjQ1mzpyJwsJCrfVCQkIAlJ1wp82xY8dQXFwMAOjVq5fJ7YiIiCyF1YX7nDlz8Mgjj+Cnn37Cvn37tNZp1qwZfH19AQCxsbFa6yiVSly+fBkAEBAQYFI7IiIiS1LP3B2oCh8fH7z//vu4e/cu/vOf/+itp5KSkqKzXlpaGgIDA6XD68a208bOzg729vbS/52dnXXWJSKgvb8/Vq3/rsLz2ZlZCA991ww9IrJeVhXuX3zxBZycnDBr1ixkZWXprNe4cWPpcXZ2ts56OTk5AP5/8BrbTpvQ0FCEh4frnE5Emmzs7ZBQml/h+Y6eHmboDZF1s5rD8mPHjkX//v1x5swZ6aQ2XdRDWtdv8gCk385Ve9jGttMmIiICLi4uUvHy8tLbZyIioupiFXvujRs3xsqVK1FaWopXXnkFQgi99RUKhUHztbOzAwAUFRWZ1E6b4uJi6UsAERFRbbKKPfdly5bBw8MDa9aswdmzZyutn5eXJz12dHTUWc/BwQEAkJuba1I7IiIiS2Lx4d61a1dMnz4dmZmZeO+99wxqk5GRIT12d3fXWc/Do+y3vNTUVJPaERERWRKLD/eAgADY2NjA09MTd+/ehRBCo6iuNV+wYIH0XGJiotTez89P57xbt24NAEhISAAAo9sRERFZEosP9wcPHqCkpERn0VZPCIELFy4AgM67uPn4+Eh74EePHgUA3L1716h2RERElsTiwz0yMhL169fXWaKjowEAS5YskZ7Lzc3F9u3bAQCTJk2CjU3FlzllyhQAQFxcHJKSkqTnjW1HRERkKSw+3I21du1a5OXlwdvbG4sXL9aYFhQUhLlz5wIAFi1aVC3tiIiILIVVXApnjIyMDMybNw+rVq3C/Pnz0b17dxw9ehTe3t547rnnYG9vjx07dmDbtm3V0o6IiMhSyDbcgbI7uNna2iIiIgI9evRAjx49AAClpaXYsGEDZsyYUa3tiIiILIHVh3vv3r31Tv/ss88QGRmJAQMGoEWLFrhx4waOHTumcWZ8dbYjIiIyN6sPd0PcuXMHmzZtqrV2RERE5iTbE+qIiIjqKoY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREclMPXN3gIgMEx6xBG6eHhrPtfVvh4SL8ebpEBFZLIY7kZVw8/RAQmm+xnMB9vZm6g0RWTIeliciIpIZhjsREZHMMNyJiIhkhuFOREQkMzyhjogsWnt/f6xa/53Gc9mZWQgPfddMPSKyfAx3IrJoNvZ2Fa4S6FjukkAi0sTD8kRERDLDcCciIpIZhjsREZHMMNyJiIhkhuFOREQkMwx3IiIimWG4ExERyQzDnYiISGYY7kRERDLDcCciIpIZhjsREZHMMNyJiIhkhjeOITKz8IglcCt3IxTe9YyITMFwJzIzN08P3vWMiKoVD8sTERHJDMOdiIhIZhjuREREMsNwJyIikhmGOxERkcww3ImIiGSG4U5ERCQzDHciIiKZYbgTERHJDMOdiIhIZhjuREREMsOx5YksUHt/f6xa/53Gc2392yHhYrx5OkREVsWq9twDAwPx/fffIzk5GYWFhbh58yb27duH8ePH62zTuHFjrFixAklJSSgsLERaWhq2bduG4OBgvcsyth1RdbCxt0NCab5GsbO3N3e3iMhKWM2ee//+/fHLL7/AyclJes7e3h5PP/00nn76aYwYMQLPP/88Hjx4IE1v3rw5Dh8+DF9fX+k5Ly8vjBgxAkOHDsXs2bPx+eefV1iWse2IiIgsgVXsubu6umLDhg1wcnLC8ePH0a1bN9jZ2cHHxwdff/01AGDUqFF44403NNpFRkbC19cXmZmZGDhwIBwcHODp6YmPP/4Ytra2WLlyJZ588skKyzO2HRERkSWwinCfMGEC3N3dkZ6ejmeffRanTp2CUqlEcnIyZsyYgW3btgEAXn75ZalNnz590KdPHzx48ADDhw/H7t27UVRUhKysLMyZMwc///wzbG1tsWzZMo1lGduOiIjIUlhFuA8fPhwAsHnzZty/f7/C9G+++QYA0L59ezRo0AAAMHHiRADAwYMHcerUqQptVq9eDQDo0aMHvL29peeNbUdEtUd1wqF6CY9YYu5uEVkMk8K9ZcuWaNGiRZXqu7u7V3k5fn5+AIDY2Fit069duyY9dnZ2BgCEhIQAAKKiorS2OXbsGIqLiwEAvXr1kp43th0R1R5tJxy6eXqYu1tEFsOkcE9OTsa///5rcP0rV67oDGh9Ll68iOjoaCQlJWmd7unpCQBQKpW4ceMGmjVrJp0Mp2t5SqUSly9fBgAEBAQAgNHtiIiILEmVz5ZXKBRa/1/++fKCgoJgY2ODJk2aVHWR6N+/v97pEyZMAAD8+eefePDgAXx8fKRpKSkpOtulpaUhMDBQOrxubDsiIiJLUqVwf//99/H+++9L/xdCwNbWFiUlJQa1F0IgOTm5Sh3UxtbWFgDg7e2N119/HVOmTEFJSQnCwsIAlF2jrpKdna1zPjk5OQD+/6F8Y9tpY2dnB3u165L11SUiIqpOJu+5V0Vubi7eeecdo9urrF27FtOnT5f+X1paiokTJyI6OhqAZkgXFhbqnI/qt3NVCBvbTpvQ0FCEh4frnE5ERFRTqhTu69evlwJUoVDg4MGDKC0txdNPP11p29zcXPzzzz8oKCgwqqPqSktL8eDBA9jYlJ0yYGtrizVr1qCoqAjbt283+AuInZ0dAKCoqAiA4V9cyrfTJiIiAp988on0f2dnZ6Snpxs0fyIiIlNUKdxTUlIq/BYthMDhw4ertVOVeeWVVzBz5kx4enqib9++CA0Nhb+/P3788UcEBAQgLy9Pquvo6Kjxf3UODg4Ayr54ADC6nTbFxcXSHj4REVFtMulseVtbW72HpmtSaWkp0tLSsGHDBoSEhCA3Nxd2dnZ4+eWXkZGRIdXTd+mdh0fZpTOpqakAYHQ7IiIiS1JtY8srFAo89NBDcHZ2rvTw9tWrVw2eb5s2bdCpUycolUrs3LlTa52bN28iJiYGQ4YMQfv27ZGYmChN8/Pz07m81q1bAwASEhIAwOh2RERElsTkcO/Zsyf++9//Ijg4GPXqVT47IQTq169v8PyDg4OxYcMGAEDDhg11HipXPV9aWoq7d+/iwoULCAwMRHBwMPbu3Vuhvo+Pj7QHfvToUQAwuh0REZElMemwfO/evbFv3z706tUL9evXh0KhqLSoToIz1Llz56THPXr00FqnXr166N69u0b97du3AwAmTZqkdZlTpkwBAMTFxWkMjmNsOyIiIkthUri/9957sLW1xfXr1zFz5kx06tQJPj4+lZaqiI+Px4ULFwAAixcv1rhcDSg78W3NmjVo1aoVlEolIiMjAZRdLpeXlwdvb28sXrxYo01QUBDmzp0LAFi0aJHGNGPbERERWQqTDst37twZQgiMGjUKJ06cqK4+VTBr1izs27cPnTp1wuXLl7Fjxw5kZGSgRYsWeOaZZ6Tx7d977z1pONyMjAzMmzcPq1atwvz589G9e3ccPXoU3t7eeO6552Bvb48dO3ZId5RTMbYdERGRpTAp3FW/sddksANAdHQ0Ro4ciTVr1sDLy0tjABsAyMzMRGhoqPTbvMrq1atha2uLiIgI9OjRQzqsX1paig0bNmDGjBlal2dsOyIiIktgUrhfvHgRXbp0QZMmTXDr1q3q6pNWUVFR+OOPPxAcHIyOHTvC2dkZubm5uHDhAo4dOwalUqm13WeffYbIyEgMGDAALVq0wI0bN3Ds2DGNM+Orsx0REZG5mRTuX331Fbp27Yo333xTY8z5mlJcXIyDBw/i4MGDVWp3584dbNq0qcrLM7YdERGROZkU7t999x369++Pd999FyUlJVi2bJneIVmJiIio5pkU7j/88AOEEHjw4AHef/99zJkzB0lJSbh//z4ePHigtY0QAr169TJlsURERKSHSeE+duxYCCGkEekaNGiARx55RG8bIYQpiyQiIqJKmBTuCxcurK5+EBERUTUxKdw/+OCD6uoHERERVROTRqgjIiIiy8NwJyIikhmTDsuXlJRUuU1V7wpHRGSI9v7+WLX+O43nsjOzEB76rpl6RGQ+JoV7Zfdtr642RESVsbG3Q0JpvsZzHT09zNQbIvMyKdz79eunc5qLiwvc3d0RHByMUaNGQalU4o033uA90ImIiGqYSeFuyDCwX331FRYsWIC9e/di9erVeOKJJ0xZJBEREVWiVk6oS0lJwezZs+Hk5MTL54iIiGpYrZ0t/+effwIAevfuXVuLJCIiqpNqLdxdXV0BAI6OjrW1SCIiojqpVsLd0dERH330EQDg6tWrtbFIIiKiOsukE+piYmIqrePo6IgOHTrA0dERQgh8//33piySyKqFRyyBW7nLs9r6t0PCxXjzdIiIZMmkcA8ODq5S/Q0bNkh78ER1kZunR4VrsQPs7c3UGyKSqxq/K1xxcTGuX7+O6OhoHpInIiKqBbwrHBERkczwxjFEREQyUy3hbmtri8mTJ+O3335DRkYGCgsLkZ+fj5SUFERFReHll19Gw4YNq2NRREREVAmTDssDgJeXF3bs2IHHHnuswk1hvLy84OXlhQEDBiA8PBwzZ87Etm3bTF0kERER6WFSuNvb22P37t3o2LEj8vLy8MsvvyA6OhrXr19HvXr14Onpie7du2PYsGFwd3fHTz/9hDFjxjDgiYiIapBJ4f7666+jY8eOuHLlCvr27YuUlJQKdb7++mvY2dnho48+wuuvv47PP/8cO3fuNOpe8ERERFQ5k35zHzt2LIQQmDVrltZgVykuLsabb76JuLg4NGvWDL169TJlsURERKSHSeHu7+8PAIiOjjao/v79+wEA7du3N2WxREREpIdJ4f7gwQONfytTWloKgDePISIiqkkmhXtiYiIAoG/fvgbVVw1Xm56ebspiiYiISA+Twv2nn36CQqHA6tWr4efnp7fua6+9huDgYCiVSuzdu9eUxRIREZEeJp0t/9lnn2HSpEno2LEjzp8/j99//x2//PILkpOTcfv2bTRr1gwdOnTA1KlT0blzZwgh8PHHHyM7O7u6+k9ERETlmBTuxcXF6Nu3L7Zt2yZdzz5s2LAK9VSD26xZswYLFiwwZZFERERUCZOHn7158yZCQkLwwgsvYM+ePcjNzYVCoZDK7du3sXXrVvTq1Quvv/56dfSZiIiI9DB5+FmVLVu2YMuWLQCARo0aoUGDBrh//z5yc3OraxFERFXS3t8fq9Z/p/FcdmYWwkPfNVOPiGqHUXvuI0eOxLZt2zB16lSt0319fREbG4tvv/0WQ4cONamDRETGsrG3Q0JpvkZx8/Qwd7eIalyV9txdXV2lQ+wA8Oeff+qs27RpU4wYMQIjRozAiRMnMG7cOL2j2BHJTXjEkgpB0ta/HRIuxpunQ0RUZxi85+7k5ISYmBj06tULCoUC//zzD86cOaO1blJSEhYtWoT4+HgoFAoEBQXh+PHjaNWqVbV1nMjSuXl6VNhrtLO3N3e3iKgOMDjclyxZgo4dO6KgoAATJkxAx44dcejQIa117969i7CwMHTp0gXPPPMMUlNT4enpybvBERER1QKDwr1hw4aYPn06hBAYNWoUNm/ebPACDhw4gKCgIFy/fh2PPfYYnn/+eaM7S0RERJUzKNyfeuopODo64syZM0aNLpeZmYnw8HAoFAqGOxERUQ0zKNx9fX0BAMePHzd6QTt37gQAdOnSxeh5EBERUeUMCncXFxcAQE5OjtELysrKAlB2Fj0RERHVHIPC/datWwCAZs2aGb0gV1dXAGVD1hIREVHNMSjck5KSAABPP/200QsKCQkBACQnJxs9DyIiIqqcQeF++PBh5ObmwtfXFxMmTDBqQXPnzoUQAvv37zeqPRERERnGoHAvKSnBF198AYVCgTVr1qBv375VWsiaNWvQvXt3lJaWYvXq1UZ1lIiIiAxj8CA2H374IS5evAgnJyfs2bMHX375JTp16qSzfv369TFq1CjEx8fjpZdeghACCxcu5GF5IiKiGmbw2PKFhYXo06cP9u3bh4cffhjTpk3DtGnTcOfOHZw/fx7Z2dnIz8+Hk5MTWrRogUceeQQODg7SvdyXL1+OJUuW1NgLISIiojJVunHMzZs30bVrV4SFhWHWrFlo2LAhHnroIfTs2RNCCKmeKtAB4Pz583j//fel69yJiIioZlX5fu5KpRILFixAREQERo4ciZCQEHTo0AGurq6wsbHBnTt3cPPmTZw6dQrR0dEmDXxDREREVVflcFfJy8tDZGQkIiMjq7M/REREZCKDT6gjIiIi68BwJyIikhmGOxERkcww3ImIiGSG4U5ERCQzDHciIiKZYbgTERHJjNWFu7OzMxYsWIDY2FjcuXMH+fn5SExMxBdffAFvb2+tbRo3bowVK1YgKSkJhYWFSEtLw7Zt2xAcHKx3Wca2IyIiMiejB7Exh1atWmH//v3w8/PTeL5t27Zo27Ytxo8fj/79++PPP/+UpjVv3hyHDx+Gr6+v9JyXlxdGjBiBoUOHYvbs2fj8888rLMvYdkREROZmVXvuGzduhJ+fH7KzszFu3Di4uLjAxcUFgwYNwpUrV+Di4oKffvoJDRo0kNpERkbC19cXmZmZGDhwIBwcHODp6YmPP/4Ytra2WLlyJZ588skKyzK2HRERkblZTbg//vjjCAkJAQCMHDkSmzdvxr1793Dv3j3s2rUL/fr1Q2FhIVq2bIlp06YBAPr06YM+ffrgwYMHGD58OHbv3o2ioiJkZWVhzpw5+Pnnn2Fra4tly5ZpLMvYdkRERJbAasJ92LBhAIC4uDgcOXKkwvQrV67g999/BwAMHDgQADBx4kQAwMGDB3Hq1KkKbVavXg0A6NGjh8bv9ca2IyIisgRW85t769atAQBnzpzRWefff/8FAClwVXv6UVFRWusfO3YMxcXFsLOzQ69evbBhwwaT2lHdFR6xBG6eHhrPtfVvh4SL8ebpEBHVaVYT7qmpqdi/f7/WPWmVZs2aAQAKCgrQrFkz6WS42NhYrfWVSiUuX76MwMBABAQESPMwph3VbW6eHkgozdd4LsDe3ky9IX3a+/tj1frvNJ7LzsxCeOi7ZuoRUfWzmnB/77339E738PDAyJEjAZSFso+PjzQtJSVFZ7u0tDQEBgZKe/vGtivPzs4O9mof7s7Oznr7T0S1w8bersIXsY7ljroQWTur+c1dn6ZNmyIqKgouLi4AgK+//hqNGzeWpmdnZ+tsm5OTA+D/h6+x7coLDQ1Fbm6uVNLT0w14JURERKaz+nAfMGAA4uPj0aVLFwDAJ598gpMnT2qEdGFhoc72xcXFACDtZRvbrryIiAjpUj0XFxd4eXkZ9HqIiIhMZTWH5ctzc3PDypUrMWHCBOm55cuXY968eQAAhUJh0Hzs7OwAAEVFRSa1K6+4uFj6AkBERFSbrHLPfezYsbh06ZIU7NeuXcOzzz4rBTsA5OXlSY8dHR11zsvBwQEAkJuba1I7IiIiS2FVe+4KhQKrVq3Ca6+9BqDsrPVPP/0UYWFhyM/XPEEmIyNDeuzu7o6rV69qnaeHR9mJNKmpqSa1o7qDl70RkaWzqnD/6KOPpGA/d+4cJk2ahL/++ktr3cTEROmxn5+fzpBWXT+fkJBgUjuqO3jZGxFZOqs5LN+pUyfMnj0bQNnIcUFBQTqDHQDu3r2LCxcuAIDOu7j5+PhIe+BHjx41qR0REZGlsJpwnzRpEmxsbJCeno7Ro0dXOAyvzfbt2zXaljdlyhQAZUPaJiUlmdyOiIjIElhNuA8aNAgAsGbNGty+fdugNmvXrkVeXh68vb2xePFijWlBQUGYO3cuAGDRokXV0o6IiMgSWEW4KxQKaeS4hQsXQqlU6i2q380zMjKkM+jnz5+PmJgYLF68GBs3bsShQ4fg6OiIHTt2YNu2bRrLM7YdERGRJbCKE+qaNGmCevXKumpra1tpfVVdoOwObra2toiIiECPHj3Qo0cPAEBpaSk2bNiAGTNmaJ2Hse2IiIjMzSrCPTs72+DBZbT57LPPEBkZiQEDBqBFixa4ceMGjh07pnFmfHW2IyLrwpvJkNxYRbhXhzt37mDTpk211o6IrAdvJkNyYxW/uRMREZHhGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDP1zN0BIksWHrEEbp4eGs+19W+HhIvx5ukQmZW27SE7Mwvhoe+aqUdE2jHcifRw8/RAQmm+xnMB9vZm6g2Zm7btoWO5sCeyBDwsT0REJDPccyf6PzwET0RywXAn+j88BE9EcsHD8kRERDLDcCciIpIZHpYnItKivb8/Vq3/TuM5noNB1oLhTkSkhY29Hc/BIKvFw/JEREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmGO5EREQyI/twb9y4MVasWIGkpCQUFhYiLS0N27ZtQ3BwcI20IyIiMjerDXcXFxcUFxfjyJEjOus0b94cZ86cwdtvv402bdrA3t4eXl5eGDFiBKKjozFr1qxqbUdERGQJrDbcx48fj/r16+utExkZCV9fX2RmZmLgwIFwcHCAp6cnPv74Y9ja2mLlypV48sknq60dERGRJbDKcO/Xrx8WLVqkt06fPn3Qp08fPHjwAMOHD8fu3btRVFSErKwszJkzBz///DNsbW2xbNmyamlHRERkKawm3CdMmIAdO3YgPT0de/fuxUMPPaS3/sSJEwEABw8exKlTpypMX716NQCgR48e8Pb2NrkdERGRpbCacO/bty+GDh2K5s2bG1Q/JCQEABAVFaV1+rFjx1BcXAwA6NWrl8ntiIiILIXVhHt4eDi6dOkila+++kpn3WbNmsHX1xcAEBsbq7WOUqnE5cuXAQABAQEmtSMiIrIk9czdAUNdu3YN165dk/6fkZGhs66Pj4/0OCUlRWe9tLQ0BAYGSofXjW1H1iU8YgncPD0qPN/Wvx0SLsbXfoeIiKqZ1YR7VTRu3Fh6nJ2drbNeTk4OAMDZ2dmkdtrY2dnB3t5e+r++ulS73Dw9kFCaX+H5ALX1RURkzazmsHxVqId0YWGhznqq385VIWxsO21CQ0ORm5srlfT0dEO6TkREZDJZhrtCoTConp2dHQCgqKjIpHbaREREwMXFRSpeXl4GzZuIiMhUsjwsn5eXJz12dHTU+L86BwcHAEBubq5J7bQpLi6W9vCJiIhqkyz33NVPtnN3d9dZz8Oj7KSq1NRUk9oRERFZElmGe2JiovTYz89PZ73WrVsDABISEkxqR0REZElkGe53797FhQsXAEDnXdx8fHykPfCjR4+a1I6IiMiSyDLcAWD79u0AgEmTJsHGpuLLnDJlCgAgLi4OSUlJJrcjIiKyFLIN97Vr1yIvLw/e3t5YvHixxrSgoCDMnTsXACrcgMbYdkRERJZClmfLA2Unx82bNw+rVq3C/Pnz0b17dxw9ehTe3t547rnnYG9vjx07dmDbtm3V0o4sk7bR6DgSHVWn9v7+WLX+uwrPZ2dmITz0XTP0iEjG4Q6U3cHN1tYWERER6NGjB3r06AEAKC0txYYNGzBjxoxqbUeWR9todByJjqqTjb2d1hEPO2oZ4piotlhtuC9cuBALFy6stN5nn32GyMhIDBgwAC1atMCNGzdw7NgxjTPjq7MdERGRuVltuFfFnTt3sGnTplprR0REZE51ItyJiGqbtt/i+Ts81RaGOxFRDdD2Wzx/h6faIttL4YiIiOoqhjsREZHMMNyJiIhkhr+5k2xwwBoiojIMd5INDlhDRFSGh+WJiIhkhuFOREQkMwx3IiIimWG4ExERyQzDnYiISGYY7kRERDLDcCciIpIZhjsREZHMMNyJiIhkhiPUERHVEt7jnWoLw52IqJbwHu9UW3hYnoiISGYY7kRERDLDcCciIpIZhjsREZHMMNyJiIhkhuFOREQkMwx3IiIimWG4ExERyQwHsSGLFx6xBG7lBvrgqF5ERLox3MniuXl6cFQvIqIq4GF5IiIimWG4ExERyQwPy5NV0nZ3rbb+7ZBwMd48HSIyEu8URzWB4U5WSdvdtQLs7c3UGyLj8U5xVBN4WJ6IiEhmGO5EREQyw3AnIiKSGYY7ERGRzDDciYiIZIZny5NF0TbULC9xIyKqGoY7WRRtQ83yEjcioqphuBMRWRgObEOmYrgTEVkYDmxDpuIJdURERDLDcCciIpIZhjsREZHM8Dd3IiIrwJPsqCoY7kREVoAn2VFV8LA8ERGRzDDciYiIZIbhTkREJDMMdyIiIplhuBMREckMw52IiEhmeCkcmQ1v70pkGm3Xvrdu2QrJqSkaz/F6+LqH4U5mw9u7EplG27XvAa6NkJDM6+HrOoY7VTtte+Ta9ia4l05EVDMY7lTttO6Ra9mb4F46EVHN4Al1REREMsNw18PBwQELFizAxYsXUVBQgMzMTOzZsweDBw82d9eIiIh04mF5HZydnXHgwAF07dpVes7DwwMeHh549tln8dFHH+Gdd94xYw+JiAzDO8rVPQx3Hf73v/+ha9euuHfvHl555RX8+uuvsLe3x/Tp0xEREYG5c+fizJkz2LJli7m7SkSkl7az6kf16snAlzGGuxZt27bF5MmTAQBTp07Fzz//DADIz8/HRx99BHd3d8yZMwdLly7F1q1bIYQwZ3fNiteqE1kn3kJW3hjuWowfPx62trZITEyUgl3d6tWrMWfOHPj4+CAkJASHDx82Qy+rh7Zw1vbtXVs9oCzId5QLcp4FTyQvhn5OkOVguGsREhICAPjtt9+0Tk9OTkZycjJat26N3r17W3W4a7tsTdvhOm0hDjDIieoCQz8nGPiWg+Fejo2NDbp16wYAiI2N1VnvwoULaN26NQICAmqrayYz9BC61lGvGOJEsqftxDvA8M8JQw/r80hAzWO4l+Pu7o6GDRsCAFJSUnTWS0tLAwB4e3trnW5nZwd7tUB0dnbW+LemhYaHoYlHM43n2vi1xa6/z2k897CjIxzq19d4ztbGxqDnqlLX0p+ztP7wtZh/2XWx3/UdHZBko6zwWgz9nOjYPgBf/hCp8dytrOuICF+o8Zxnq5b4u9wXg/atWtba52NV3Lt3z9xdMIoCQN09G0yL9u3b49KlSwCAjh074uLFi1rrRUREYP78+bh48SI6duxYYXpYWBjCw8NrsqtERFTDXFxcrDLguedeTuPGjaXHhYWFOusVFxcDgMbeubqIiAh88sknGs899NBDuH37tumdpBrh7OyM9PR0eHl5WeWbmWoXt5e6wVrXLcO9HIVCYVA9Ozs7AEBRUZHW6cXFxdIXABVr3Ujqmnv37nFdkcG4vZAl4vCz5eTl5UmPHR0dddZzcHAAAOTm5tZ4n4iIiKqC4V5ORkaG9Njd3V1nPQ+PsjM9U1NTa7xPREREVcFwLyc7Oxt37twBAPj5+ems5+PjAwBISEiolX5RzSsqKkJ4eLjOn1qI1HF7IUsnWDRLVFSUEEKI77//Xut0BwcHUVhYKIQQom/fvmbvLwsLCwsLi3rhnrsW27dvBwCMGDECjRo1qjD9hRdegL29PW7cuIHo6Oha7h0REVHlzP4Nw9KKg4ODSE9PF0IIsXHjRqFQKKRpfn5+4saNG0IIId566y2z95WFhYWFhaV84SA2OgwePBg7duyAjY0N4uLi8Mcff8DNzQ1jxoyBs7MzTp8+jaeeegpKZcXRnIiIiMzN7N8wLLWMHj1a3L59W5T3+++/i0aNGpm9fywsLCwsLDqK2Ttg0cXJyUk899xzYu7cueKll14Sjz76qNn7xFI9pXHjxmLFihUiKSlJFBYWirS0NLFt2zYRHBxcI+1YLKs4OzuLBQsWiNjYWHHnzh2Rn58vEhMTxRdffCG8vb25zbBYezF7B1hYqrW4uLiI4uJiceTIEZ11mjdvLv79998KR2WEEKKkpETMmjWrWtuxWFZp1aqVuHz5stb1KIQQd+/eFUFBQdxmWKy5mL0DLCzVWl599VUhhNAb7gcOHBBCCJGRkSEGDBgg7O3thYeHh1ixYoX0ofvkk09WWzsWyyqHDx8WQghx8+ZN8cILLwhnZ2fh7OwsBg4cKJKSkoQQQqSkpIgGDRpwm2Gx1mL2DrCwVFvp16+fuHXrlt5w79OnjxBCiNLSUvHEE09UmL5161YhhBAxMTHV0o7Fssrjjz8u7TmHhIRUmN6mTRtRUFAghBDijTfe4DbDYq3F7B1gYTGpTJgwQezYsUO6fFFFV7ivW7dOCCHEvn37tE7v1auXNA/1316NbcdiWeWDDz4QQggRGxurs87PP/8shBBiz5493GZYrLJwEBuyen379sXQoUPRvHlzg+qHhIQAAKKiorROP3bsmHRHv169epncjixL69atAQBnzpzRWefff/8FAHh7ewPgNkPWh+FOVi88PBxdunSRyldffaWzbrNmzeDr6wsAiI2N1VpHqVTi8uXLAICAgACT2pHlSU1Nxf79+3Hq1CmddZo1awYAKCgo4DZDVon3cyerd+3aNVy7dk36v/qd/cpT3fAHAFJSUnTWS0tLQ2BgoLTnZmw7sjzvvfee3ukeHh4YOXIkgLJQ5jZD1oh77lSnNG7cWHqcnZ2ts15OTg4AwNnZ2aR2ZF2aNm2KqKgouLi4AAC+/vprbjNklRjuVKeof+AWFhbqrKf6HdTe3t6kdmQ9BgwYgPj4eHTp0gUA8Mknn+DkyZPcZsgqMdypTlEoFAbVs7OzAwDpXt3GtiPL5+bmhsjISOzatUs6KXP58uV4++23AXCbIevEcKc6JS8vT3rs6Oios56DgwMAIDc316R2ZNnGjh2LS5cuYcKECQDKzt949tlnMW/ePKkOtxmyRgx3qlPUT7Zzd3fXWc/DwwNA2ZnVprQjy6RQKLB69Wps3rwZbm5uUCqVWLFiBQICArB3716NutxmyBox3KlOSUxMlB77+fnprKe6FjohIcGkdmSZPvroI7z22msAgHPnzqFr166YO3cu8vPzK9TlNkPWiOFOdcrdu3dx4cIFAEBwcLDWOj4+PtLe1NGjR01qR5anU6dOmD17NgDg4MGDCAoKwl9//aWzPrcZskYMd6pztm/fDgCYNGkSbGwqvgWmTJkCAIiLi0NSUpLJ7ciyqNZfeno6Ro8erXVvvTxuM2SNzD4GLgtLdZawsDC9Y8s3b95c3L9/XwghREREhMa0oKAgkZ+fL4QQYuTIkdXSjsWyiupWr++9957BbbjNsFhhMXsHWFiqtVQW7gDEzJkzpRt2xMTEiMWLF4uNGzeKwsJCIYQQv/76a7W2Y7GMolAohFKpFEKU3WpVqVTqLYmJidxmWKy1mL0DLCzVWgwJdwDijTfeEHl5eUJdSUmJWL9+vbCzs6v2dizmL25ubqIqrl69ym2GxSqL4v8eENVJrq6uGDBgAFq0aIEbN27g2LFjGmc5V3c7sn7cZsgaMNyJiIhkhmfLExERyQzDnYiISGYY7kRERDLDcCciIpIZhjsREZHMMNyJiIhkhuFOREQkMwx3IiIimWG4ExERyQzDnYiISGYY7kRERDLDcCciIpKZ/wfN26udlnEZDwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "normal = distribution.Normal(150., 30.)\n",
    "samples = normal.sample((10000, ))\n",
    "figure(640, 480)\n",
    "sns.displot(samples)\n",
    "print(samples[0])\n",
    "plt.title(\"Samples from a standard Normal\")\n",
    "plt.show()\n",
    "import torch\n",
    "# Uncomment to compute probability of an event\n",
    "# print(torch.exp(normal.log_prob(torch.Tensor(150))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have access to this complete probability distribution (its exact parameterization and function), we can generate "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An example of continuous random variable is a random variable with *exponential density*\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential*\n",
    "\n",
    "$$Z \\sim \\text{Exp}(\\lambda)$$\n",
    "\n",
    "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is\n",
    "\n",
    "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"distribs\"></a>\n",
    "### PyTorch distributions\n",
    "\n",
    "Here, we rely on the [PyTorch distributions module](https://pytorch.org/docs/stable/_modules/torch/distributions/), which is defined in `torch.distributions`. Most notably, we are going to rely both on the `Distribution` and `Transform` objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports for plotting\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# Define grids of points (for later plots)\n",
    "x = np.linspace(-4, 4, 1000)\n",
    "z = np.array(np.meshgrid(x, x)).transpose(1, 2, 0)\n",
    "z = np.reshape(z, [z.shape[0] * z.shape[1], -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inside this toolbox, we can already find some of the major probability distributions that we are used to deal with\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = distribution.Normal(loc=0, scale=1)\n",
    "p = distribution.Bernoulli(probs=torch.tensor([0.5]))\n",
    "p = distribution.Beta(concentration1=torch.tensor([0.5]), concentration0=torch.tensor([0.5]))\n",
    "p = distribution.Gamma(concentration=torch.tensor([1.0]), rate=torch.tensor([1.0]))\n",
    "p = distribution.Pareto(alpha=torch.tensor([1.0]), scale=torch.tensor([1.0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interesting aspect of these `Distribution` objects is that we can both obtain some samples from it through the `sample` (or `sample_n`) function, but we can also obtain the analytical density at any given point through the `log_prob` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x2f7c26640>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.distributions as distrib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "x = np.linspace(-4, 6, 1000)\n",
    "# Based on a normal\n",
    "n = distrib.Normal(0, 1)\n",
    "n2 = distrib.Normal(1, 1.5)\n",
    "# Obtain some samples\n",
    "samples = n.sample((1000, ))\n",
    "# Evaluate true density at given points\n",
    "density = torch.exp(n.log_prob(torch.Tensor(x))).numpy()\n",
    "density2 = torch.exp(n2.log_prob(torch.Tensor(x))).numpy()\n",
    "# Plot both samples and density\n",
    "plt.figure(figsize=(20, 10))\n",
    "# Compare both distributions\n",
    "plt.plot(x, density); plt.fill_between(x, density, 0, alpha=0.5)\n",
    "plt.plot(x, density2); plt.fill_between(x, density2, 0, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here you can experiment with different distributions, and try to compare how they behave depending on their parameters and also on how much _samples_ you draw from these."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "######################\n",
    "# YOUR CODE GOES HERE\n",
    "######################\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"sampling\"></a>\n",
    "## Sampling from distributions\n",
    "\n",
    "The advantage of using probability distributions is that we can *sample* from these to obtain examples that follow the distribution. For instance, if we perform sampling repeatedly (up to infinity) from a Gaussian PDF, the different values will be distributed following the exact Gaussian distribution. However, although we know the PDF, we need to compute the *Cumulative Distribution Function* (CDF), and then its inverse to obtain the sampling function. Therefore, if we denote the PDF as $f_{X}(x)$, we need to compute the CDF \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "F_{X}\\left(x\\right)=\\intop_{\\infty}^{x}f_{X}\\left(t\\right)dt\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Then, the *inverse sampling method* consists in solving and applying the inverse CDF $F_{X}^{-1}\\left(x\\right)$. Here, we recall that the Exponential probability is defined with the following function.\n",
    "\n",
    "$$\n",
    "p_{\\lambda}(x) = \\lambda e^{-\\lambda x}\n",
    "$$\n",
    "\n",
    "with $\\lambda$ defining the _rate_ parameter. Therefore, to be able to define our own `sample` method, we need to solve for\n",
    "\n",
    "$$\n",
    "F^{-1}_Y(x) = \\left(\\int_0^x \\lambda e^{-\\lambda y} dy\\right)^{-1}\n",
    "$$\n",
    "\n",
    "***\n",
    "\n",
    "<div class=\"alert alert-success\" markdown=\"1\" style=\"color:white; background-color: #013220; border-color: #03C03C\">\n",
    "\n",
    "> ### Question 1.1 - Inverse transform method for sampling\n",
    "\n",
    "> 1. Code the exponential probability density functions \n",
    "> 2. Perform the inverse transform method on the exponential distribution PDF\n",
    "> 3. Code the `sample_exponential` function to sample from the exponential\n",
    "> 4. (**optional**) Perform the same operations for sampling from the Beta distribution\n",
    "  \n",
    "</div>\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2f7de91c0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "nb_samples = 500\n",
    "nb_bins = 50\n",
    "\n",
    "def sample_exponential(mu, n, m):\n",
    "    \n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "    \n",
    "    return samples\n",
    "\n",
    "# Exponential distribution\n",
    "mu = 2\n",
    "samples = np.random.exponential(mu, nb_samples)\n",
    "samples_ex = sample_exponential(mu, nb_samples, 1)\n",
    "# Compute the PDF\n",
    "X = np.linspace(0, np.max(samples), int(np.max(samples)) * 100)\n",
    "y1 = expon.pdf(X) #* (nb_samples / nb_bins) * int(np.max(samples) * 1.5)\n",
    "# Display both\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.subplot(2,1,1)\n",
    "plt.hist(samples, 50, label='Samples')\n",
    "plt.plot(X,y1*nb_samples/10,ls='--',c='r',linewidth=2, label='Exponential PDF')\n",
    "plt.legend(loc=1)\n",
    "plt.subplot(2,1,2)\n",
    "plt.hist(samples_ex[0], 50, label='Our exponential samples')\n",
    "plt.plot(X,y1*nb_samples/10,ls='--',c='r',linewidth=2, label='Exponential PDF')\n",
    "plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2f7f83d00>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sample_beta(a, b, M, N):\n",
    "    \n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "    \n",
    "    return samples\n",
    "\n",
    "from scipy.stats import beta\n",
    "# Beta distribution\n",
    "a = 0.6\n",
    "b = 1.5\n",
    "samples = np.random.beta(a, b, nb_samples)\n",
    "samples_beta = sample_beta(a, b, nb_samples, 1)\n",
    "# Compute the PDF\n",
    "X = np.linspace(0, 1, 100)\n",
    "y1 = beta.pdf(X, a, b) * (nb_samples / nb_bins) * (np.max(samples) * 1.5)\n",
    "# Display both\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.subplot(2,1,1)\n",
    "plt.hist(samples, 50, label='Samples')\n",
    "plt.plot(X,y1,ls='--',c='r',linewidth=2, label='Beta PDF')\n",
    "plt.legend(loc=1)\n",
    "plt.subplot(2,1,2)\n",
    "plt.hist(samples_beta, 50, label='Samples')\n",
    "plt.plot(X,y1,ls='--',c='r',linewidth=2, label='Beta PDF')\n",
    "plt.legend(loc=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"recap\"> </a>\n",
    "# Bayesian inference\n",
    "\n",
    "Here, we discuss *Bayesian inference* and how to use the **Bayes theorem** to perform classification. First, we will see how to derive *estimators* for the different properties of the distributions, and verify that these are *unbiased*. Then, we will implement the **Maximum Likelihood** Estimators (MLE) in order to perform classification of a dataset. First, we will assess the case where parameters are known to implement the discriminant function and decision rule. Then, we will perform the MLE to obtain the means and covariance matrix for each class.\n",
    "\n",
    "To understand these concepts graphically, we will rely on both the `scikit-learn` and `Pytorch` libraries (with the `probability` package)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.distributions as distribution\n",
    "import torch.distributions.transforms as transform\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian framework\n",
    "\n",
    "Two alternative interpretations of probability can be considered  \n",
    "\n",
    "  * **Frequentist** (*classical* approach), assumes that probability is the *long-term frequency of events*. This becomes harder to interpret when events have no long-term frequency (eg. probability in an election, which happens only once). In that case, frequentists consider the *frequency of occurrences across alternative realities*, which defines the probability. \n",
    "  * **Bayesian** interprets probability as measure of *believability in an event*. Therefore, a probability is measure of *belief*, or confidence, of an event occurring. This definition leaves room for conflicting beliefs based on the different *information* about the world. Hence, bayesian inference is mostly based on *updating your beliefs* after considering new *evidence*.\n",
    "\n",
    "To align with probability notation, we denote a belief about event $a$ as $p\\left(a\\right)$, called the *prior probability* of an event to occur. We denote the updated belief as $ p\\left( a \\mid e \\right) $, interpreted as the probability of $a$ *given* the new evidence $e$, called the *posterior probability*. The prior belief is not completely removed, but we *re-weight this prior* to incorporate new evidence $e$ (i.e. we put more weight, or confidence, on some beliefs versus others). By introducing prior uncertainty about events, we admit that any guess we make can be wrong. As we gather an *infinite* amount of evidence $N \\rightarrow \\infty$, the Bayesian results (often) align with frequentist results. Hence for small $N$, inference is *unstable*, where frequentist estimates have more variance and larger confidence intervals. However, by introducing a prior, and returning probabilities, we *preserve the uncertainty* that reflects the instability on a small $N$ dataset.  \n",
    "\n",
    "Updating the *prior belief* to obtain our *posterior belief* is done via the the Bayes' Theorem\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    " p\\left( a \\mid e \\right) \\propto \\frac{ p\\left(e \\mid a\\right) p\\left(a\\right) } {p\\left(e\\right) }\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "We see that our posterior belief of event $a$ given the new evidence $e$ is proportional to ($\\propto$) the *likelihood* of observing this particular evidence $e$ given the event $a$ ($p\\left(e \\mid a\\right)$) multiplied by our prior belief in that particular event $a$ ($p\\left(a\\right)$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "### Using Bayesian classification (in `scikit-learn`)\n",
    "\n",
    "The Bayesian classification methods rely on Bayes's theorem, where we are interested in finding the probability of a label $y$ given some observed features, which we can write as $p(y~|~\\mathbf{x})$. Bayes's theorem tells us how to express this in terms of quantities that we can compute more directly\n",
    "\n",
    "$$\n",
    "p(y~|~\\mathbf{x}) = \\frac{p(\\mathbf{x}~|~y)p(y)}{p(\\mathbf{x})}\n",
    "$$\n",
    "\n",
    "If we are trying to decide between two labels ($y_1$ and $y_2$), then one way to make this decision is to compute the ratio of the posterior probabilities for each label\n",
    "\n",
    "$$\n",
    "\\frac{p(y_1~|~\\mathbf{x})}{p(y_2~|~\\mathbf{x})} = \\frac{p(\\mathbf{x}~|~y_1)}{p(\\mathbf{x}~|~y_2)}\\frac{p(y_1)}{p(y_2)}\n",
    "$$\n",
    "\n",
    "All we need now is some model by which we can compute $p(\\mathbf{x}~|~y_i)$ for each label.\n",
    "Such a model is called a *generative model* because it specifies the hypothetical random process that generates the data.\n",
    "Specifying this generative model for each label is the main piece of the training of such a Bayesian classifier.\n",
    "The general version of such a training step is a very difficult task, but we can make it simpler through the use of some simplifying assumptions about the form of this model. If we make *very naive assumptions* (called *Naive Bayes*) about the generative model for each label, we can find a rough approximation of the generative model for each class, and then proceed with the Bayesian classification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "#### Gaussian Naive Bayes\n",
    "\n",
    "Perhaps the easiest naive Bayes classifier to understand is Gaussian naive Bayes. In this classifier, the assumption is that *data from each label is drawn from a simple Gaussian distribution*. Imagine that we have the following data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "X, y = make_blobs(200, 2, centers=2, random_state=2, cluster_std=3.2)\n",
    "figure(6, 8); plt.scatter(X[:, 0], X[:, 1], c=y, s=80, cmap='RdBu', edgecolor='w'); plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "One extremely fast way to create a simple model is to assume that the data is described by a Gaussian distribution with no covariance between dimensions. This model can be fit by simply finding the mean and standard deviation of the points within each label, which is all you need to define such a distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "With this generative model for each class, we have a simple recipe to compute the likelihood $P({\\rm features}~|~L_1)$ for any data point, and thus we can quickly compute the posterior ratio and determine which label is the most probable for a given point. This procedure is implemented in Scikit-Learn's ``sklearn.naive_bayes.GaussianNB`` estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "model = GaussianNB()\n",
    "model.fit(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "Now let's generate some new data and predict the label:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "Xnew = [-6, -14] + [14, 18] * rng.rand(2000, 2)\n",
    "ynew = model.predict(Xnew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "Now we can plot the data and see where the decision boundary is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = figure(6,8); ax = fig.add_subplot(111)\n",
    "# predict the classification probabilities on a grid\n",
    "xlim = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
    "ylim = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
    "xx, yy = np.meshgrid(np.linspace(xlim[0], xlim[1], 71), np.linspace(ylim[0], ylim[1], 81))\n",
    "Z = model.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]\n",
    "Z = Z.reshape(xx.shape)\n",
    "ax.contourf(xx, yy, Z, cmap=plt.cm.RdBu, alpha=.8)\n",
    "ax.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu', edgecolor='w');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "We see a slightly curved boundary in the classifications (generally, the boundary in Gaussian naive Bayes is quadratic). A nice piece of this Bayesian formalism is that it naturally allows for probabilistic classification, which we can compute using the ``predict_proba`` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.74, 0.26],\n",
       "       [1.  , 0.  ],\n",
       "       [1.  , 0.  ],\n",
       "       [0.96, 0.04],\n",
       "       [0.86, 0.14],\n",
       "       [0.95, 0.05],\n",
       "       [0.01, 0.99],\n",
       "       [0.79, 0.21]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yprob = model.predict_proba(Xnew)\n",
    "yprob[-8:].round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true
   },
   "source": [
    "The columns give the posterior probabilities of the first and second label, respectively. If you are looking for estimates of uncertainty in your classification, Bayesian approaches like this can be a useful approach. Of course, the final classification will only be as good as the model assumptions that lead to it, which is why Gaussian naive Bayes often does not produce very good results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian inference\n",
    "\n",
    "Suppose we have coin and want to estimate the probability of heads ($p$) for it. The coin is Bernoulli distributed:\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "\\phi(x)= p^x (1-p)^{(1-x)} \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where $x$ is the outcome, *1* for heads and *0* for tails. Based on $n$ *independent* flips, we have the likelihood:\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "\\mathcal{L}(p|\\mathbf{x})= \\prod_{i=1}^n p^{ x_i }(1-p)^{1-x_i} \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "(the independent-trials assumption allows us to just substitute everything into $ \\phi(x)$). \n",
    "\n",
    "The idea of *maximum likelihood* will be to maximize this as the function of $p$ after given all of the $x_i$ data. This means that our estimator, $\\hat{p}$, is a function of the observed $x_i$ data, and as such, is a random variable with its own distribution.\n",
    "\n",
    "**Defining the estimator**\n",
    "\n",
    "The only way to know for sure that our estimator is correctly defined is to check if the estimator is unbiased, namely, if\n",
    "\n",
    "$$ \\mathbb{E}[\\hat{p}] = p $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Understanding this behavior with `pytorch`\n",
    "\n",
    "Without solving for the previous exercise, we can  Let's say that we have 100 samples from a Bernoulli distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0., 0., 1., 0., 0., 1., 0., 1., 0., 1.])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "bernoulli = distribution.Bernoulli(0.2)\n",
    "\n",
    "sample = bernoulli.sample((10000, ))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "sns.displot(sample)\n",
    "plt.title(\"Samples from a Bernoulli (p = .2)\")\n",
    "torch.mean(sample)\n",
    "print(sample[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([10, 2, 2])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[-0.9019, -0.6059],\n",
       "        [ 1.3130, -0.5718],\n",
       "        [-0.9561,  1.3796],\n",
       "        [-0.5950,  0.4329],\n",
       "        [ 0.1047,  0.4365],\n",
       "        [ 0.6093, -0.8010],\n",
       "        [-0.6378,  1.6016],\n",
       "        [ 1.8907,  0.6025],\n",
       "        [-0.0135,  0.6308],\n",
       "        [-1.1516,  1.7666]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch.distributions as distrib\n",
    "normal1d = distrib.Normal(0, 1)\n",
    "samples = normal1d.sample((10,2,2))\n",
    "print(samples.shape)\n",
    "normal2d = distrib.MultivariateNormal(torch.Tensor([0, 1]), torch.eye(2))\n",
    "normal2d.sample((10,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use our estimator, and define our problem more formally, by defining our input samples as a dataset of observations $x$, and we are trying to model this set, as a `Bernoulli` distribution, for which the $p$ parameter is unknown (here defined as a `Variable`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.autograd import Variable\n",
    "x = torch.Tensor(sample)\n",
    "#p = Variable(torch.rand(1), requires_grad=True)\n",
    "p = torch.Tensor(1)\n",
    "p[0] = 0.55\n",
    "p.requires_grad = True\n",
    "#p = Variable(torch.Tensor([0.9]), requires_grad=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use our estimator to gradually compute the Maximum Likelihood, in order to uncover the estimated probability of the underlying distribution, solely based on observing the samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "unexpected indent (1382376269.py, line 11)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Cell \u001b[0;32mIn[24], line 11\u001b[0;36m\u001b[0m\n\u001b[0;31m    print(\"loglik = %.4f - p = %.4f - dL/dp = %.4f\"%(NLL.data.numpy(), p.data.numpy(), p.grad.data.numpy()))\u001b[0m\n\u001b[0m    ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m unexpected indent\n"
     ]
    }
   ],
   "source": [
    "learning_rate = 0.00002\n",
    "for t in range(100):\n",
    "    # Forward pass\n",
    "    # Negative log-likelihood\n",
    "    NLL = -torch.sum(torch.log(x*p + (1-x)*(1-p)) )\n",
    "    # Automatic differentiation\n",
    "    NLL.backward()\n",
    "    p.data\n",
    "    p.grad.data\n",
    "    #if t % 10 == 0:\n",
    "    print(\"loglik = %.4f - p = %.4f - dL/dp = %.4f\"%(NLL.data.numpy(), p.data.numpy(), p.grad.data.numpy()))   \n",
    "    p.data -= learning_rate * p.grad.data\n",
    "    p.grad.data.zero_()\n",
    "print('Final probability p =', p.data[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "***\n",
    "\n",
    "<div class=\"alert alert-success\" markdown=\"1\" style=\"color:white; background-color: #013220; border-color: #03C03C\">\n",
    "\n",
    "> ### Question 2.1 - Log-likelihood learning\n",
    "\n",
    "> 1. Compute the *log-likelihood* $J=\\log(\\mathcal{L}(p \\mid \\mathbf{x}))$ of our given problem\n",
    "> 2. Based on this, compute its derivative $ \\frac{dJ}{dp} $\n",
    "> 3. Solve it to find the estimator $\\hat{p}$\n",
    "> 4. Verify that this estimator is unbiased $ \\mathbb{E}(\\hat{p}) = p $\n",
    "> 5. Compute the variance of the estimator $ \\mathbb{E}\\left(\\hat{p}^2\\right) $\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final probability p = tensor(0.2982)\n"
     ]
    }
   ],
   "source": [
    "x = Variable(sample).type(torch.FloatTensor)\n",
    "p = torch.mean(x)\n",
    "learning_rate = 0.2\n",
    "for t in range(100):\n",
    "    ...\n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "\n",
    "print('Final probability p =', p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Full estimator density\n",
    "\n",
    "In general, computing the mean and variance of the estimator is insufficient to characterize the underlying probability density of $\\hat{p}$, except if we knew that $\\hat{p}$ were normally distributed. This is where the [*central limit theorem*](http://mathworld.wolfram.com/CentralLimitTheorem.html). Indeed, the form of the estimator, implies that $\\hat{p}$ is normally distributed, but only *asymptotically*, which doesn't quantify how many samples $n$ we need. Unfortunately, in the real world, each sample may be precious. Hence, to write out the full density for $\\hat{p}$, we first have to ask what is the probability that the estimator will equal a specific value such as\n",
    "\n",
    "$$  \n",
    "\\begin{equation}\n",
    "\\hat{p} = \\frac{1}{n}\\sum_{i=1}^n x_i  = 0 \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "This can only happen when $x_i=0$,  $\\forall i$. The corresponding probability can be computed from the density\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "f(\\mathbf{x},p)= \\prod_{i=1}^n \\left(p^{x_i} (1-p)^{1-x_i}  \\right) \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "f\\left(\\sum_{i=1}^n x_i  = 0,p\\right)= \\left(1-p\\right)^n  \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Likewise, if $\\lbrace x_i \\rbrace$ has one $i^{th}$ value equal to one, then\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "f\\left(\\sum_{i=1}^n x_i  = 1,p\\right)= n p \\prod_{i=1}^{n-1} \\left(1-p\\right)\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where the $n$ comes from the $n$ ways to pick one value equal to one from the $n$ elements $x_i$. Continuing this way, we can construct the entire density as\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "f\\left(\\sum_{i=1}^n x_i  = k,p\\right)= \\binom{n}{k} p^k  (1-p)^{n-k}  \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where the term on the left is the binomial coefficient of $n$ things taken $k$ at a time. This is the binomial distribution and it's not the density for $\\hat{p}$, but rather for $n\\hat{p}$. We'll leave this as-is because it's easier to work with below. We just have to remember to keep track of the $n$ factor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum Likelihood Estimation\n",
    "\n",
    "Maximum Likelihood Estimation (MLE) allows to perform typical statistical pattern classification tasks. In the cases where **probabilistic models and parameters are known**, the design of a Bayes' classifier is rather easy. However, in real applications, we are rarely given this information and this is where the MLE comes into play.\n",
    "\n",
    "MLE still **requires partial knowledge** about the problem. We have to assume that the **model of the class conditional densities is known** (usually Gaussian distributions). Hence, Using MLE, we want to estimate the values of the parameters of a given distribution for the class-conditional densities, for example, the *mean* and *variance* assuming that the class-conditional densities are *normal*  distributed (Gaussian) with \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "p(\\pmb x   \\mid   y_i) \\sim N(\\mu, \\sigma^2)\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parameters known\n",
    "\n",
    "Imagine that we want to classify data consisting of two-dimensional patterns, $\\pmb{x} = [x_1, x_2] \\in \\mathbb{R}^{2}$ that could belong to 1 out of 3 classes $y_1,y_2,y_3$. \n",
    "\n",
    "Let's assume the following information about the model where we use continuous univariate normal (Gaussian) model for the class-conditional densities\n",
    "\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "p(\\pmb x \\mid y_j) \\sim N(\\pmb \\mu \\mid \\Sigma) = \\frac{1}{(2\\pi)^{d/2}   \\mid \\Sigma|^{1/2}} exp \\bigg[ -\\frac{1}{2}(\\pmb x - \\pmb \\mu)^t \\Sigma^{-1}(\\pmb x - \\pmb \\mu) \\bigg]\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Furthermore, we consider for this first problem that we know the distributions of the classes, ie. their mean and covariances.\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "p([x_1, x_2]^t \\mid y_1) ∼ N([0,0],3I), \\\\\n",
    "p([x_1, x_2]^t \\mid y_2) ∼ N([9,0],3I), \\\\\n",
    "p([x_1, x_2]^t \\mid y_3) ∼ N([6,6],4I),\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Therefore, the means of the sample distributions for 2-dimensional features are defined as  \n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "\\pmb{\\mu}_{\\,1} = \\bigg[ 0, 0 \\bigg],    \\pmb{\\mu}_{\\,2} = \\bigg[ 9,  0 \\bigg],    \\pmb{\\mu}_{\\,3} = \\bigg[ 6,  6 \\bigg] \n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "The **covariance matrices** for the statistically independent and identically distributed ('i.i.d') features\n",
    "\n",
    "$$ \n",
    "\\begin{array}{ccc}\n",
    "\\Sigma_1 = \\bigg[ \n",
    "\\begin{array}{cc}\n",
    "3 & 0\\\\\n",
    "0 & 3 \\\\\n",
    "\\end{array} \\bigg], \n",
    "\\Sigma_2 = \\bigg[ \n",
    "\\begin{array}{cc}\n",
    "3 & 0\\\\\n",
    "0 & 3 \\\\\n",
    "\\end{array} \\bigg], \n",
    "\\Sigma_3 = \\bigg[ \n",
    "\\begin{array}{cc}\n",
    "4 & 0\\\\\n",
    "0 & 4 \\\\\n",
    "\\end{array} \\bigg] \n",
    "\\end{array}$$\n",
    "\n",
    "Finally, we consider that all classes have an **equal prior probability**  \n",
    "\n",
    "$$p(y_1)   =    p(y_2)   =   p(y_3)   = \\frac{1}{3}$$\n",
    "\n",
    "\n",
    "***\n",
    "\n",
    "<div class=\"alert alert-success\" markdown=\"1\" style=\"color:white; background-color: #013220; border-color: #03C03C\">\n",
    "\n",
    "> ### Question 3.1 - Data generation\n",
    "\n",
    "> 1. Generate some data (samples from the multivariate Gaussians) following classes distributions\n",
    "> 2. Plot the class-dependent data\n",
    "  \n",
    "</div>\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'ellipsis' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[26], line 35\u001b[0m\n\u001b[1;32m     33\u001b[0m \u001b[38;5;66;03m# Plot the corresponding data\u001b[39;00m\n\u001b[1;32m     34\u001b[0m plt\u001b[38;5;241m.\u001b[39mfigure(figsize\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m12\u001b[39m, \u001b[38;5;241m8\u001b[39m))\n\u001b[0;32m---> 35\u001b[0m plt\u001b[38;5;241m.\u001b[39mscatter(\u001b[43mx1samples\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m, x1samples[:, \u001b[38;5;241m1\u001b[39m], s\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m60\u001b[39m, marker\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mo\u001b[39m\u001b[38;5;124m'\u001b[39m, color\u001b[38;5;241m=\u001b[39m[\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0.8\u001b[39m, \u001b[38;5;241m0\u001b[39m], edgecolors\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mw\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m     36\u001b[0m plt\u001b[38;5;241m.\u001b[39mscatter(x2samples[:, \u001b[38;5;241m0\u001b[39m], x2samples[:, \u001b[38;5;241m1\u001b[39m], s\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m60\u001b[39m, marker\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mo\u001b[39m\u001b[38;5;124m'\u001b[39m, color\u001b[38;5;241m=\u001b[39m[\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0.8\u001b[39m], edgecolors\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mw\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m     37\u001b[0m plt\u001b[38;5;241m.\u001b[39mscatter(x3samples[:, \u001b[38;5;241m0\u001b[39m], x3samples[:, \u001b[38;5;241m1\u001b[39m], s\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m60\u001b[39m, marker\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mo\u001b[39m\u001b[38;5;124m'\u001b[39m, color\u001b[38;5;241m=\u001b[39m[\u001b[38;5;241m0.8\u001b[39m, \u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0\u001b[39m], edgecolors\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mw\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "\u001b[0;31mTypeError\u001b[0m: 'ellipsis' object is not subscriptable"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x800 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 7.0 - Generate data with known parameters\n",
    "\n",
    "nb_patterns = 100\n",
    "# Generate random patterns for class 1\n",
    "mu1 = np.array([0,0])\n",
    "cov1 = np.array([[1,0],[0,1]])\n",
    "# Generate random patterns for class 2\n",
    "mu2 = np.array([9,0])\n",
    "cov2 = np.array([[3,0],[0,3]])\n",
    "# Generate random patterns for class 3\n",
    "mu3 = np.array([6,6])\n",
    "cov3 = np.array([[7,0],[0,7]])\n",
    "\n",
    "######################\n",
    "# YOUR CODE GOES HERE\n",
    "######################\n",
    "\n",
    "x1samples = ...\n",
    "x2samples = ...\n",
    "x3samples = ...\n",
    "\n",
    "######################\n",
    "from cml.plot import gaussian_ellipsoid\n",
    "# Prepare concatenated versions of class properties\n",
    "mu_vals = {}; \n",
    "mu_vals[0] = np.array([mu1]).transpose() \n",
    "mu_vals[1] = np.array([mu2]).transpose() \n",
    "mu_vals[2] = np.array([mu3]).transpose()\n",
    "cov_vals = {}\n",
    "cov_vals[0] = cov1\n",
    "cov_vals[1] = cov2\n",
    "cov_vals[2] = cov3\n",
    "# Plot the corresponding data\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.scatter(x1samples[:, 0], x1samples[:, 1], s=60, marker='o', color=[0, 0.8, 0], edgecolors='w')\n",
    "plt.scatter(x2samples[:, 0], x2samples[:, 1], s=60, marker='o', color=[0, 0, 0.8], edgecolors='w')\n",
    "plt.scatter(x3samples[:, 0], x3samples[:, 1], s=60, marker='o', color=[0.8, 0, 0], edgecolors='w')\n",
    "h = gaussian_ellipsoid(mu1, cov1, 2, color=[0, 0.8, 0]); \n",
    "h = gaussian_ellipsoid(mu2, cov2, 2, color=[0, 0, 0.8]); \n",
    "h = gaussian_ellipsoid(mu3, cov3, 2, color=[0.8, 0, 0]);\n",
    "plt.title('Training Dataset')\n",
    "plt.ylabel('x2')\n",
    "plt.xlabel('x1');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, our **objective function** is to maximize the discriminant function $g_i(\\pmb x)$, which we define as the posterior probability to perform a **minimum-error classification** (Bayes classifier). \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "g_1(\\pmb x) = p(y_1 \\mid   \\pmb{x}), \\quad  g_2(\\pmb{x}) = p(y_2 \\mid   \\pmb{x}), \\quad  g_3(\\pmb{x}) = p(y_3 \\mid   \\pmb{x})\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "So that our decision rule is to choose the class $\\omega_i$ for which $g_i(\\pmb x)$ is max., where  \n",
    "\n",
    " $$ \n",
    " \\begin{equation}\n",
    " \\quad g_i(\\pmb{x}) = \\pmb{x}^{\\,t} \\bigg( - \\frac{1}{2} \\Sigma_i^{-1} \\bigg) \\pmb{x} + \\bigg( \\Sigma_i^{-1} \\pmb{\\mu}_{\\,i}\\bigg)^t \\pmb x + \\bigg( -\\frac{1}{2} \\pmb{\\mu}_{\\,i}^{\\,t}  \\Sigma_{i}^{-1} \\pmb{\\mu}_{\\,i} -\\frac{1}{2} ln(\\left|\\Sigma_i\\right|)\\bigg) \n",
    " \\end{equation}\n",
    " $$\n",
    "\n",
    "***\n",
    "\n",
    "**Exercise**\n",
    "\n",
    "  1. Implement the discriminant function\n",
    "  2. Implement the decision rule (classifier)\n",
    "  3. Classify the data generated in the previous exercise\n",
    "  4. Plot the confusion matrix\n",
    "  5. Calculate the empirical error\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'ellipsis' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[27], line 40\u001b[0m\n\u001b[1;32m     38\u001b[0m conf_matrix \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros((\u001b[38;5;241m3\u001b[39m, \u001b[38;5;241m3\u001b[39m))\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(nb_patterns):\n\u001b[0;32m---> 40\u001b[0m     x, g \u001b[38;5;241m=\u001b[39m classify_data(\u001b[43mx1samples\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m:\u001b[49m\u001b[43m]\u001b[49m, discriminant_function, mu_vals, cov_vals);\n\u001b[1;32m     41\u001b[0m     x1classes[i] \u001b[38;5;241m=\u001b[39m g;\n\u001b[1;32m     42\u001b[0m     conf_matrix[\u001b[38;5;241m0\u001b[39m, g] \u001b[38;5;241m=\u001b[39m conf_matrix[\u001b[38;5;241m0\u001b[39m, g] \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m;\n",
      "\u001b[0;31mTypeError\u001b[0m: 'ellipsis' object is not subscriptable"
     ]
    }
   ],
   "source": [
    "import operator\n",
    "\n",
    "def discriminant_function(x_vec, mu_vec, cov_mat):\n",
    "    # Calculates the value of the discriminant function for a dx1 dimensional\n",
    "    # sample given the covariance matrix and mean vector.\n",
    "    #\n",
    "    #   x_vec: A dx1 dimensional numpy array representing the sample.\n",
    "    #   cov_mat: numpy array of the covariance matrix.\n",
    "    #   mu_vec: dx1 dimensional numpy array of the sample mean.\n",
    "    #\n",
    "    #   Returns a float value g as result of the discriminant function.\n",
    "\n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ###################### \n",
    "    \n",
    "    return float(g)\n",
    "\n",
    "def classify_data(x_vec, g, mu_vecs, cov_mats):\n",
    "    #    Classifies an input sample into 1 out of 3 classes determined by\n",
    "    #    maximizing the discriminant function g_i().\n",
    "\n",
    "    #    Keyword arguments:\n",
    "    #        x_vec: A dx1 dimensional numpy array representing the sample.\n",
    "    #        g: The discriminant function.\n",
    "    #        mu_vecs: A list of mean vectors as input for g.\n",
    "    #        cov_mats: A list of covariance matrices as input for g.\n",
    "    #    \n",
    "    #    Returns the max probability and class id.\n",
    "\n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "    \n",
    "    return (max_value, max_index)\n",
    "\n",
    "x1classes = np.zeros((nb_patterns, 1))\n",
    "conf_matrix = np.zeros((3, 3))\n",
    "for i in range(nb_patterns):\n",
    "    x, g = classify_data(x1samples[i, :], discriminant_function, mu_vals, cov_vals);\n",
    "    x1classes[i] = g;\n",
    "    conf_matrix[0, g] = conf_matrix[0, g] + 1;\n",
    "x2classes = np.zeros((nb_patterns, 1))\n",
    "for i in range(nb_patterns):\n",
    "    x, g = classify_data(x2samples[i, :], discriminant_function, mu_vals, cov_vals);\n",
    "    x2classes[i] = g;\n",
    "    conf_matrix[1, g] = conf_matrix[1, g] + 1;\n",
    "x3classes = np.zeros((nb_patterns, 1))\n",
    "for i in range(nb_patterns):\n",
    "    x, g = classify_data(x3samples[i, :], discriminant_function, mu_vals, cov_vals);\n",
    "    x3classes[i] = g;\n",
    "    conf_matrix[2, g] = conf_matrix[2, g] + 1;\n",
    "\n",
    "print('%16s \\t %s \\t %s \\t %s\\n' % (' ', 'class 1', 'class 2', 'class 3'));\n",
    "print('%16s \\t %f \\t %f \\t %f\\n' % ('class 1', conf_matrix[0, 0], conf_matrix[0, 1], conf_matrix[0, 2]));\n",
    "print('%16s \\t %f \\t %f \\t %f\\n' % ('class 2', conf_matrix[1, 0], conf_matrix[1, 1], conf_matrix[1, 2]));\n",
    "print('%16s \\t %f \\t %f \\t %f\\n' % ('class 3', conf_matrix[2, 0], conf_matrix[2, 1], conf_matrix[2, 2]));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unknown parameters\n",
    "\n",
    "In contrast to the previous case, let us assume that we only know the number of parameters for the class conditional densities $p (\\pmb x \\mid  y_i)$, and we want to use a Maximum Likelihood Estimation (MLE) to estimate the quantities of these parameters from the training data.\n",
    "\n",
    "\n",
    "Given the information about the our model (the data is normal distributed) the 2 parameters to be estimated for each class are $\\pmb \\mu_i$ and $\\pmb \\Sigma_i$, which are summarized by the   \n",
    "parameter vector \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\pmb \\theta_i = \\bigg[ \\begin{array}{c}\n",
    "\\ \\theta_{i1} \\\\\n",
    "\\ \\theta_{i2} \\\\\n",
    "\\end{array} \\bigg]=\n",
    "\\bigg[ \\begin{array}{c}\n",
    "\\pmb \\mu_i \\\\\n",
    "\\pmb \\Sigma_i \\\\\n",
    "\\end{array} \\bigg]\n",
    "\\end{equation}\n",
    "$$ \n",
    "\n",
    "For the Maximum Likelihood Estimate (MLE), we assume that we have a set of samples $D = \\left\\{ \\pmb x_1, \\pmb x_2,..., \\pmb x_n \\right\\} $ that are *i.i.d.* (independent and identically distributed, drawn with probability $p(\\pmb x \\mid   y_i, \\pmb \\theta_i) )$.  Thus, we can **work with each class separately** and omit the class labels, so that we write the probability density as $p(\\pmb x \\mid \\pmb \\theta)$ \n",
    "\n",
    "**Likelihood of $ \\pmb \\theta $**\n",
    "\n",
    "Thus, the probability of observing $D = \\left\\{ \\pmb x_1, \\pmb x_2,..., \\pmb x_n \\right\\} $ is  \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "p(D  \\mid    \\pmb \\theta ) = p(\\pmb x_1   \\mid   \\pmb \\theta )  \\cdot   p(\\pmb x_2   \\mid  \\pmb \\theta )   \\cdot  ...    p(\\pmb x_n   \\mid   \\pmb \\theta ) = \\prod_{k=1}^{n}   p(\\pmb x_k \\pmb   \\mid   \\pmb \\theta  )\n",
    "\\end{equation}\n",
    "$$  \n",
    "\n",
    "Where $p(D  \\mid    \\pmb  \\theta )$ is also called the ***likelihood of $\\pmb\\ \\theta$***\n",
    "\n",
    "We know that $p([x_1,x_2]^t)  ∼   N(\\pmb \\mu,\\pmb \\Sigma) $ (remember that we dropped the class labels, since we are working with every class separately). And the mutlivariate normal density is given as  \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\quad \\quad p(\\pmb x) = \\frac{1}{(2\\pi)^{d/2}   |\\Sigma|^{1/2}} exp \\bigg[ -\\frac{1}{2}(\\pmb x - \\pmb \\mu)^t \\Sigma^{-1}(\\pmb x - \\pmb \\mu) \\bigg]\n",
    "\\end{equation}\n",
    "$$  \n",
    "\n",
    "Therefore, we obtain  \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "p(D  \\mid    \\pmb \\theta ) = \\prod_{k=1}^{n}   p(\\pmb x_k \\pmb   \\mid   \\pmb \\theta  ) =  \\prod_{k=1}^{n}   \\frac{1}{(2\\pi)^{d/2}   |\\Sigma|^{1/2}} exp \\bigg[ -\\frac{1}{2}(\\pmb x - \\pmb \\mu)^t \\Sigma^{-1}(\\pmb x - \\pmb \\mu) \\bigg]\n",
    "\\end{equation}\n",
    "$$\n",
    "and the log of the multivariate density\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "l(\\pmb\\theta) =  \\sum\\limits_{k=1}^{n} - \\frac{1}{2}(\\pmb x - \\pmb \\mu)^t \\pmb \\Sigma^{-1}   (\\pmb x - \\pmb \\mu) - \\frac{d}{2}   ln   2\\pi - \\frac{1}{2}  ln   |\\pmb\\Sigma|\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "In order to obtain the MLE $\\boldsymbol{\\hat{\\theta}}$, we maximize $l (\\pmb  \\theta)$, which can be done via differentiation  \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\nabla_{\\pmb \\theta} \\equiv \\begin{bmatrix}  \n",
    "\\frac{\\partial   }{\\partial   \\theta_1} \\\\ \n",
    "\\frac{\\partial   }{\\partial   \\theta_2}\n",
    "\\end{bmatrix} = \\begin{bmatrix} \n",
    "\\frac{\\partial   }{\\partial   \\pmb \\mu} \\\\ \n",
    "\\frac{\\partial   }{\\partial   \\pmb \\sigma}\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\nabla_{\\pmb \\theta} l = \\sum\\limits_{k=1}^n \\nabla_{\\pmb \\theta}  ln  p(\\pmb x| \\pmb \\theta) = 0 \n",
    "\\end{equation}\n",
    "$$  \n",
    "\n",
    "</div>{: .notice--blank}\n",
    "\n",
    "***\n",
    "\n",
    "**Exercise**\n",
    "<div markdown = \"1\">\n",
    "\n",
    "  1. Perform the differentiation for $\\frac{\\partial   \\mathcal{L}}{\\partial   \\pmb \\mu}$ to obtain the estimator of the mean $\\hat{\\mu}$\n",
    "  2. Perform the differentiation for $\\frac{\\partial   \\mathcal{L}}{\\partial   \\pmb \\Sigma}$ to obtain the estimator of the covariance matrix $\\hat{\\Sigma}$\n",
    "  3. Implement the two estimators as functions based on a set of data\n",
    "  4. Apply these estimators (MLE) in order to obtain estimated parameters\n",
    "  5. Re-compute the classification errors on the previous dataset\n",
    "  \n",
    "***\n",
    "\n",
    "\n",
    "***\n",
    "\n",
    "<div class=\"alert alert-success\" markdown=\"1\" style=\"color:white; background-color: #013220; border-color: #03C03C\">\n",
    "\n",
    "> ### Question 1.2 - Finetuning the autoencoder\n",
    "\n",
    "> 1. Transfer the weights from the pretrained layers to the full architecture\n",
    "> 2. Fill in the training criterion and optimizer\n",
    "> 2. Finish the training loop to finetune your deep AE\n",
    "  \n",
    "</div>\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 \t mu1_1    \t mu1_2   \t mu2_1   \t mu2_2   \t mu3_1   \t mu3_2  \n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'ellipsis' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[28], line 12\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;66;03m######################\u001b[39;00m\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m%16s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m%\u001b[39m (\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmu1_1   \u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmu1_2  \u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmu2_1  \u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmu2_2  \u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmu3_1  \u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmu3_2  \u001b[39m\u001b[38;5;124m'\u001b[39m));\n\u001b[0;32m---> 12\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m%16s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m%\u001b[39m (\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mMLE\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[43mmu_est_1\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m, mu_est_1[\u001b[38;5;241m1\u001b[39m], mu_est_2[\u001b[38;5;241m0\u001b[39m], mu_est_2[\u001b[38;5;241m1\u001b[39m], mu_est_3[\u001b[38;5;241m0\u001b[39m], mu_est_3[\u001b[38;5;241m1\u001b[39m]));\n\u001b[1;32m     13\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m%16s\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;130;01m\\t\u001b[39;00m\u001b[38;5;124m \u001b[39m\u001b[38;5;132;01m%f\u001b[39;00m\u001b[38;5;124m'\u001b[39m \u001b[38;5;241m%\u001b[39m (\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mTruth\u001b[39m\u001b[38;5;124m'\u001b[39m, mu1[\u001b[38;5;241m0\u001b[39m], mu1[\u001b[38;5;241m1\u001b[39m], mu2[\u001b[38;5;241m0\u001b[39m], mu2[\u001b[38;5;241m1\u001b[39m], mu3[\u001b[38;5;241m0\u001b[39m], mu3[\u001b[38;5;241m1\u001b[39m]));\n\u001b[1;32m     15\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmle_covariance\u001b[39m(x_samples, mu_est):\n\u001b[1;32m     16\u001b[0m     \u001b[38;5;66;03m#    Calculates the Maximum Likelihood Estimate for the covariance matrix.\u001b[39;00m\n\u001b[1;32m     17\u001b[0m     \u001b[38;5;66;03m#    \u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     25\u001b[0m     \u001b[38;5;66;03m# YOUR CODE GOES HERE\u001b[39;00m\n\u001b[1;32m     26\u001b[0m     \u001b[38;5;66;03m######################\u001b[39;00m\n",
      "\u001b[0;31mTypeError\u001b[0m: 'ellipsis' object is not subscriptable"
     ]
    }
   ],
   "source": [
    "########################################################\n",
    "# YOUR CODE GOES HERE (Perform mu estimates)\n",
    "########################################################\n",
    "\n",
    "mu_est_1 = ...\n",
    "mu_est_2 = ...\n",
    "mu_est_3 = ...\n",
    "\n",
    "######################\n",
    "\n",
    "print('%16s \\t %s \\t %s \\t %s \\t %s \\t %s \\t %s' % ('', 'mu1_1   ', 'mu1_2  ', 'mu2_1  ', 'mu2_2  ', 'mu3_1  ', 'mu3_2  '));\n",
    "print('%16s \\t %f \\t %f \\t %f \\t %f \\t %f \\t %f' % ('MLE', mu_est_1[0], mu_est_1[1], mu_est_2[0], mu_est_2[1], mu_est_3[0], mu_est_3[1]));\n",
    "print('%16s \\t %f \\t %f \\t %f \\t %f \\t %f \\t %f' % ('Truth', mu1[0], mu1[1], mu2[0], mu2[1], mu3[0], mu3[1]));\n",
    "\n",
    "def mle_covariance(x_samples, mu_est):\n",
    "    #    Calculates the Maximum Likelihood Estimate for the covariance matrix.\n",
    "    #    \n",
    "    #    Keyword Arguments:\n",
    "    #        x_samples: np.array of the samples for 1 class, n x d dimensional \n",
    "    #        mu_est: np.array of the mean MLE, d x 1 dimensional\n",
    "    #        \n",
    "    #    Returns the MLE for the covariance matrix as d x d numpy array.\n",
    "    \n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "    \n",
    "    return cov_est\n",
    "\n",
    "cov_est_1 = mle_covariance(x1samples, np.array([mu_est_1]).transpose());\n",
    "cov_est_2 = mle_covariance(x2samples, np.array([mu_est_2]).transpose());\n",
    "cov_est_3 = mle_covariance(x3samples, np.array([mu_est_3]).transpose());\n",
    "\n",
    "print('%16s \\t %s \\t %s \\t %s \\t %s \\t %s \\t %s' % ('', 'cov1_1   ', 'cov1_2  ', 'cov2_1  ', 'cov2_2  ', 'cov3_1  ', 'cov3_2  '));\n",
    "print('%16s \\t %f \\t %f \\t %f \\t %f \\t %f \\t %f' % ('MLE', cov_est_1[0, 0], cov_est_1[1, 0], cov_est_2[0, 0], cov_est_2[1, 0], cov_est_3[0, 0], cov_est_3[1, 0]));\n",
    "print('%16s \\t %f \\t %f \\t %f \\t %f \\t %f \\t %f' % ('Truth', cov1[0, 0], cov1[1, 0], cov2[0, 0], cov2[1, 0], cov3[0, 0], cov3[1, 0]));\n",
    "\n",
    "mu_estimates = {}; \n",
    "mu_estimates[0] = np.array([mu_est_1]).transpose()  \n",
    "mu_estimates[1] = np.array([mu_est_2]).transpose()  \n",
    "mu_estimates[2] = np.array([mu_est_3]).transpose() \n",
    "cov_estimates = {}; \n",
    "cov_estimates[0] = cov_est_1; \n",
    "cov_estimates[1] = cov_est_2; \n",
    "cov_estimates[2] = cov_est_3;\n",
    "\n",
    "# Plot the corresponding data\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.scatter(x1samples[:,0], x1samples[:,1], s=40, marker='o', color=[0, 0.8, 0], edgecolors='w');\n",
    "plt.scatter(x2samples[:,0], x2samples[:,1], s=40, marker='s', color=[0, 0, 0.8], edgecolors='w');\n",
    "plt.scatter(x3samples[:,0], x3samples[:,1], s=40, marker='^', color=[0.8, 0, 0], edgecolors='w');\n",
    "h = gaussian_ellipsoid(mu1, cov1, 2, color=[0.2, 0.6, 0.2]);\n",
    "h = gaussian_ellipsoid(mu2, cov2, 2, color=[0.2, 0.2, 0.6]);\n",
    "h = gaussian_ellipsoid(mu3, cov3, 2, color=[0.6, 0.2, 0.2]);\n",
    "h = gaussian_ellipsoid(mu_est_1, cov_est_1, 2, color=[0.1, 0.99, 0.1]);\n",
    "h = gaussian_ellipsoid(mu_est_2, cov_est_2, 2, color=[0.1, 0.1, 0.99]);\n",
    "h = gaussian_ellipsoid(mu_est_3, cov_est_3, 2, color=[0.99, 0.1, 0.1]);\n",
    "plt.title('Comparing estimated MLE Gaussians');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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