Count models with neuralnets.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Cross entropy and maximum likelihood\n",
    "\n",
    "\n",
    "In this notebook, I'll try to explain how to deal with count data using neural networks and how to implement in Python using [TensorFlow](http://tensorflow.org). Before going into details of count data modelling, let's first remember the link between the loss functions and maximum likelihood estimates.\n",
    "\n",
    "## Binary classification\n",
    "\n",
    "For classification problems, a commonly used loss (error) function in deep learning is [cross entropy](https://en.wikipedia.org/wiki/Cross_entropy):\n",
    "\n",
    "$$ H(p,q)=-\\sum_x p(x)\\log q(x) $$\n",
    "\n",
    "where $p$ and $q$ represents data and model distributions respectively and the aim is to make the model distribution $q$ (our predictions) as close as possible to $p$ (labels of the data) in terms of cross entropy. Therefore this quantity is minimized.\n",
    "\n",
    "If the task is binary classification, then it's called binary cross entropy (BCE) which looks like: \n",
    "\n",
    "$$ \\text{BCE}(y,\\hat{y})=-y\\log\\hat{y} - (1-y)\\log(1-\\hat{y})$$\n",
    "\n",
    "where $y$ and $\\hat{y}$ represent the ground truth (data distribution) and our prediction (model distribution), respectively. To see that it is actually the negative log likelihood of [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution), let's have a closer look at Bernoulli. Likelihood function of Bernoulli is given below\n",
    "\n",
    "$$ L_{bernoulli}(x;p) = \\begin{cases}\n",
    "                            p   & \\text{if } x = 1, \\\\\n",
    "                            1-p & \\text{if } x = 0.\n",
    "                        \\end{cases}\n",
    "$$\n",
    "\n",
    "$p$ here, in the interval $[0-1]$, is the only parameter of Bernoulli, which also corresponds to the mean of the distributon. Same likelihood function can also be expressed as \n",
    "\n",
    "$$ L_{bernoulli}(x;p) = p^x + (1-p)^{(1-x)}$$ \n",
    "\n",
    "whereas the negative log likelihood can be written as\n",
    "\n",
    "$$ NLL_{bernoulli}(x; p) = -x\\log p - (1-x)\\log(1-p) $$\n",
    "\n",
    "Here we, unsurprisingly, ended up with binary cross entropy and showed that binary cross entropy loss function used in deep learning is basically MLE of Bernoulli. (It is trivial to extend this to categorical cross entropy for multiclass problems. For regression and the link between the mean squared error function and MLE of Normal distribution, see chapter 5.5.2 in the [deep learning book](http://www.deeplearningbook.org/contents/ml.html).)\n",
    "\n",
    "In logistic regression (and deep learning for binary classification), we try to find the maximum of conditional likelihood, meaning that we estimate the mean parameter of Bernoulli ($p$) given data $X$: \n",
    "\n",
    "$$ \\text{arg}\\max\\limits_{W}\\,\\sum_i y_i\\log f(x_i,W) + (1-y_i)\\log(1-f(x_i, W))  $$\n",
    "\n",
    "where\n",
    "\n",
    "$$f(x_i, W) = \\text{sigmoid}(W\\cdot x_i)$$\n",
    "\n",
    "in a linear model. Sigmoid function here, which converts the linear transformation of the data into the mean of the distribution, is referred to as the *inverse [link function](https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function)* in generalized linear model (GLM) literature and stats community whereas it is called the *activation function* in the neural network community. We can formulate $f$ as a n-layer feed-forward neural network as follows:\n",
    "\n",
    "$$f(X, W) = g_n(... (g_2(g_1(X, W_1), W_2))..., W_n)$$\n",
    "\n",
    "where $g_n$ is sigmoid (bias terms are avoided for brevity). We can now generalize loss functions via formulations of MLEs: \n",
    "\n",
    "$$ \\hat{W} = \\text{arg}\\max\\limits_{W}\\, P(Y|X, W)$$\n",
    "\n",
    "Now let's explore how to model the count data using other discrete probability distributions such as Possion or negative binomial.\n",
    "\n",
    "## Loss functions for count data \n",
    "\n",
    "### Poisson case\n",
    "\n",
    "Now let's imagine that our labels, which were binary in previous case, can only take non-negative integer values ${0,1,2,...}$. Although, this might look similar to classification labels where we again have integer values, in this case there is no fixed upper bound and the variable is ordinal so that the distance between $1$ and $3$, and $1$ and $2$ are not the same as we have in categorical data e.g. one-hot encoded class labels. \n",
    "\n",
    "This type of data, called [count data](https://en.wikipedia.org/wiki/Count_data), can be generated through a process where the number of occurences of an event, is counted. If the interval where we count the occurences is fixed, then this process is called the Possion process and the data can be modelled using the [Possion distribution](https://en.wikipedia.org/wiki/Poisson_distribution). Now we can derive the loss function based on the Possion distribution, instead of Bernoulli:\n",
    "\n",
    "$$ L_{poisson}(x;\\lambda) = \\frac{\\lambda^x \\exp(-\\lambda)}{x!}$$\n",
    "\n",
    "where the only parameter $\\lambda$ represents both the mean and the variance of the distribution. The negative log likelihood is:\n",
    "\n",
    "$$ NLL_{poisson}(x;\\lambda) = \\lambda - x\\log{\\lambda}+ \\log(x!)$$\n",
    "\n",
    "For the maximizing the conditional likelihood, we can now define the minimization of negative log likelihood as\n",
    "\n",
    "$$ \\text{arg}\\min\\limits_{W}\\,\\sum_i f(x_i, W) - y\\log{f(x_i, W)} $$\n",
    "\n",
    "where we estimate the $\\lambda$ parameter of Possion conditioned on data $X$ and our parameters $W$.\n",
    "\n",
    "Now, the only missing ingredient is the correct activation function which was sigmoid in Bernoulli case. The exponential function (which corresponds to log link function) is the classical one used in Possion regression, which makes sense since it brings the range from ($-\\infty,\\infty$) to ($0, \\infty$).\n",
    "\n",
    "We can implement the loss function and test it simply by finding MLE of generated toy data and comparing it to sample mean which is an unbiased MLE of Possion mean parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set(color_codes=True)\n",
    "%matplotlib inline\n",
    "np.random.seed(42)\n",
    "\n",
    "# In the implementations, I try to keep the function signature\n",
    "# similar to those of Keras objective functions so that\n",
    "# later on we can use them in Keras smoothly:\n",
    "# https://github.com/fchollet/keras/blob/master/keras/objectives.py#L7\n",
    "def poisson_loss(y_true, y_pred):\n",
    "    y_pred = tf.cast(y_pred, tf.float32)\n",
    "    y_true = tf.cast(y_true, tf.float32)\n",
    "    \n",
    "    # we can use the Possion PMF from TensorFlow as well\n",
    "    # dist = tf.contrib.distributions\n",
    "    # return -tf.reduce_mean(dist.Poisson(y_pred).log_pmf(y_true))\n",
    "    \n",
    "    # last term can be avoided since it doesn't depend on y_pred\n",
    "    # however keeping it gives a nice lower bound to zero\n",
    "    return tf.reduce_mean(y_pred - y_true*tf.log(y_pred+1e-10) + \\\n",
    "                          tf.lgamma(y_true+1.0))\n",
    "\n",
    "# Apparently this is already implemented in Keras:\n",
    "# https://github.com/fchollet/keras/blob/master/keras/objectives.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's draw samples from Poisson:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
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9x0xIkqShGQQkSSqYQUCSpIIZBCRJKphBQJKkghkEJEkqmEFAkqSCGQQkSSqYQUCSpIIN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\nBTMISJJUMIOAJEkFMwhIklSw/w801qzmmy8megAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f406c3956a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# true Poisson mean parameter\n",
    "poisson_mean = 4\n",
    "poisson_numsample = 200\n",
    "\n",
    "# Poisson sampling is still not implemented in TF\n",
    "samples = np.random.poisson(poisson_mean, poisson_numsample)\n",
    "_ = sns.distplot(samples, kde=False, bins=range(max(samples)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we generated samples from a Poisson with $\\lambda=4$. Now we will estimate the mean using gradient descent in TensorFlow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial value of mean parameter: [ 0.00684278]\n",
      "\n",
      "--> Step 0, possion loss: 8.117\n",
      "--> Step 50, possion loss: 4.466\n",
      "--> Step 100, possion loss: 2.346\n",
      "--> Step 150, possion loss: 2.092\n",
      "--> Step 200, possion loss: 2.092\n",
      "--> Step 250, possion loss: 2.092\n",
      "\n",
      "Estimated mean: 3.805508613586426\n",
      "Sample mean: 3.855\n",
      "True mean: 4\n"
     ]
    }
   ],
   "source": [
    "# random poisson mean parameter\n",
    "param = tf.Variable(tf.random_uniform([1], 0.001, 0.01))\n",
    "\n",
    "# create the optimizer\n",
    "optimizer = tf.train.RMSPropOptimizer(0.1)\n",
    "loss = poisson_loss(samples, param)\n",
    "\n",
    "# let's minimize neg. log lik.\n",
    "train_step = optimizer.minimize(loss)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    print('Initial value of mean parameter: {}\\n'\n",
    "          .format(param.eval()))\n",
    "    for i in range(300): \n",
    "        sess.run(train_step)\n",
    "        if i % 50 == 0: \n",
    "            print('--> Step {}, possion loss: {:.4}'\n",
    "                  .format(i, loss.eval()))\n",
    "    print('\\nEstimated mean: {}'.format(param.eval()[0]))\n",
    "    print('Sample mean: {}'.format(np.mean(samples)))\n",
    "    print('True mean: {}'.format(poisson_mean))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Negative binomial case\n",
    "\n",
    "The major limitation of Poisson distribution is that the mean and variance are equal and are controlled by a single parameter, $\\lambda$. This, however, is not realistic in many real world cases. [Negative binomial](https://en.wikipedia.org/wiki/Negative_binomial_distribution) (NB) is another discrete distribution which can be used when mean and variance of the data are not equal. Although the classical textbook definition of NB is *the number of successes before a specified number of failures occur in i.i.d Bernoulli trials*, the alternative parameterization with mean ($\\mu$) and dispersion ($\\theta$) is more intuitive and useful. See these [lecture notes](https://www.unc.edu/courses/2010fall/ecol/563/001/docs/lectures/lecture6.htm) for a nice derivation of this parameterization. Here is the probability mass function according to this parameterization:\n",
    "\n",
    "\n",
    "$$ L_{nbinom}(x;\\mu,\\theta) = \\frac{\\Gamma(x+\\theta)}{\\Gamma(\\theta)\\Gamma(x+1)}\\left( \\frac{\\theta}{\\theta+\\mu}\\right)^\\theta\\left(\\frac{\\mu}{\\theta+\\mu}\\right)^x$$\n",
    "\n",
    "where parameters $\\mu$ and $\\theta$ represent the mean and dispersion. The negative log likelihood is:\n",
    "\n",
    "$$ NLL_{nbinom}(x;\\mu,\\theta) = -\\log\\Gamma(x+\\theta)+\\log\\Gamma(\\theta)+\\log\\Gamma(x+1)-\\theta\\left(\\log\\theta-\\log(\\theta+\\mu)\\right)-x\\left(\\log\\mu-\\log(\\theta+\\mu)\\right)$$\n",
    "\n",
    "Note that, this reduces to Poisson as $\\theta\\to\\infty$. Here we will use $\\theta^{-1}$ as the dispersion parameter since it is more convenient e.g. we can initialize $\\theta^{-1}$ to $0$. We can now implement NB loss in Tensorflow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# We need a class (or closure) here,\n",
    "# because it's not possible to\n",
    "# pass extra arguments to Keras loss functions\n",
    "# See https://github.com/fchollet/keras/issues/2121\n",
    "\n",
    "# dispersion (theta) parameter is a scalar by default.\n",
    "# scale_factor scales the nbinom mean before the \n",
    "# calculation of the loss to balance the\n",
    "# learning rates of theta and network weights\n",
    "\n",
    "class NB(object):\n",
    "    def __init__(self, theta=None, theta_init=[0.0],\n",
    "                 scale_factor=1.0, scope='nbinom_loss/',\n",
    "                 debug=False, **theta_kwargs):\n",
    "        \n",
    "        # for numerical stability\n",
    "        self.eps = 1e-10\n",
    "        self.scale_factor = scale_factor\n",
    "        self.debug = debug\n",
    "        self.scope = scope\n",
    "        \n",
    "        with tf.name_scope(self.scope):\n",
    "            # a variable may be given by user or it can be created here\n",
    "            if theta is None:\n",
    "                theta = tf.Variable(theta_init, dtype=tf.float32,\n",
    "                                    name='theta', **theta_kwargs)\n",
    "\n",
    "            # keep a reference to the variable itself\n",
    "            self.theta_variable = theta\n",
    "\n",
    "            # to keep dispersion always non-negative\n",
    "            self.theta = tf.nn.softplus(theta)\n",
    "           \n",
    "    def loss(self, y_true, y_pred, reduce=True):\n",
    "        scale_factor = self.scale_factor\n",
    "        eps = self.eps\n",
    "        \n",
    "        with tf.name_scope(self.scope):\n",
    "            y_true = tf.cast(y_true, tf.float32)\n",
    "            y_pred = tf.cast(y_pred, tf.float32) * scale_factor\n",
    "            \n",
    "            theta = 1.0/(self.theta+eps)\n",
    "\n",
    "            t1 = -tf.lgamma(y_true+theta+eps) \n",
    "            t2 = tf.lgamma(theta+eps)\n",
    "            t3 = tf.lgamma(y_true+1.0) \n",
    "            t4 = -(theta * (tf.log(theta+eps)))\n",
    "            t5 = -(y_true * (tf.log(y_pred+eps)))\n",
    "            t6 = (theta+y_true) * tf.log(theta+y_pred+eps)      \n",
    "\n",
    "            if self.debug:\n",
    "                tf.summary.histogram('t1', t1)\n",
    "                tf.summary.histogram('t2', t2)\n",
    "                tf.summary.histogram('t3', t3)\n",
    "                tf.summary.histogram('t4', t4)\n",
    "                tf.summary.histogram('t5', t5)\n",
    "                tf.summary.histogram('t6', t6)\n",
    "\n",
    "            final = t1 + t2 + t3 + t4 + t5 + t6\n",
    "            \n",
    "            if reduce:\n",
    "                final = tf.reduce_mean(final)\n",
    "            \n",
    "        return final"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's generate random samples from negative binomial using Gamma and Poisson distributions since it also corresponds to a [Poisson-Gamma mixture](https://en.wikipedia.org/wiki/Negative_binomial_distribution#Gamma.E2.80.93Poisson_mixture):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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RQ4QkSSpiiJAkSUWG6u4QEUcDnwSeC+wDbgTOyMxtEfEM4FPAauAB4OOZ+fGOfV8NnA8c\nDfwIODszb5rpQUiSpN4rGYn4ErAZeBxwLPBU4G8jYilwA/AvwCrgZOCDEfEygIhYA3wGeD+wnCqI\nrI+Io2Z4DJIkqQ9qhYiIGAY2Audm5khm/oYqGDwfeAmwCHhfZu7OzO8Anwbe2t79jcCXM/OLmflQ\nZl4JfA943ewciiRJ6qVapzMycztwWtfqJwCbqE5hfDczWx1td3Zsv5pqpIKu9rV1+iBJkuaG2nMi\nOkXEWuCdwH8FXgFs6dpkC7CyfX/VJO1Pr/OcjUYDaNJoDDA01GBoyLmhUxkcbOx3qwOzZmWsW33W\nrIx1q++RqlVxiIiI51DNj3hvZn41Il5R+FCtA2/ysCVLFgEwuncxhx++jBUrDil82oVleHhpv7sw\n71izMtatPmtWxrr1X1GIiIgTgc8Bb8/Ma9qrNwFP6tp0FdVVGuPtR0zQvqnOc+/Zs49ms8nIyF62\nbdsNLK7V94VmcLDB8PBStm8fYWys2e/uzAvWrIx1q8+albFu9Y3XbLaVXOL5bKrJlK/IzJs7mjYC\nb42IRmaO/6+eAGzoaF/T9XDHA1fXef5ms8lYs0Wz2WJ0tMnoqC+g6Rgbs1Z1WbMy1q0+a1bGuvVf\nrRAREYPA5cB7ugIEwFeAHcCFEfFhqgmTpwKvbLdfAWyIiJOB64A3U41c/EN59yVJUr/UHYn4Y+Ap\nwN9HxKVU8xkG2rdBdZnnOqpTFJuowsaNAJn5/Yh4LXARcBXwQ+Almbl5Ng5EkiT1Vt1LPG8FBg+w\n2XOn2H89sL7Oc0qSpLnJ62MkSVIRQ4QkSSpiiJAkSUUMEZIkqYghQpIkFTFESJKkIoYISZJUxBAh\nSZKKGCIkSVIRQ4QkSSpiiJAkSUUMEZIkqYghQpIkFTFESJKkIoYISZJUxBAhSZKKGCIkSVIRQ4Qk\nSSpiiJAkSUUMEZIkqYghQpIkFTFESJKkIoYISZJUxBAhSZKKGCIkSVIRQ4QkSSpiiJAkSUUMEZIk\nqYghQpIkFTFESJKkIoYISZJUxBAhSZKKGCIkSVIRQ4QkSSpiiJAkSUUMEZIkqYghQpIkFTFESJKk\nIoYISZJUxBAhSZKKDNXdISL+DLgKuDkzT+lqezVwPnA08CPg7My8qaP9o8CbgMOAbwFvycz7Sjsv\nSZL6p9ZIREScA3wCuHeCtjXAZ4D3A8uBTwLrI+KodvtZwBuAPwUeA/wM+KcZ9F2SJPVR3dMZI8Dx\nwE8maHsj8OXM/GJmPpSZVwLfA17Xbj8VuCgzv5eZO4F3A0+LiBMK+y5JkvqoVojIzE9l5o5JmlcD\nd3StuxNYGxGPAp7aXh5/rJ3Aj4G1dfogSZLmhtpzIqawCtjStW4L8HTgCGBgkvYjS56s2WyydeuD\njI01f7du+fLlNBrOFZUkqRdmM0RMpjXD9v1UIaHJnpGd3PrdraxYOQLAyK4d/MkfBytXrizs5sFp\ncLCx360OzJqVsW71WbMy1q2+R6pWsxkiNlGNOHRa1V7/ANCcon3alixZBMDSpYs5dNFhPPoxjwZg\nx7bFLF++jBUrDqnf8wVgeHhpv7sw71izMtatPmtWxrr132yGiI3Amq51xwP/mJl7I+J77fZbASJi\nJfCHwIY6T7Jnzz6azSYjI3sZGmuwe/dDAOwe2cvWrbtpNJbM9DgOKoODDYaHl7J9+8h+p340OWtW\nxrrVZ83KWLf6xms222YzRFwBbIiIk4HrgDcDTwI+226/FPhQRHwD+Dnwd8CGzOyejDmlZrPJWLNF\nq9VirFn9q9a3GB1tMjrqC2oiY2PWpi5rVsa61WfNyli3/qsVIiJihGoOw6L28suBVmYuy8zvR8Rr\ngYuoPozqh8BLMnMzQGaui4jHAF8DDgVuBk6etSORJEk9VStEZOaUYyGZuR5YP0X7BcAFdZ5TkiTN\nTU5tlSRJRQwRkiSpiCFCkiQVMURIkqQihghJklTEECFJkooYIiRJUhFDhCRJKmKIkCRJRQwRkiSp\niCFCkiQVMURIkqQihghJklTEECFJkorU+irwuazZbLJ164P7rVu+fDmNhjlJkqRHwkETIkZ27eDW\nux9g5ao9AOzevYMXHn8MK1eu7HPPJEk6OB00IQJgybJDOXR4eb+7IUnSguBYvyRJKmKIkCRJRQwR\nkiSpiCFCkiQVMURIkqQihghJklTEECFJkooYIiRJUpGD6sOmOvkx2JIkPbIO2hDhx2BLkvTIOmhD\nBPgx2JIkPZIc25ckSUUMEZIkqYghQpIkFTmo50R06r5awys1JEmamQUTIjqv1vBKDUmSZm7BhAjw\nag1JkmbTggoR01Wd+ti63zpPf0iStD9DxAS2bt3KTRvuZdmywwA/qEqSpIkYIiaxbNlh0z714ciF\nJGkhMkTw+yFg69YHaTVb097fkQtJ0kK0IENE9+WeW7c+yMZ/3cwhh1YhYPOmX3LIoSs4jBXTfsw6\nIxeSJB0MFmSI6P5yrvHQMB4Cdu3Ytt/23aGj2WwyMAADA9XpirojF5IkHQwWZIiA/S/37A4N3SYK\nHYONRaxc9Qe/W55q5KL7dMlU8yWcXyFJmi96GiIi4mjgMuC5wE7gM5n5F73sQ6nu0DEwuGjaIaRz\nzsSundt45lMezfLlDweOzpDg/ApJ0nzR65GI9cA9wFHAY4AbI+LXmfmJHvej58bnTOzasY1b7/63\n341qTBQSOudXdJ9KgXojGUNDDQ4/fOlsH44kSb0LERHxTOCPgP+YmduB7RFxIfAu4KAKERNN3Oyc\nM9E5qnGgbbtPpXSHjomuLOmcJLpn13Ze2NxDo7GE0dFmrVMjMz21Uuc0jiRp/unlSMRxwH2Z2Tn2\nfydwTEQckpm7etiXR9RkEzcnmjMxnW0PFDomurJkfPvdu7Zz03d+yrJDlrNj+9b9TqV0TxCdaMJo\n52PXPbXSeWrmQOEHZjZXZKr22Q5Ddfvay+eq+3xzxcFyHNJC08sQsQrY0rVufPlIYFohovql0mRg\nYIC9e3axe2eVSR7as4uBwcXTWq6z7UyWG40BAAYHBnhoz+4pn3uibSd67K2//TU3/Wovy1dUQeDB\n325i2aErOKwxPMn+u1m6bCmNRoOHRnZx0//51/32HWgsmnK5+7F37tzG0ND0frHv3LmNwYEBGo2B\n39t369YH+eYdP+VRS5a2+znC89c8ab+5Ip0OtP1U7XWfa3BwgGZzDzt2jDA21ppRXw+0bd3jnOn2\nj6TuutUxl46jl2ZSs4Wsbt2cUwaDg49MIB9otXrzwo2I9wEvzcwTOtY9GbgXeFJm/rwnHZEkSbOi\nl2OFm4Ajutatat9u7mE/JEnSLOhliNgIHB0RneOTJwA/yMzdPeyHJEmaBT07nQEQEbcBPwPeATwB\n+Crw4cxc17NOSJKkWdHrqc8nA8uBXwFfAy41QEiSND/1dCRCkiQdPLwIW5IkFTFESJKkIoYISZJU\nxBAhSZKKGCIkSVIRQ4QkSSrSyy/gKhYRRwOXAc8FdgKfycy/6G+v5p52nT5JVad9wI3AGZm5LSKe\nAXwKWA08AHw8Mz/et87OQRHxceDMzGy0l18AXAwEcD9wfmZe3ccuzikR8QHgdOBQ4DvAmzPzPus2\nsYg4DvgYsAYYofqsnHdl5oPW7GER8WfAVcDNmXlKV9urgfOBo4EfAWdn5k0d7R8F3gQcBnwLeEtm\n3tebnvfPAWr234APAk+i+oymj2Xm5R3tZwJnUX0R5j3A6Zl513Sfe76MRKyn+u6No4DnAa+KiHf1\nt0tz0peovofkccCxwFOBv42IpcANwL9QfV/JycAHI+Jl/eroXNMOWa8DWu3lxwLXApcDK4CzgSsi\nYk3fOjmHRMTbgROB44HHAz8HzoqIo7BuvyciGsCXgduovkPoqcBjgEut2cMi4hzgE1RfzNjdtgb4\nDPB+qg8t/CSwvl0/IuIs4A3An1LV9mfAP/Wk4310gJqtBf4BOBcYBt4JfCointNufzlwAfB6qr8N\nXwFuaP/NmJY5HyIi4pnAH1G9o96emfcCFwJv7W/P5paIGKb6fpJzM3MkM39D9QP3fOAlwCLgfZm5\nOzO/A3waawhARAwAl1K9Exx3CnBvZl6SmXsy83qqX/Sn9aOPc9B7gP+Rmb/IzG2ZeVpmnol1m8y/\nAx4NXJ2ZY5m5lerN0WqsWacRqmD6kwna3gh8OTO/mJkPZeaVwPeowj/AqcBFmfm9zNwJvBt4WkSc\nMMFjHUymqtkRwF9m5pczs5WZXwO+S/VmHKqaXZmZt7T/blxA9UbqpOk++ZwPEcBxwH2Zua1j3Z3A\nMRFxSJ/6NOe0A9ZpmflAx+onUI3grAa+m5mdH096J7C2l32cw94G7AI6h4+PA+7o2s6aAe13fo+n\n+hm8NyIeiIhrImIl1WvNunXJzF9S1eHNEbE0Io4EXgFcjzX7ncz8VGbumKR50jpFxKOoRnfu7His\nncCPOcjrOFXNMvPGzPyr8eWIGKQa0f9Ne9VENb2bGjWbDyFiFbCla9348pE97su80R7GeifwUSav\n4cpe92uuiYhHA+dRBYlOk9XM11x1uqwFvJTqHdCxwBOphuOt2+ROBl5GNa/r18AA1dC8NZueqep0\nBFU9rePU/gbYA1zTXp7xa28+hIip+MUfE2if77oReG9mfrXf/ZnjLgYuy8wfT3N7X3PVqbEh4M8z\nc2v7XfZ5VH8gJ6vPgq5bRCymGnW4hmoi6mOA7cDnpthtQdeshgPVyToCEXER8CrgP2fmSHv1jH9e\n58PVGZuoUmanVe3bzT3uy5wXESdS/WJ6e2aOp81NVDNzO62iukpjwWrPiF9LNZsbqncy4yZ73W3q\nQdfmuvF3Lts71t1HVb8hrNtEXgj8+8z8QHt5JCI+DNxFNenZmh3YVD+TDwDNKdoXrPacr89QXRX0\nrMz8RUfzZiau2T3Tffz5MBKxETg6IlZ0rDsB+EFm7u5Tn+akiHg21YvlFR0BAqoaHtueIT7uBGBD\nD7s3F72Wamj+lxGxmerc4EBEbKL6Ieo+L3g81gyqS+u2U/1SGvdEqsuKb8C6TWQAaLR/oY9bTPWO\n72as2XRsZP/XHFR1+k5m7qWaZPm79vYcnT/EOn4SOAZ4dleAgK6atv9GrKZGzeb8SERmfjciNgD/\nMyLeQTVZ8L3Ah/vbs7mlPWHmcuA9mXlzV/NXgB3Ahe13P2upZuW+sre9nHPOAj7Qsfx44NtU5/iH\ngHMj4gxgHdXljC+i+qW1oGXmaERcCVwUEScBY1SnM64CPkt1+bB129+3qX4Gz4+IvwaWUv0eu42q\nZh+yZgd0BbAhIk4GrgPeTDXC+tl2+6VUdfwG1SXHfwdsyMzuiYMLRvvU9muAp2bm9gk2uQz4QkSs\nB26n+jneTVXfaRloteb+6aL2bPB1wH+iegd0SWb+ZX97NbdExH8Avgk8RPWup9VxG1TnYddRpcxN\nwF91fuCIfvdhXT/NzMH28nOoPqArqH4pvTczv9THLs4ZEbGIaj7Ja4FRqs8oeVdm7rJuE2tPdv4b\nqit/HgL+merDkn5lzSoRMUL1O2tRe9Uo0MrMZe32lwEXUQX+HwLvzMxvdex/Hg9/ANrNwNsy81e9\nO4Lem6pmEXEF1Wdn7Ova7ZbMfFF7/7cA76OaTHk7Vc1+ON3nnxchQpIkzT3zYU6EJEmagwwRkiSp\niCFCkiQVMURIkqQihghJklTEECFJkooYIiRJUhFDhCRJKmKIkCRJRQwRkiSpiCFCkiQV+f8K2gKs\nRranbgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4028e74e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def random_nbinom(mean, disp, n=None):\n",
    "    eps = 1e-10\n",
    "    # translate these into gamma parameters\n",
    "    gamma_shape = 1 / (disp+eps)\n",
    "    gamma_scale = (mean / (gamma_shape+eps))+eps\n",
    "    gamma_samples = np.random.gamma(gamma_shape, gamma_scale, n)\n",
    "    return np.random.poisson(gamma_samples)\n",
    "\n",
    "nb_mean = 4\n",
    "nb_disp = 5.5\n",
    "nb_numsample = 1000\n",
    "nb_samples = random_nbinom(nb_mean, nb_disp, nb_numsample)\n",
    "_ = sns.distplot(nb_samples, kde=False, bins=range(max(nb_samples)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's jointly estimate mean and dispersion parameters using batch gradient descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial (random) value of parameter mu: [ 0.00910472]\n",
      "Initial value of parameter theta: [ 0.69314718]\n",
      "\n",
      "--> Step 0, nbinom loss: 14.97\n",
      "\n",
      "Estimated parameter mu: [ 0.04072684]\n",
      "--> Step 200, nbinom loss: 2.568\n",
      "\n",
      "Estimated parameter mu: [ 1.42107105]\n",
      "--> Step 400, nbinom loss: 2.083\n",
      "\n",
      "Estimated parameter mu: [ 3.1341207]\n",
      "--> Step 600, nbinom loss: 2.046\n",
      "\n",
      "Estimated parameter mu: [ 4.27606487]\n",
      "--> Step 800, nbinom loss: 2.046\n",
      "\n",
      "Estimated parameter mu: [ 4.28098059]\n",
      "Estimated parameter theta: [ 5.53214502]\n",
      "Sample mean: 4.276\n",
      "True parameter mu: 4\n",
      "True parameter theta: 5.5\n"
     ]
    }
   ],
   "source": [
    "# nb mean parameter should be positive\n",
    "# we can ignore it for now though\n",
    "param_mu = tf.Variable(tf.random_uniform([1], 0.001, 0.01))\n",
    "nb = NB()\n",
    "nbinom_loss, param_theta = nb.loss, nb.theta\n",
    "\n",
    "optimizer = tf.train.RMSPropOptimizer(0.01)\n",
    "loss = nbinom_loss(nb_samples, param_mu)\n",
    "\n",
    "# let's minimize neg. log lik.\n",
    "train_step = optimizer.minimize(loss)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    print('Initial (random) value of parameter mu: {}'\n",
    "          .format(param_mu.eval()))\n",
    "    print('Initial value of parameter theta: {}\\n'\n",
    "          .format(param_theta.eval()))\n",
    "    for i in range(1000): \n",
    "        sess.run(train_step)\n",
    "        if i % 200 == 0: \n",
    "            print('--> Step {}, nbinom loss: {:.4}'\n",
    "                  .format(i, loss.eval()))\n",
    "\n",
    "            print('\\nEstimated parameter mu: {}'.format(param_mu.eval()))\n",
    "            \n",
    "    print('Estimated parameter theta: {}'.format(param_theta.eval()))\n",
    "    print('Sample mean: {}'.format(np.mean(nb_samples)))\n",
    "    print('True parameter mu: {}'.format(nb_mean))\n",
    "    print('True parameter theta: {}'.format(nb_disp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Negative Binomial Regression in Keras\n",
    "\n",
    "## Generate toy data\n",
    "\n",
    "Let's generate a toy data with 1000 observations, 10 features (predictors) and 10 response (output) variables:\n",
    "\n",
    "$$ \\textbf{Y} \\sim \\text{NB}(\\exp(\\textbf{X}\\cdot \\textbf{W}), \\theta)$$\n",
    "\n",
    "where $X\\in \\mathbb{R}^{1000\\times10}$ and $W\\in\\mathbb{R}^{10\\times10}$ are randomly generated data and parameter matrices, respectively.\n",
    "\n",
    "Finally, we sample from negative binomial where the mean is $\\exp(\\textbf{X}\\cdot \\textbf{W})$ and the dispersion parameters for response variables are sampled from $\\text{Uniform}(0, 2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  0  1  2  0 15  1  1  3  0]\n",
      " [ 1  0  1  0  2  0  0  0  2  2]\n",
      " [ 0  0  0  2  2  0  2  2  0  1]\n",
      " [ 0  0  1 19  0  0  3  2  2  4]\n",
      " [ 4  0  0  4  0  0  2 18  0  0]]\n"
     ]
    }
   ],
   "source": [
    "num_sample = 1000\n",
    "num_feat = 10\n",
    "num_out = 10\n",
    "dispersion = np.random.uniform(0, 2, [1, num_out])\n",
    "\n",
    "X = np.random.normal(0, 0.5, (num_sample, num_feat)).astype(np.float32)\n",
    "W = np.random.normal(0, 0.5, (num_feat, num_out)).astype(np.float32)\n",
    "b = np.random.normal(0, 0.5, (1, num_out)).astype(np.float32)\n",
    "y_mean = np.exp(np.dot(X, W) + b)\n",
    "y_disp = np.zeros_like(y_mean) + dispersion\n",
    "\n",
    "Y = random_nbinom(mean=y_mean, disp=y_disp)\n",
    "print(Y[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use matplotlib to visualize the comparison of true parameters and the estimated ones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def visualize(x, y, x_label, y_label):\n",
    "    x, y = x.squeeze(), y.squeeze()\n",
    "    plt.scatter(x, y)\n",
    "    plt.plot([min(x), max(x)], [(min(x)), max(x)], \"g--\") #poor man's abline\n",
    "    plt.xlabel(x_label)\n",
    "    plt.ylabel(y_label)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement a neural network model in TensorFlow using NB loss function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Summary name fc/weights:0 is illegal; using fc/weights_0 instead.\n",
      "INFO:tensorflow:Summary name fc/biases:0 is illegal; using fc/biases_0 instead.\n",
      "Step 0 - nbinom loss = 1.715, (0.024 sec/step)\n",
      "Step 100 - nbinom loss = 1.476, (0.009 sec/step)\n",
      "Step 200 - nbinom loss = 1.366, (0.004 sec/step)\n",
      "Step 300 - nbinom loss = 1.362, (0.005 sec/step)\n",
      "Step 400 - nbinom loss = 1.362, (0.004 sec/step)\n"
     ]
    },
    {
     "data": {
      "image/png": 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mIiID7+ChfC443onDXWtJdC6ODAQ/RbIzgWfCH0eXZ68FJvc1IBER6V+9FcEuLlvEz+55\nkIz5LqH9Y2jddjh7N64mPdfhxptv6bhX5+JIf/OToNQD04F3u1w/Htjb14BERKSzQ+2qSfRZPRXB\nGnM4laOryDu1jja3nUDOXqr+tY6sopNoK5jC1i4FszoXR/qTnwTlXmC5MeYHgGOMmY+XnHwbWJ7E\n2ERERrx4dtUkIlYRLEXzuWfVw4xpGM3GfZsBCDpBMndkU1h8Bk64vVXkXjVfk4HgpwblBuAlYCVe\nw7aXgN8Aj+AlKSIikiTx7KpJRH1z55OGwSVt4hZqj6ruSE6KcyZz/QlfoX1TTkdyEuE4jreLR6Sf\n+emDcgD4sjHmemAWXh3KRmttY/gwQRERSZJ4dtUkomMHTjhJSZ/+FmnjtwPerMk500+juHkKd/xm\nOVu27aCpvZr8yUeQne+VGKr5mgwUP9uMN1lrZ1prG4B1UdcLw58XJzG+yLOnAbcBpwD7gT9aa2+I\ncd+NwPc4eD6Qg5dATbPWVic7LhGR/tY1oYD4koRI3cr+Ay5j8jK46KNnMmf2HBaXLWLpspUQnpVp\n3VVMsGg74zPHctWxn6Zuex1Lf+ctKeXPOZo816Vm4xoAsvImHbL5WjLrZWRkiztBMcYch1drcpgx\n5iq8v/yjzQEKkxhbtIfwkp/JwETg78aY96y1t8a490/W2iv6KQ4RkQHVNaGI1aE1khRUVu1hz57d\n5OSPpaq6mrxpCxhVMIU9B1xu/u1DfCtct9JpB47rcMq4RSw86hSCgSB3rFjebUmpaNYCatc/wJy5\nh/e6WyfZ9TIysiUygzIJ+BzeYYC3x/h6IxArYegTY8wJwJHAh621dUCdMeaneGcCJf37iYikkkNt\n6Y0kBc3pk2jcX8/Yko/jOA4TJrns3rQGx3HIzp+MG1Xc2tsOnJ6WlGbOnM1NS67tNdaeCnBVVCt+\nxJ2gWGsfBR41xlRaayf1Y0xdHQtsttbui7r2CjDHGDM6vNQU7WhjzL+AUuAdYIm19okBilVEJOl6\nSygiSUG9fYrx5rROycHYmQuosk+RnT857roVv0tKkPx6GRnZEt7FE0lOjDFBY8yM5IfUTRGwp8u1\nyOfjulzfjpeUXI4343M38H/GmDn9GqGIyCCJ7MoJBNO77M4Bx4H8uQ5pE9+NO8mI1SV278bVnHjs\n3EO+9mAX2oNUVCt++SmSzcI7i+dKvALUTGNMAXAPcGmXmY7+1un/BGvt74HfR1261RjzCeBTeMWz\ncQkGfZ2hOGJFxkvjFj+NmT8jYdzWV1Tw5/tXUd8cIjcrwKUXLmJuSUmP9+dlB6h1XULtrbhRMx9O\nZgPpM94gO68VN7SBti27uOyyC0lL633sjjqylE+cvYVf/+/9ONnjcENt5E4s5b4nXmf27Bm9xnLZ\nRedy828fwo2ql6FmLZddfcEhv2+qGQnvtWRL9lj52Rb8Q+Ak4FLgT1HXM4BfAFclIa5oVcDYLteK\nwr/HszPnXbzC2rjl5WUncruEadwSpzHzZ7iO27o317P0jpWECo/DyXLY47osvWMl//mNbOYdGXsG\n4/Of/Tjf/eVycieWsnvTGsbOPJm0iVtJP2wDTtA7SyejOY0vfOZcFhw/P644Xn5jA+PnXdhlmWcy\n9z/8OLec1PMzFpw0n5/kZvOHPz/MvoY28kcF+ey3PtFj7EPBcH2vDQV+EpQy4Fxr7QZjzJ8ArLV7\njTGfBV5OanSel4BpxphCa21t+NqJwHprbWP0jcaYbwPPWWufjb6M1/02bnV1TbS3h/oS84gSDAbI\ny8vWuCVAY+bPcB+32//wgJecRNWRhAqP4/Y/PsB/fmdazNcUT5nG9Z87n7888Dd2pLUQmraKjInh\nP9pDcNKY47nmos/QuL+F2tquJXux7alrwcnqXkuyu671kM8onjKN7193Tadr8X7fVDLc32v9ITJm\nyeInQZkMvB3j+i4gr2/hdGetfd0Y8yLwG2PMl4CpwPXATQDGmArgCmvt83jbnH9jjLkA2Al8Ga+Z\n3B8T+Z7t7SHa2vSGTJTGLXEaM3+G67jVNYViFpnWNfb+886ZPYdFlzdwd/m9tLneH+uhhjwObDyS\np7Zt4LQpluIp0+Ies5xMb/ama6FsTibDctx7M1zfa0OBnwWjbcDJMa5fCGztWzg9uggowEs6Hgd+\na629I/y1w4Gc8MdLgCeB54D3gI8Cp1prK/spLhGRpOlLkem4UWNpC7Xjhhxat8/mwPr3Q3MeFM3n\nD/esTCiOWIWybs1aFpctSug5In3hZwblFmClMeb3QNAY8w28Bm4fA76azOAirLU7gfN6+Fow6uM2\n4BvhXyIiQ0o8Tdl6Mj1vKmlv57H/wFG4Tbkd1x3HYV9je0JxHKr3ishA8LPN+HbgC8AHgQa8AwKn\nAZdZa29LbngiIiNHJDGY6rxBQdNrTGVdQl1YC2pHE2rM6XTNdV3yRwV7eEXvsSy+4Bxys7zDAZev\nWEV5hU34OSJ+OV2nEwW3trZBa44JSEsLUFg4Go1b/DRm/mjcetep1XzUNt+ffOsTCdWg9PQst2bt\niGlbr/da4sJjlrSmN75OHzbGHAWUAN3Kda21f+r+ChER6Yuqxmq21e9g/oRjerwn1tLMZVdfwLwj\n5ya8k0Zt62Ww+WnUdjPeLppYXDr3RhERkT4IuSGe2b6Ghzc+hovLlJzJTBw9vsf7u7bF99sgTW3r\nZbD5mUH5HPBp4AFrbVOS4xERGXYipw3XN3s7chaXLYprmaSqsZq7y+9j477NAASdIFvqtvWaoCRL\nX87kEUkGPwlKO/AXa21iZeEiIiNQp1qObO8v/aXLVvZayxE9a9IaagWgOGcyC7JPZNUfn+Wvzf9I\nKNHxoy87ikSSwU+CcjveLMpvkxyLiMiwE6uWoyl9Et+7+b+YOn12t0SjqrGGu8vv7TRrcs700yhu\nnsIvfvdIQolOX2irsQy2hHfxGGOmAc/g1ZtsBTqVN1trT01WcINEu3gSpGr3xGnM/BmK4/b1G3/F\n3uyDha1N+3bSULOJsTMXdJqZuPiMo3nh1fXsyzxA69F7wPFmTT419xKm5EzixptvYSvzui25FNQ/\nT15uTo/LR0NxzFKBxi1xqbCLZzmQDqwBGg9xr4jIkOG3VqQ3XWs56irXM96c1m1GZdn9/6Rg1kKc\nFoe0ygrc+irO+/BZTMmZBPRctPr2tlrGzT0ZJ9th594dfOOmW5h6WDETxoxicdkijjqytE/xiwwW\nPwnKMcB0a+2uZAcjIjJY/NSKxKNrLYcTSOs0CwJQ/155p6SlbXsJrmv4wU9/w4+WfJXSEtNj0Woo\nkOklOft20rj7XSbMu4gWx2FrOP5vX+2woJcTiEVSlZ/9ZxVAW7IDEREZTLFqRZxw34++iNRy1K5/\nkOq3/0HTvh3dztuJlbQ4jkNzsIily1ZSXmFjno9T+85q8icfAXgzM5Flo+j4//xA3+IXGSx+ZlC+\nDvzeGPNbYAvda1A2JCMwEZGB1J99P0pLDEfPnc1W5tFct5O6Pc+SN+aDHTUooaYqXNelua6Susr1\nBILptLe10HZgP87hHwo3R7u2W9Fq/rgA+/K8JaBAMD1mkqO+JTJU+UlQngr//lG8QtkIJ/x54oc+\niIgMsv7u+7G4bBE/u+dB8k90CYxuZsfKJ2nfd4DDiwu56PIy7lzxNI3tmR1LPa7rUvPOszTXVVKf\n4f1R27UJW2RZiqL5hNpbcWPFn62+JTI0+UlQzgRakx2IiMhg6s++HyE3xHujq8k7tY4212shNXtB\nJv9x7Gc66lueePZF9uae3GmJpmj2B9lV8SRzSmI3ZoveCpxeGKR642qv0DYq/kuvvqDP8YsMhoQT\nFGvtkz19zRjze+AffYpIRGQQJKvvR9edQGd/5AP868BL3fqanPnhhQQDByecnfTRMZdoAqEDLC5b\n1GvckVmV8grbLf65JSUJxS+SKvweFngm8H4gK+ryVLxlnyuTEJeIyIDruoSSqM47gaB+/BbuqrwP\nJ5yHRPc16aqnJabDiwvjTpL6Gr9IKvFzWODXgF8C7wETge3AZOBdej5EUERk2IveCeSM3kvG9Arv\nCyE4b9aZnDmt86xJtJ6WmD531cUD+BOIpA4/24y/BJxrrZ0CtFhrpwHT8BKUfyczOBGRoaS++eAM\niNtQQFtVMaGGPNJfGcs5M07vMTmBg0tMU503KGh6jams67c29iJDgZ8lnknW2sfCH7sA1tqdxpgv\nA3cCJycrOBGRoaTrMk3r1hLcEIx334zr9bGWaPqju63IUOBnBmWfMWZq+OPdxpji8McbgXnJCUtE\nZOjp1kytPYBb/WqvRa69idS0bGUee7OPYSvzOhq3iQx3fhKUR4B/GGNygJeAu4wx5wO3ApXJDE5E\nJJW1tHfuuJDsZZr+6m4rMhT47SR7M9AMLAEeBlYA+4BPJy80EZHB0XVZ5cRj5/LCq+s7Pr/kgnN4\nL6eax7es5lvHX8OYrMKO1yZzJ01/drcVSXV++qA0Al+NfAoYY8xYoNZaqzOpRWRI63po4M69O3jl\n3n9SdPhCnGyHvRn7+fVbfyI4xjuSbLldwRePvqLHZ/WlfqS/u9uKpLKEEhRjTBqwGyiw1nak8Nba\n3ckOTERkIEWSiTff3k5Tewb5GZVk50+OOmkYghM2k37YBpyg92+x4pzJnD/rnB6f19fTkfuzu61I\nqkuoBsVa2wa8BZzSP+GIiAy86GLU/DnnMqHkdBpqNtG0byeBYDqBrEYySl8kY1oFTjCEG3IIvpvD\ndcdfE7PpGiSnfkRbj2Uk81OD8ne8wthX8HbutER/0Vr77WQEJiIyUGIlE2NnLqDKPkVwlEvmkWs6\nZk1CDXkc2HgkxU3v9trXJFn1I+oOKyOVnwTlM0AIOCb8K5oLKEERkSGlp2QiEExnVN5sGja/xegZ\nDm07Z9G6c4a3dbiXZZbyCsvWze+QW3K06kdEfPJTJDujp68ZY8b0LRwRkYHXUzFqsKUak1/AccUf\n4MW3ymnas5/crDd7PUQwslyUNukkdm9aw9iZC1Q/IuKDr8MCYwn3RXkLiL0gKyKSonoqRr35O1/t\nSETOP/u8uJ4VWS4a5Tg4jkOVfRonECSrvYYfLfmq6kdE4uTnsMBxwH/R/TTjfKAqSXGJiPSrrluA\nLz7jaF547Q3qm0LelmCfxaiVVXuoqn2KQDCdUHsreZPmkp0/mYKm15SciCTAzwzKr4FS4C/At4Cf\nACcAucAnkxeaiEj/iN4CHChopHFqBfc9+wrf+vTH+pRElFdYquvd8LZkbyZm96Y1uK5Lcb5qT0QS\n4afV/ULgLGvtd4BWa+2N1tpFwPPAx5IanYhIP/CWYY4jbeIWMo9cQ7Cwmsz5afxlxaN9fm7BrIXd\ndgPVbVnj+zwekZHKT4Iyylq7K/xxuzEmss/uRxzsMCsikrL2Oa1kzn2pU1+TUEM+9c19ayFf39y5\n0Ba8JGVqcbGWd0QS5CdBedcY86nwxzuAM8IfjwbGJiUqEZF+EHJDPL3tn7TOryGYW+tda8jjwFsn\n07pjFnlZfv5IPCg3y+k4ybhp3052VTxJ1YZnqNm1QycQiyTITw3KL4A/GmMeAe4D/mqMeRo4Gm+Z\nR0Rk0PR0/k1Lewv//drv2LhvMwTBDUHrjtm0vzcTN+QkZQtwZDdQU/okGne/26kWJdE29yIjXcL/\nXLDW3gUcb63dC/wA+CleovMoOs1YRAbRqsf+zrd/cRdbmcfe7GPYyjyWLltJeYUlI5hBQWY+4J2h\n84kJZUyubKSgcV3SWshHWtO3vffvjv4n4K/NvchI56sPirX21fDv7cDNSY1IRMSH8grLf9+5ggnz\nLuqUGBBODG5aYrh4zgUU507h1OJTCAaCnHLUSUmPo7TEMHXaLPbGqEVJtM29yEjmpw/KKOBnwPnA\nZOAAsA1v2/FPrLUtvbxcRKRfLF+xikD2+JhFqpHEICdjNGdM+3C/x9JTZ1q1uReJn5+KsP8BPo6X\nkHwZ+Cbwf8AX8Bq4iYgMuPpmFzfU1lGkGjEYicHiskW4NWs7Yuloc6+txiJx87PEcy6w0Fr7VvRF\nY8yfgMeBq5MRmIhI14LXyy46lwUnzY95b04WFJ0wntryf1I45ZSO4tS9G1fzrW9+KuZr+kukFmX5\nQ3/rc2cuc90jAAAgAElEQVRakZHKT4LiAOUxrlcAPZ89LiKSgOhur062t2Ry828f4ie52RRPmdZx\nz/IVq6ijleZZ1eQUOTjZsPXRv5CWmUvQbeLLl5cNSmJQWmK46QYlJCJ++VniuQe4Isb1y4G7+xZO\nbMaYacaYvxlj9htj3jPG/LSXe79qjNlsjGkwxvzLGHNsf8QkIv0rcuhe14LXP9yzEogkMA+xc0I+\nB47fTaDIuy97XB5TT7yQUaNG8+XLy1h09lmD9jOIiH9+ZlAygJ8bY67BO704ABhgNvCgMeZ/Izda\na2MlMn48BKzDK8qdCPzdGPOetfbW6JuMMWXAD4GPAC8B1wGPGmNmWWubkhSLiAyA+mYXJ7t7weu+\nxnYA7ln1MFmntBPMqwDADTm07ZxFW+VMHDdAwayFvPDquqQnKD31WRGR5PIzgzIPeA3YA0wCJgB7\ngZeBqcCMqF99Zow5ATgS+Iq1ts5auwGv98rnY9x+JfB7a+2z1toma+0PARf4aDJiEZGBE92VNcJ1\nXfJGBXhqyz+pPaqaYN5eAFr2OBx462Tads4G1/tjzXGcPreu7yqy7BSrz4qIJFfCMyjW2g/0RyC9\nOBbYbK3dF3XtFWCOMWa0tbYh6vpxeLuLor0GHA/8tX/DFJFkinRlJbzM47ou1Kzls9ct5tGaZ8Ld\nYL1Zk52r32X8nByidxi7rovb2sCNN9+StNmOnpadIn1WRCR5fDVqG2BFeLM10SKfjwMa4rh3XCLf\nMBjs23kcI01kvDRu8dOYxba+ooI/37+K+uYQuVkBPnH2Mfz7lTepawqRm+3wyS99jKOPOoIx1UXs\nfn4PGx5vxM2cRd7EUdRsXEPRrAUdyUxr5b+pPNDM3tyTO4psf7ZsJUuuvoC5JSW+4tt/wMXJ6r7s\ntL8Z0tJS87+l3mv+aNwSl+yxGgoJSm+6zt/2NJ+b0DxvXl62v2hGOI1b4jRmB617cz1L71hJqPA4\nnCyHPa7Ltide4T+/sZh5R87tdG/xuAn88vzvsW7Wev7w54fZ195GKA0CB16EtFHkjwpSm99OzahT\nO812uEXzuf/hx7mlh63KhzImL4M9B7o3YBubl05h4Wj/P/wA0HvNH43b4BkKCUoV3U9JLgr/Xt3l\nenUP965L5BvW1TXR3h5K5CUjWjAYIC8vW+OWAI1Zd7f/4QEaAhOpt08RCKYTam8ld2Ipt//xAf7z\nO9624q7jVjxlGt+/7pqYz/vqd38Rs6vs7rpWamsbYr7mUC766Jnc/NuHcLssO1149QW+n9nf9F7z\nR+OWuMiYJctQSFBeAqYZYwqttbXhaycC6621jTHunU94u7MxJoBXl/K7RL5he3uItja9IROlcUuc\nxuygnbt207i/jvHmNAJZjYRa09j99kvsPNDabYziGbecTG8WputsR04mvsd8zuw5fCtGA7Y5s+ek\n/H9Hvdf80bgNHj9n8ay21i6Mcb0QeNxae0JSIguz1r5ujHkR+I0x5kt4O4WuB24Kf98K4Apr7fPA\nbcC9xpiH8HYVfR9oBB5JZkwikhzRW3Y3b9nClBM+TdrELaQftoH22omMbV/AnooHfD07VpGtW7OW\nxVed36eY1YBNZGDEnaAYY2bi9To5yRhzBl5H2WglwNxuL0yOi4A7gJ1AHfA/1to7wl87HMgBsNb+\n3RhzHXAnXmHsy8AiHWAoknq6dorNmryLzLkvEcz1JkqDYyoJ7JhF0YQpHa9ZX1HBfQ8/zp66Ftqb\n9+IE0nHSR8fcoaN28yJDWyIzKCcBtwDpwN97uOeuPkcUg7V2J3BeD18Ldvn8DrxkRkSi9EeDsb48\n8+CWXQhO2MyU41wCaV5yEmrIo2XTUYSaRzGhcFTH9/pZeEak+UAl+2v2UzTrZBzH26GzdNlKru+S\ngGi2Q2TointPkLX2HrymbK10bsYW+TXeWnt5fwQpIn3THw3G+vrM+maXQFYjGaUvkjGtgkAauO3Q\nsm02B9a/n1BjTqcTgJevWOUlJ3WVVG1YjRtqo8o+RdO+nTiOgxPuRyIiw0NCNSjWWtcYM95aW9df\nAYlI8vVHg7G+PjM3y6Gh2HYs6YQa8qh7fTwt77xO8bT93ZZk6ptdmlsqaajZxNTjL+2oK9m9aQ0A\n2fmTqW9KbudYERk8fnbxZBtjfojXfn5U1y9aa0/uc1QiklQ9nWvTl7/Q+/rMxWWL+NldDxL8YDpt\nu6bRunMG6bWv8t0bvhJzmSg3y6Fi81tMKDm9U1I0duYCquxTZOVNIjera2mciAxVfhKUPwHHAE8D\nzckNR0T6Q26WV6fRdcttX/5CT/SZ0fUqbmsDbqiVzPZMqu/bS2FugKnjG3otYl1ctoi1P749Zm8T\nJ5CWlB06IpI6/CQoJwNHWWs3JzkWEeknydxyG0k0Kqv2sLd+NQWzFh7ymV137LhZLjUb15Azbho5\ns95P9cbVwB6Wr1jF4jJiJimlJYY5UwtjJkVNe97l4os/qR06IsOIn8b5+/C2+4rIEBHZcjvVeYOC\npteYyrpuO17iEV0Y2zZhIZlFhl3r7idjz79iPnN9eQXf/+mvWPLj/+pWr1I0awF1letxHIeCWQvZ\nUdt+yELbL3z2EvZueqbjlONIDcq4kjN54dX1PkdHRFKRnxmU/wK+CNya5FhEpB8lY8tt18LYUQVT\nyM6/kKx9/wBGsewvj5KbtYrFZYvY21bHnRUrcKdPoP3tcTGXZgLB9E4fH6rQdm5JCZMKgmyxTxMI\nphFqbyVv0txwgWzXky9EZCiLK0Exxvxvl0tnGWM+CbwDdOoBbK29NEmxiUiKiVUY21xXSW11iML8\neeFTg0P88onlZJY0EBwDsIP0oiBujKWZUHtrt48PVWg7ZVIRTWNKk1pPIyKpJ94lnq49TzYA9Xh9\nUSZ1+SUiw1RultOxvBKxb+dbFM726lCczAYy575E5hENEAQ35NC6fTaZwbns3rSm09JMzcY15E2a\n27FMkzdpbsfXeks2rrjsfKhZ2+lZ0f1SRGR4iGsGJdbZOyIy8sQqtg2EDnR0g00/bANO0JtUbd3j\n0rb9ZGjOIzsPcB22vvRnsgum0NZcTyjUTntrI9VvP0vR7FPIzp8cV/HuvCPnsuTqC7jn/lVqYS8y\njPk5LPA0vG6ysbQD26y1W/sUlYikpFjn2xQUF9JQbEmftBkIz5rsmMXoDe+xt3kDzemTqH+vHCeQ\nBoTInTCH7PzJHc9s2reTpu3/YnLmrLiTjbklJdx0w5x+/ElFZLD5KZJ9AojM8UbmYaM/d40xLwMX\nWmu39TE+EUkxXYttyyssP7v7QdLGB3GbR3Ng45GEtm3g81ddwrubN7PsgX8y3pzWMeNSs/Fg51eA\nrLxJzJk7m5uWXDsoP4+IpCY/CcqpeDt4bgNewEtO3gdcCXwXr2j228DPgcXJCVNEBoKfw/9KSwzf\n+uTHuOuJlTTtDjI+892OWZDlK1ZRMHNht+3FuyqejHtJR0RGJj8Jyo+Ay621r0dde80Y829gqbX2\nHGPMm8CrSYlQRAZE12ZqPZ0Q3FMS85OSb3V7Zk/t8LPTWihoek31IyLSIz+N2o4FKmJcrwA+EP54\nN5DjNygRGXixDv/rekJwoicYx9r147ouR84+jF/d9HVuWnKtkhMRiclPgvIusMQY0zH7YoxxgK8A\n74UvfRNvK7KIDBH1zW7MZmp1zSGe3vZPVrzzaFxJTLTFZYtwo7YEN+7dwa5197FrTyM33nxLj4mN\niIifJZ5vAw8CXzXGbMWrOSkGCoGrjDHpwI3AhUmLUkT6JJ7akliH/5Gxn1DJHh54+xEA0jMLcVq6\nJzFvbthOeYXt9szoXT+Vu3ZzoN5lwryLaHEctvawhCQiAuB0nX6NhzGmBCgDpuHt3NkJPGqtfTn8\n9QnW2l3JDHQAubW1DbS1hQ59pwCQlhagsHA0Grf4DeSYdaotCe+k2btxNeNyHSaNH8OJx87lhVfX\nU1m1h+p6N3z4X6SvicUJes8pzplM/fMt7Gya362L666KJxlfVNhrsnHjzbewlXndXjuVdXHv4NF7\nLXEaM380bokLj1nSWjr7mUHBWlsB3NzL14dqciIy7MRalimYtZAd9ilax8/jlXtXM3q8YdSEo8nM\n3MHuzQ9w2Bn5OGPaAQg6Qc6ZfhpnTlvIhrx3ujVq271pDfmTj8DJm9TjGTrQc8Fsb23tRWTkivcs\nntWRbrLGmH9xsO9JN9bak5MUm4gkQU+JQeRwvqLDF1Jln2JUwRRyZgQZc1oeTtBLTopzJvOpuZcw\nJcc7xSKyZLPkx7+mPaOo02F9QK/JRqwlJJ2hIyI9iXcG5e2oj2Pt4BGRJIunbsRvbUnXw/kipwq7\nTbneom0Izpt1JmdOW0gwEOz0vNISw9FzZ8dcrukt2YjVJl89UESkJ75qUIY51aAkSGu1iTvUmMWq\nG3Fr1naq8Yjnnp7u271pDaOLZnY0S6uyTzGh5HQAAmN2MqFxJz/+Wve+JonE19Protvkx9MILpFx\nk+40Zv5o3BKX7BoUv0WyU4HPAtOstVeEr73PWvtisgIbREpQEqT/kRN3qDHrWlDatG8n+3a+RXaw\nhSMPP4zFZYtYvmJV3EWnkcRg154Gtm7bRt60BYwqmOK1nt/wNKMnlHR83lr5b77zxQsPmTj0Ndnw\nQ++1xGnM/NG4JW7Qi2SNMQuAJ4F3gMOBK4wxM4B/GmMuttauTFZwIiNVdN1I076dNNRsYkLJ6ThR\n23MzQvU4E+IrOo0+P+dgYlGN29pAbXs99e+V01D9Du1tLeRmxdceqeuZPCIiyeSnUduPgSXW2qMI\nF8taa98FLge+l8TYREas6A6sdZXrGTtzQbfmaHv27I7ZpbW3OpCqxmp259Zy0w1f41c3fZ283BwK\nS89nQsnpjDv8Q0wsPYNR00/tsfGaiMhA8ZOgHAX8v/DH0X863gfon1MiSRDdgTWy2yaa4zgUTZjS\nqUtrR9Fp2aJuzwu5XjfYn7x4K8vtCjbt2wL03D22vlm1aSIyuPz0QQkAWUBLl+uTgNY+RyQinTqw\n1rZU48bYhTOhcJRXixJdBxLeEXPjzbd07Ow5+yML+NeBl9m4b7P34hD811/uoqB2NG5rA26Wtv6K\nSOrxk6A8BfzSGPPVyAVjjMGbVXk6WYGJjHSRGo/IjplY23NLSwyLL6Bjq/Htf7yHmsZM0ie9Hycb\n6ids5q7K+zu6wbbvC9Ky5URozqMOl8bdT5O+/9/e/dr6KyIpxE+Cci3wf0AdEDDG7AeygTfxdvaI\nSBJFz6ZEz5SUlpjO232zHd7b/AQTSj5EIKuJ9JlvEMytBcBtd2lY18KBmvmMys8DvKWcUdNPJX/f\nP8h33uj2bBGRwZRwgmKt3WaMOQY4C5iDV4digSestVq4FukHPe2Y6drGPpiW4X0caCcwei8AoYZc\nWjbNI9CSQ2PNGhwCHZ1fHcchkFnATTd8beB+GBGROPjZZvwcsAr4m7X2seSHJCLx6trGPtTe6hXN\nNuVS+6pDzvhZtL83E9wAjgNjZy6gyj7VkaCo3kREUpWfJZ5ngY8APzDG1ACPAX8DHrfW7ktmcCLS\nu+g29k37dtLe2sTONx4hmJ5NqK2F7KNmd7rfcRycgPe/vepNRCSV+Vni+TaAMSYX+BCwEPg2cJcx\n5gVr7YeSG6KI9CRyvk1T+iQad7/LpCPP6yh2rap4gtptr9PSUE0gmE6ovZXciaVkhXZT0PSa6k1E\nJKX5mUEBwFpbb4x5HGgAGvG2Hy9IVmAi0rOQG2Jz3baOAtrv/fTXjDUf69TMLXfSEdRXvsn4kjM7\nkpaat1dz9eKPsujsswb5JxAR6Z2fGpSTgVPDv07EO934H8D38ZZ/RCSG6JOH87IDfP6zH6d4yrSE\nn1PVWM3d5ffxbt1Wrpv/ZUpLDFOnzWJvl4Zr9e+VdyQnEG7udvhCXnh1nRIUEUl5fmZQngNeB34F\nfMxauze5IYkMP123A9e6Lt/95XKu/9z5zJk9J65nhNwQz2xfw8MbH6M15PVEfHrbP/nMEZ/oVIsS\n4QTSYneJjXFWj4hIqvHT6n4JUE24MZsx5hfGmEXGmJzkhiYyfHTdDuw4DqHC4/jzA/GdeVPVWM2t\nr9zGA28/QmuolaAT5LwZZ/Gp0ouBzq3xwSuADTVVJXxWj4hIqvBTJLsUWGqMyQBOAU4HbgKONMa8\naq09Ockxigx5XbcDg5ekvLlhG1+/8VdewWrZom4Fq7FmTYpzp/Cp0ouZkjOp477SEsPFZxzN/y5/\nkDaySHOb+NiZ7+e5N9fG7EArIpLq+lIk22KMeRkYBWTidZM9LlmBiQwnsZZgXNelsS2DvdnHUOu6\nLF22kuu77KrZ1VjNinceJeSGCDpBzpl+OmdO+zDBQLDT88srLPc+8Tq54UJZ13V57s21XHzG0bzw\nmrrEisjQ46dI9hy8rcULgWOAbcDfge8CTyY1OpFhIrIdOHo2o2bjGvInHwF4sykUzWf5ilXctORg\nAjFp9ATOmraQN3dXdJs1iRZrCYmi+bzw6jpuWnJt//+AIiJJ5mcG5QG83Tr3AJ+y1lYkNySR4afr\neTqbNr1DzmEnd3R0hZ4LWKcfmMqLT73FL//vLz0uBfW0hKSCWBEZqvwkKGOstc1Jj6QHxpgxeAW5\n5wBtwIPAl621B2Lceznwv0Dkaw7eWUEftNa+PDARi8QWfZ7OD356K1vczrMhsQpYyyssv/jdI512\n/8RaCuppCUkFsSIyVCW8i2cgk5OwPwBFwCzgSOBYYGkv9//DWjsq/Cs7/LuSE0kZ5RWWvftqqd34\njLfLJtB2sIC1bFGne2Mt3TjhpaBosXbxxHqeiMhQ4btIdiAYY8YB5wHHWGtrwte+A9xrjPmmtbZt\nUAMUSdDBfigfJJudNAeeoOCodjJeGc0XrvpEj0s3Tft2Ule5vqNlfXph5yLZrktIKogVkaEupRMU\nvNmSVmvtG1HXXgFyAQO8FeM1xcaYJ4H5wA7gZmvtPf0eqUgcIjMigaxG8uduJ5gbAhw4spUS071h\nW26Ww869O2jc/S7jzWkdBbY77ZN87Ybv8/nPXNaRhEQvIYmIDHWpnqAUAV1PSN4T/n1cjPurgQ14\nO4rWA2V4hxjutNaujvebBoN++teNXJHx0rgdWv2BEGnTtpB+2AacYAiAUEMegQ0ZpKcHu91/2UXn\n8rXv/YoJ8y7qtMwzzpzOhoon+dmylSy5+gLmlpQM6M8xWPReS5zGzB+NW+KSPVa+EhRjzCXAF4Cp\n1tpZ4aZtX7XW/tzHsy4D7sIrZo2IFLd+r5eXdtueYK1dBUQvzi83xpQBVwBxJyh5ednx3ipRNG69\nq6yvwj1uLxk5uwBwQw5tO2fRunMGxRmWwsLR3V6z4KT5zJw+jcYYLeuDaRlQNJ/7H36cW06aPyA/\nQ6rQey1xGjN/NG6Dx08flCuBW4A7gfeHL48DrjHGBK21P03keeHll5hLMMaY04ECY4xjrY0kJEXh\n36vi/Bbv4i33xK2uron29lAiLxnRgsEAeXnZGrde7G9p4Nv//AktOd4Gs1BDLi2b5hFqzIGatVx4\n9QXU1jbEfG1RfjZbYuzQCbW34jgOu+tae3ztcKP3WuI0Zv5o3BIXGbNk8TODcg1wvrV2tTHmPwCs\ntTuMMR8DlgMJJSiH8AreTqN5eAcUgneC8l68pZxOjDGfA2qstQ9GXwY2JfJN29tDtLXpDZkojVvP\nsgLZfHDKSTy97Z8cn3M0m15+j6aWzWSnu1xylXdgYE9jd8kF53Rr8rZ70xryJs3FdV1yMhlx4673\nWuI0Zv5o3AaPnwRlJvBM+OPoZZa1wORud/eBtXaPMeZe4BZjzGK8dvo/Bm6z1rYDhAtib7fW3gek\nA782xmzEK6C9CK9/yonJjEtGrvIKy/IVq6hvdntsmtaTc2ecwfsmHsfknImknRSgsHA0tbUNh/zD\nL7JDZ9ld97Jhay2hQCb5k48gK2+SztYRkWHLT0VLPTA9xvXj8WY2ku1qYCfwDl4S9BTw/aivzwQK\nAay1/4PX1O0hvGLar+PN9ryOSB9FtghvZR57s49hK/NYumwl5RU2rtenB9OZnDPR1/cuLTH86sff\n4+ff+TwnlE5gUkYVU1nXrWGbiMhw4XQ9jv1QjDG3ACcDP8Dr6voBvOTk28AD1tqvJznGgebG869a\nOSgtLf7ZgKHsxptvYSvzutWCTCXx825Gypglm8YtcRozfzRuiQuPWdLaV/uZQbkBeAlYiXeK8UvA\nb4BH8JIUkWGpvrlzoSqEz7tpdqlqrOY3ry5jV0O8tdsiItKbhGtQwmfgfNkYcz1e+3kX2GitbUx2\ncCKpJPZ5NyHSpjfykxdvpTXUyl3l9/H1+VcTcHrP/ddXVHDfw4+zp66FnMzEallEREaChGdQjDEZ\n4b4nrUAFYIG28PVRyQ5QJFV0Pe+GjP1kHv40DdPqaA21EnSCHDHWcKhl0/IKy82/fYh3DpRSm5V4\nLYuIyEjgZ4mnGWjq4Vd98kITSS2R3TTFzjpyxqwh+6jnCI7xjoMqzpnM9Sd8hXNmnE4w0L0jbLTl\nK1Z1bBmGng8AFBEZyfxsM76CztuLA8AM4BLgR8kISiRVzZkzm8Izs9i9txKAoBPknOmncea0hYdM\nTCIiBwBGcxyH+qbECtZFRIYzPzUof4x13RjzJ+DnwN19jEkkZQUDQQ7Lmcw7e9+lOGcyn5p7CVNy\nJiX0jNi1LF5fFRER8STtZB9r7TvAyDixTEa0j846h48f/hGuO/6ahJMT8GpZiKplcV3Xa7hWtijZ\noYqIDFlJS1CMMR8A8pP1PJFUlRnM4NTiU+Je0umqtMSw5OoLODyrgsLm19VwTUQkBj+HBVbS/STh\nDLxurv8vGUGJDHdzS0q45aT5agIlItIDP0Wyt8W41gS8Za19tI/xiAyqkBviH9uf56iiUoqyxw52\nOCIiI1ZCCYoxJgD8zVr7Yj/FIzJoqhpruLv8Xjbu28zr1W/ylWM/d8iGayIi0j8SnUFxgdXGmFxr\nrealZViIzJqs3Pg3WkOtADS3NdPQ2khuRs4gRyciMjIl9M9Da60L3ANca4zRnkgZ8qoaa7j1ldu4\n/+2HO7rBnjfjTK47/holJyIig8hPDco44CPAEmPMZqAl+ovW2pP7HpZI/1u97blOsyZ++5qIiEjy\n+UlQ9gKPJTsQkYFW2bCrY9Yk0W6wIiLSv/x0kv1sfwQiMtDKZp9LXUs9H5l5lmZNRERSTNw1KMaY\nxv4MRGSgZadl8YV5n1FyIiKSghKZQVFRrAya8grL8hWrqG/2zqxZXLZInVdFRIaxRHbx6KhVGRTl\nFZaly1aylXnszT6Grcxj6bKVlFfYXl9X1VhNbfPeAYpSRESSKZEZlDRjzFX0PpPiWmuX9TEmkU6W\nr1iFUzS/4/Rfx3GgaD7LV6zipiXdZ1FCbohntq/h4Y2PMbtgBl86+spOJweLiEjqSyhBAW4/xD0u\noARF4hLvsk19s4uT3TnBcByH+qbuk3rR3WABNtRuZPv+SopzJ/fLzyAiIv0jkQSl2Vo7qt8ikREl\nsmzjFM3HyXaodV2WLlsZ81Tf3Czv69GzIK7rJTURsbrBqq+JiMjQpYNGZFDEWrZxwss2XS0uW4Rb\nsxbX9WZMXNfFrVnL4rJFQO/dYJWciIgMTdrFI4MikWWb0hLD9Vedz/KH/kZ9U8hbDoqaaXliyzMd\nSzqaNRERGR4SSVDu6rcoZMSJZ9kmWmmJ4aYbYm8rLpu9iIratzl50gnqBisiMkzEnaBYaz/Xn4HI\nyLK4bBFLl62E8DJPx7LNVef3+rqeCmu/f+I3SQ+mD1D0IiLS3/ycxSPSZ4datoklVmHtj//f/RSN\nOkAgs0AN3EREhhElKDJoelu2iRZyQxxob4lZWJs+6f1sqHiSiaXH9LoTSEREhhbt4pGUVtVYza2v\n3Mad65dT1xzq1nDNcRyCaRkdH/e0E0hERIYWzaBISoruBhvpa5I7qRC3tnthbai9tePznnYCiYjI\n0KIERVJOVWM1d5ff17F1OOgEOWf6aRRPmsIvfvdIp8Lamo1ryJs0t+O1ve0EEhGRoUMJiqSMWLMm\nXfuaXH9VoKOw1m1toDF4gKw872vx7gQSEZHUpwRFUsbfNj/FqnefAA7OmnTta9K1sLa8wia0E0hE\nRIYGJSjSZ+srKrjv4cfZU9dCTqb/rb4fnHISz25/nsLM/Li7wca7E0hERIYWJSjSJ+UVlp9FGq5l\nOezpw1bf3IwcvnbcFxifXaRusCIiI5y2GUufLF+xqqNoFfq+1XfS6AlKTkRERAmK9E19sxuzN0l9\ns7b6ioiIf0pQpE9ys7ztvtFibfUNuSFWb3uOu9bfO5DhiYjIEKUERfpkcdkiqFnbkaR0bPUtW9Rx\nT1VjDbe+chv3v/0w/37vZV6pWjdY4YqIyBChIlnpk9ISw5KrL+D+R55g974WcjLp2OobckP8Y/vz\nrNz4t059TSaMGjfIUYuISKobEgmKMeZ44C9AtbX25EPc+1XgWmAcsA74orX21f6PcuSaW1LCLSfN\np7a2gba2EODNmtxdfm+3brBd+5qIiIjEkvIJijHmUuBm4E2g8BD3lgE/BD4CvARcBzxqjJllrW3q\n71jF80bNen7/5j09doMVERE5lKFQg5IJnAi8GMe9VwK/t9Y+a61tstb+EHCBj/ZngNLZ1NzDSA+k\nEXSCnDfjTK47/holJyIikpCUn0Gx1v4BwJi4mn4dh7cUFO014Hjgr8mNTHqSn5nH5XMXU5hVoMRE\nRER8SfkEJUFFwJ4u1/bg1aPIADqyqHSwQxARkSFs0BMUY8xlwF14SzERTvjzz1pr/5TA43rqDpZQ\n17BgcCisfKWOyHhp3OKnMfNH45Y4jZk/GrfEJXusBj1BsdbeA9yTpMdVA2O7XCvC280Tt7y87CSF\nMzxV1lfxwvZXuaD0rE7XNW6J05j5o3FLnMbMH43b4Bn0BCXJXgLmA3cDGGMCeHUpv0vkIXV1TbS3\nh9pXSAYAABO+SURBVJIf3RAXckM8vfU5Hnrb62tSECjk6PFHEAwGyMvL1rglQGPmj8YtcRozfzRu\niYuMWbIMpQTFiXXRGFMOXGmtfR64DbjXGPMQ8DLwfaAReCSRb9TeHuro5yGeWH1Nqhv2dBonjVvi\nNGb+aNwSpzHzR+M2eFI+QTHGVABT8WINGGOa8GpKjLV2GzAHyAGw1v7dGHMdcCdeYezLwCJrbcug\nBD+ElVdYlq9YRV1ziPRpTRyY0UCb2w6or4mIiPS/lE9QrLUlh/h6sMvndwB39GtQw1x5hWXpspUE\nJs8lY+4btOTWgQsBAiyacbq6wYqISL9TebJ0s3zFKpyi+TiOQyC7HoBQQy5568ZwzozTlZyIiEi/\nS/kZFBl49c0uTraD25JN69ZSnIwm2ipn0tSoU4hFRGRgKEGRbnKzHGpdF8dxaK+ZAoDruuRmxaxT\nFhERSTot8Ug3i8sW4dasxXW9/nau6+LWrGVx2aJBjkxEREYKJSjSTWmJ4fqrzmeq8wYFTa8xlXVc\nf9X5lJbEdR6SiIhIn2mJR2IqLTHcdIMSEhERGRyaQREREZGUowRFREREUo4SFBEREUk5SlBEREQk\n5ShBERERkZSjBEVERERSjhIUERERSTlKUERERCTlKEERERGRlKMERURERFKOEhQRERFJOUpQRERE\nJOUoQREREZGUowRFREREUo4SFBEREUk5SlBEREQk5ShBERERkZSjBEVERERSjhIUERERSTlKUERE\nRCTlKEERERGRlKMERURERFKOEhQRERFJOUpQREREJOUoQREREZGUowRFREREUo4SFBEREUk5SlBE\nREQk5ShBERERkZSjBEVERERSjhIUERERSTlKUERERCTlKEGR/9/evUfJVVV5HP82EKIhyFPlYYKA\n8gNEGBRkgkxcSXipgKKiAipDUHAkgojIQ5GFoIiIyagIZgxPMyiOERWQl6AshAWEl8DAD4FEg7yC\nITCQIBF6/tinoKhUd6qSqvRN9/6slZW+t07de+r06bq7ztmnbkoppVQ5GaCklFJKqXIyQEkppZRS\n5awy0BVohaTtgAuBubZ37KfcCcDxwAtlVw/QC2xke27XK5pSSimljqh8gCJpP+AU4G5grRaecr7t\nid2tVUoppZS6aUWY4hkO7ADcPNAVSSmllNLyUfkRFNvnAEhq9SnbSLoR2AJ4ADjW9lVdql5KKaWU\nuqDyAUqbHiaCkuOBOcAhwCWS3m77/lYPsvLKK8LAUnXU2ivbrXXZZksn26192WZLJ9utfZ1uq57e\n3t6OHrBdkvYHLiCSWWtqya0H2j6/lDsB2K2/JNk+jn8TcKXt4ztU5ZRSSil12YCPoNieDkzv4ilm\nAet18fgppZRS6rBBNXYl6ThJYxt3Aw8NRH1SSimltHQGfASlDT3Ndkq6FzjI9g3EMuTvS/og8Agw\nCdgUOHd5VTKllFJKy67yAYqk+4DRRF1XkrSQyE+R7TnAZsDIUvxYYlToemAE8CdgvO1Hl3vFU0op\npbTUBjxJNqWUUkqp0aDKQUkppZTS4JABSkoppZQqJwOUlFJKKVVOBigppZRSqpwMUFJKKaVUORmg\npJRSSqlyKv89KN0maTvgQmBuf/f5KfcCOh54oeyq3S9oI9tzu17Rimm13UrZw4EjgNcT303zOdu3\nd7+W1SFpbeCHwHuBfwIzgEm2/9Gk7AHA2UDtsVpfG2t75vKp8cCQtBFwFvBvwLPAubaP6aPskO9X\nNa22W76PvZqk3YDzgGts77eEst8AJgKrAzcAB9ue3fVKVkyrbSbpHOATwKKyqwdYaHvtVs81pAMU\nSfsBpwB3E99CuyTn257Y3VpVXzvtJmlv4OvAnsAtwFHApZI2tb2w23WtkHOA1YhvNh4G/AY4FfhC\nH+X/YHv8cqpblVxMBBsbEPfQukLSY7an1BfKfrWYltqtyPcxQNJRRMCxxDvdSzoCOADYlbi/2+nA\nL4Ftu1nHqmmnzYqTbH99ac831Kd4hgM7ADcPdEVWMO2020HANNvX2V5YOmsvsFc3K1glkl4P7AEc\nYfvJ8s3GXwEOlDSkPyTUk7Q9sBVwmO1nbN8PfAs4pEnxId+vatpst/SKhcC7gAdbKHsQcKrtu2w/\nCxwJbClph25WsILaabNlNqQDFNvn2H6sjadsI+lGSfMlzZS0S9cqV2Fttts7gFsb9t0BbNfZWlXa\ntsAi23fV7buNGCpWH88ZJelqSU9JulvS/l2v5cDbFpht++m6fbcBm0laraFs9qtXtNNukO9jANj+\nge3/W1I5ScOBLYg2rT33WeABhlh/a7XN6oyXdGd5H7tO0jvbOd+QDlDa9DDRIQ8A1gd+AlwiabMB\nrVX1rQvMa9g3j8gbGCrWBZ5u2Fdrk2btMJcYQj2KGK4/GThX0riu1bAa+uorsHg7Zb96RTvtlu9j\n7VuHyJ/I/taeB4n3sT2AUcSI+5UlH68lg3p4uXzqvIAY+q2pJYUdaPv8Vo9lexowrW7XFEn7Ap8k\nks4GjU62W8MxWtm/QlpCm/XXPxZrB9uXAZfV7fppybmYCFy77LVdITW205DoVx3wqvYYSu9jy0n2\ntz7YPrl+W9KXgX2BvXl1H+zToA5QbE8HpnfxFLOIT7iDSofbbS7xCaTeukRC36DRX5tJ2hlYU1KP\n7dob2rrl/ydaPMUsoK3h0RXQEzTvKxD9qN6Q6FctaqfdmhmU72Md9CTwEs3buNW/3yHP9kuS5tBG\nX8spnhZJOk7S2MbdwEMDUZ8VyC3UXVglrUTkDwylxOTbiL+1rev27QDMp0k2vKSDJX2ocTeDv6/d\nAmwkqX5l2A7A/9pe0KTsUO9XNS23W76Ptc/2C8BdvLq/rQ28haHZ31oi6XRJW9ZtrwJsQht9bVCP\noLShp9lOSfcCB9m+gVhO+31JHwQeASYRS0bPXV6VrKBW2u0s4CJJFwMzga8BC4hltkOC7XmSLgIm\nS/o48FrgG8BZtl8EkHQ18CPbPyeWIX9P0oPAPcA+xPenDOoVA7bvlHQz8Xd2KDAaOBo4EUDSfcDE\n7Fev1ma75ftYCyRtAPwO2N32X4AzgRMkXQv8BfgecLPtxkTtIatJm40m3sf2B54DTgKeJ5bEt2RI\nByjlD3c00Q4rSVpIzCnK9hxgM2BkKX4s8Sn4emAEMZQ8viwZHVLaaTfbV5S18+cRCWUzgfeVTyVD\nyX8QX9T2APElWT8hLqo1m1C+U8b2GZLWIP6Q1wEMfMD2ncu1xgNjH2AqcfF8BjjD9tTy2FvJftWX\nltqNfB97Wd371rCyvTfQa3tE2bcZ8ZUK2J4qaT3gSqItryHafEhpp82IpdlTiD62MjHaNKGd7ynq\n6e3NHJ+UUkopVUvmoKSUUkqpcjJASSmllFLlZICSUkoppcrJACWllFJKlZMBSkoppZQqJwOUlFJK\nKVVOBigppZRSqpwMUFJKKaVUORmgpJRSSqlyMkBJaQBJGi1poaQJA12XJZF0o6Szl9O5ppb7nrRa\n/trlVbeU0vIxpO/Fk1I7JP0e2Im4l069HuL+FDvavqOF4xwKXGh7nu2/EjcP7BpJqwGftX16N8/T\nSbYP7vQxy03LbrQ9JO7cK+n9wKO2bxvouqS0NDJASal1vcBFtvdb2gNIWpO4gdZVwLxOVWwJxgNf\nAlaYAKXTJPUAk4FP0Mbt3pfxnKvY/ufyOFcfTiRuILhUAUoF6p+GuAxQUuowSeOBbwBbAC8BtwBf\nIP7eZhJTq3dK+hlwAjCLuEX5lZKuB24FFhF3A30R+DZwKXA2sBVxd+P9bd9bzvcu4FvAvxCjOX8C\nvmj71jJaM4W46/QCYJLtsyWNBb4JbAs8BdwAHFnuRo2k9YEfEyNG84mLe1+v9zVEsPVh278t+44G\nTgF2sn1D2fdNYKztnSSNKsecUNroLuArtv9Yyp4DbG57TNnes9R3Y+B24HjijrK72P5dXV2OAg4H\n1iiv6VPAQuAJ4m6rv5Z0o+1xTV7H9aXtXgD2JwLSS4FDbS8oZT5JBHsbAwuAa4HDbM8tj88CzgV2\nA94GrCFpBPBdYM9Sr0eJuw1PKc/ZmbhL7oRSbnPgDuDjwKeBQ4i7wU61fWxdfQ8BjgBGEXcx/iXw\nNdvPS3oUeAPwA0nH2N5E0nCin3wUWJ0I1L5ve1o53gFEX/kScFr5/Z0m6cTSjq8n+spFwNEZvKRu\nyxyUlDpI0irEhWKa7TWBNxEBxVTbdwG7lqJb2/73JodYRFyYbgHWJS7i3yQuLHsD65dyJ5fzDQMu\nAe4D1iuPPwT8CsD2GaXs47ZHlOBkFHAZcB5xwdyauCj/tow0UB5bB3grcaEdTQRHi7H9PHAdUH/R\nnwDcSYze1IwDLivnuIS42G1U6nwxcLWk0XXle8tr3ByYAfyi1GkScSHtLe1Vs1vZ3gR4OxGwHWv7\nGUBE8LZns+CkWATsC9wNvLHUd3ciQETStkTw8R3brwO2IYLQ/2w4zkTgGGDNsn1KqdsY2yOBzwOn\nS6r1hdprOBzYGXgzEXT8ngg81i+PHS3p7aUuHyGC4IOAkcD7ib41GcD2+uX1Hmp7k3L804EdiaBz\nDSK4mSzpY3V1Hw68G9jQ9mnlsc8A40rdxwHvBQ7sow1T6pgcQUmpPR+V9MEm+6+zvTvxyXQ1ykWn\nfPI+rEn5nib7ambZ/hmApBnAScTU0iNl31XAHuX4iyRtDCyy/UJ5/ELgU5JGlxyXRp8D7rH9X2V7\nnqQjgMeBsZLuJi6UH7b9RDnmscTFsC+XE6MOSFoVGFPOcyBwsqTVgXeWfbXRhTG1kQlgiqSDSvkT\nG469N/AscHL51H6npLOAMxrKPVoblQBmS7qGxYOq/tod4K+2f1x+vkfSBUTQMsn27ZLWsT0fwPbj\nki4tj9e7zfZ1ddtHEqNDz5bnXS7pMeBfiZGTmjNt/x1A0h+B7W2fWbZ/AZxPjK7cVY45rTbiBNwv\n6WTgvyVNsv1i/esteUgHAx+wPas8dq2k84DPAj8r+4YDU2wvLNvrESNc/yh1fwDYcgltmFJHZICS\nUnv6zUGx/VSZZviRpGOAq4GL66chWjC77ufaBXxOw776xNq9gcMlbQq8hpgOoPzcjIB3limfmh4i\nqNoYeIYYnahdyLD9D0l/6afOlxPTAWsA2wF/Bn4DnFUClvcAT5aL/GHE6O2TkurP30OMqDTaiAgc\n6qcUbmLxYOOBhu3ngRH91LmZexq2ZwEbAEhaGThS0j7AhkQ7DwPmNjznwYbtTYFTJG1PjAD1AKvy\n6t9PL1DfvguAl4NL2wtLW9V+7wLeIenzDefqJUa7ZjXs35R4v58hqbfsq7XfIw1l63N0ziGC4dkl\naLoKmN5H4JtSR2WAklKH2Z5ccih2Lf9mSJphu9Vh8Zda3IekHYnpmKOBH9peIGkcERj1pRe43PYe\nfRxzTF25eis3lq2xfZ+kOcBYYhrhGtvzJd1HTBmMI4KY2nEXlCmDVvSw+OtvrBtNyiyNxmnvHsro\nAfBlYjTsY8BVtl8s+RmfaXhO4yqvXxN5JzvW5fg0C/Ya69/f6+kFjmtjZVatvXayfesSyr5c/zI9\ntoukLYiRr72Ar0r6sO3L+zpASp2QOSgpdVhtGsD2RbY/TXwCPUDS67pwujHAM7a/Uzdd8q4lPMfA\n1pJe/vuX1COpNnoxh7gwv7nu8dVoPrpR7woiENmZSGAF+AORhzIe+G3d+V+ruuGTco6N+zjuI8Co\nuvwYiNfYLEhZVmrY3pRXRq9qgdfldVMo2/d7MKmWxzO5LjjZgDIqswxMjFTVn2vNskqsmQeBfzZ5\nzoZlhKspSatKGmn7XttTbI8HfkpMF6XUVRmgpNRBkt5NDIfvImmlsnLi3cBj5dPoc8TFf8syHbKs\nZgOrSxpTzvdxXknErSWcPkesJtlQ0kjgTGKq4VRJq5f8kG8DN0kaYfthYiXRkZLeUAKrbxErivpz\nRTn3VkTSLESAsheRTFrLt7iKSET9oaQ3SVq51Pu+siKp0aXAWqU+q0ramv7zYZp5rvy/uaS1+in3\nFkkHSxouaRsir+bC8thsYBtJb5Q0UtKpRM7RGqVdm3kKeBqYUH4/byWmTWbxyu8Hlpwb0+i7wIck\n7StpmKQ3AT8HpteVWQBsJmmtErxOBY6TtH0JSLcDbiQScPtyBrHyaRS8vLprc+D+NuubUtsyQEmp\nPftIWtDwb2H5/7iStHgEsZpiPvA3YlThfeX5dxDTL9OJZcMQIwH9jQb099gM4sJzCZHkOg74ABEY\n/FzSbqXMw8C9wCHlk/z7iNGXR4lch62A8XWjMB8iLnAPEHkZDxHLdof1U5ergbcAt9cSQolA5W3A\nTbafBrDdSyy5fYpY1jufWNr6Uds3Nx7U9kxiGuUQ4O/AqcBXiYv6koKm2jGeBC4gVtRc2U/RGUQS\n6N9KuV8Sq6ggVkP9mWiTu4HHiO9VeQL4s6S1afhd2X6JWKL7XiK35zxihc9kYC9J00rRVkaDXi5j\n+3+IwOIEIgCaSQRQ9flRU4gE2D8pVpd9iVgJ9SsiYPspMS14Wj/n/CLxu79J0nNE7s/N5bwpdVVP\nb283RklTSqlzJA2zvahuewIRQGzcqYRNxVfrz7I9sRPHSyktm0ySTSlVmqQ3EtNmJwLfIaanjgNm\n5mqSlAavnOJJKVWa7ceBj5R/84hvkp1btlNKg1RO8aSUUkqpcnIEJaWUUkqVkwFKSimllConA5SU\nUkopVU4GKCmllFKqnAxQUkoppVQ5GaCklFJKqXIyQEkppZRS5WSAklJKKaXK+X9KstsNmaI0AwAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f402460b780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MoNwC3AdcC7wD4O5/N7MbgG8DJ2UvPBERyabOsyagviYST5kUKEcBH3P3NjPr2AvlTuC/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\nhBBCCE0nJighhBBCaDr/AMK4Dku+mOu8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4028fa0518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VZjbE3c/OYk0ikmOraleztXEbEysPiboUEekmUp4HxN3PNrOYmR1nZp9v3W5m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\n0LbrZ3QAMAp9RrskM7vezA7Z5XExMBJ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fdcc01c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "slim = tf.contrib.slim\n",
    "\n",
    "tf.reset_default_graph()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    predictions = slim.fully_connected(X, num_out,\n",
    "                                       activation_fn=tf.exp,\n",
    "                                       scope='fc')\n",
    "\n",
    "    nb = NB(theta_init=tf.zeros([1, num_out]),\n",
    "            debug=True)\n",
    "    \n",
    "    nb_loss, nb_theta = nb.loss, nb.theta\n",
    "    loss = nb_loss(Y, predictions)\n",
    "    slim.losses.add_loss(loss)\n",
    "    tf.summary.scalar('loss', loss)\n",
    "\n",
    "    optimizer = tf.train.RMSPropOptimizer(1e-2)\n",
    "    train_op = slim.learning.create_train_op(loss, optimizer)\n",
    "    \n",
    "    [tf.summary.histogram(x.name, x) for x in slim.get_model_variables()]\n",
    "    summary_ops = tf.summary.merge_all()\n",
    "\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    swriter = tf.summary.FileWriter('logs_tf', sess.graph)\n",
    "\n",
    "    for i in range(500):\n",
    "        start_time = time.time()\n",
    "        step_loss, summaries = sess.run([train_op, summary_ops])\n",
    "        swriter.add_summary(summaries)\n",
    "        \n",
    "        duration = time.time() - start_time\n",
    "\n",
    "        if i % 100 == 0:\n",
    "            print('Step {:d} - nbinom loss = {:.3f}, ({:.3f} sec/step)'\n",
    "                  .format(i, step_loss, duration))\n",
    "    swriter.close()\n",
    "    \n",
    "    x = slim.get_variables_by_name('fc/weights')[0].eval().reshape(-1)\n",
    "    y = W.reshape(-1)\n",
    "    visualize(x, y, 'Estimated weight parameters', 'True weight parameters')\n",
    "    \n",
    "    x = slim.get_variables_by_name('fc/biases')[0].eval().reshape(-1)\n",
    "    y = b.reshape(-1)\n",
    "    visualize(x, y, 'Estimated bias parameters', 'True bias parameters')\n",
    "    \n",
    "    x = nb_theta.eval().reshape(-1)\n",
    "    y = dispersion.reshape(-1)\n",
    "    visualize(x, y, 'Estimated theta params', 'True theta params')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now implement it in Keras:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:525 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:525 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n"
     ]
    },
    {
     "data": {
      "image/png": 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03ufiNVXsPNjEqzvr2bD1GMvmlfDWMzQcSEREskvKC6wNo+j0p0gPx3FwOU6/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\nlONNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fdcc01fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import os\n",
    "os.environ['KERAS_BACKEND'] = 'tensorflow'\n",
    "\n",
    "from keras.models import Model\n",
    "from keras.layers import Input, Dense\n",
    "from keras.callbacks import EarlyStopping, TensorBoard\n",
    "from keras.optimizers import RMSprop\n",
    "from keras import backend as K\n",
    "\n",
    "K.clear_session()\n",
    "\n",
    "inputs = Input(shape=(num_feat,))\n",
    "predictions = Dense(num_out, activation=tf.exp)(inputs)\n",
    "model = Model(input=inputs, output=predictions)\n",
    "\n",
    "nb = NB(theta_init=tf.zeros([1, num_out]))\n",
    "\n",
    "# add theta as a trainable variable to Keras model\n",
    "# otherwise, keras optimizers will not update it\n",
    "model.layers[-1].trainable_weights.append(nb.theta_variable)\n",
    "\n",
    "opt = RMSprop(lr=1e-2)\n",
    "model.compile(optimizer=opt,\n",
    "              loss=nb.loss) #nbinom loss function\n",
    "\n",
    "early_stop = EarlyStopping(monitor='val_loss', patience=5)\n",
    "tb = TensorBoard(log_dir='./logs', histogram_freq=1)\n",
    "\n",
    "losses = model.fit(X, Y,\n",
    "                   callbacks=[early_stop, tb],\n",
    "                   batch_size=256,\n",
    "                   validation_split=0.2,\n",
    "                   nb_epoch=5000, verbose=0)\n",
    "\n",
    "val_hist = losses.history['val_loss']\n",
    "train_hist = losses.history['loss']\n",
    "\n",
    "plt.plot(range(len(val_hist)), val_hist, 'b.-',\n",
    "         range(len(train_hist)), train_hist, 'g.-')\n",
    "plt.ylabel('Loss')\n",
    "_ = plt.xlabel('Steps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compare true parameters to model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Z5RA+Z1MWR5ZUpGXWJFpvhwUmWsgrMhh4OiwwnnBflHetten9F5x+OiwwSTpU\nK3kaM29SNW6xh/odTAT88Iu+p8MCb1l0O1uY1WWGJfqwwc70WfNG45Y8PxwWOBb4BV1PMx4B7EpR\nXCIifdbdckj0bErn2RK/xHrN5z7VJR71R5GhxEsNyi+BCuB+4FvAbcBHgCLgX1IXmoiId70th0Qa\nqu1qrKGmaTcVYzKbnCSydJNIjYrIYOGl1f0c4Bxr7XeAVmvtLdbaucCLwGdTGp2IiEe9tYsPukGe\n2fo8t710B797+//Ye2Cfb2ON6HzWT0eNSpJn/YgMBF4SlGHW2p3hr9uNMZFy9u9zsMOsiEhGNTS7\nXXbqOI5DQ7PLrsYa7nj1Lh5+91Fag620tLdSvXdTZgKl51ijpeqsH5GBwMsSz3vGmCustX8EtgFn\nAU8Aw4ExqQxORMSr+MshQbKnNnLbS3f0S1+TaD1tD05m6SYVZ/2IDAReEpSfAr83xjwKPAQ8YIx5\nBjia0DKPiEi/ivfLv/OWXXI/JG/yP9k/ug2C6esG2118PdWY9La9WGQoSnqJJzxzcry1di/wPeBH\nhBKdx9BpxiLSzyK//Lcwi70Fx7CFWaFf9tCxHJK9cxUH9jxFYHTo3JyxOWO46SNf49xpZ6Y9OYHe\na0y0dCPSlZcZFKy1r4X/bgcWpTQiEZEkxPvlf/CQvxuYfwEsXrKC3OGn0VbzFsHmAja9WUf92Hom\nlvdP26ZEtgdr6UYklpc+KMOAHwPnAxOAA8BWQtuOb7PWtvTwdBGRlOrtl390AtP63pGAgzPG7Til\nuD9oe7BI8rzs4vlv4EJCCclXgX8H/gL8K6EGbiIi/aYo36FzR+zoX/6xO2QOzrJ03iGTTtoeLJI8\nL0s8nwLmWGvfjr5ojLkHeBK4NhWBicjQlcyBeAcLTI8jq6CRYNPwmAJTP8xe+LFzrYjfeUlQHKAy\nzvUqIP3VZiIyqPW04+WoIyu63Lt02Upy8+txpz5O9sgAu5fvZ3TxBJYuW8n8eb0fwNdfVGMikhwv\nSzz3AVfHuX4lcG/fwonPGDPFGPO4MeZDY8wHxpgf9XDv9caYTcaY/caYfxhjjk1HTCKSHol2VQ0l\nMsvZPn4E2ae1kTs+QFYejDz1CFrGnBR3N492yIgMHF5mUHKBnxhjrgPeJpTkGOAw4M/GmN9GbrTW\nxktkvFgOrCNUlHsI8FdjzAfW2juibzLGzANuBT4NvAzcCDxmjCmz1jalKBYRSaNED8S7b+Uj5J/a\nTqC4CgCrOtU3AAAgAElEQVS3HVq3H0b7B9M7nhO9mycdsxfJLEWJSHK8zKDMAl4H9gClwHhgL/AK\nMBmYFvWnz4wxHwGOBL5mra231q4n1Hvly3Fu/wLwG2vtc9baJmvtrYALfCYVsYhI+vVW9Bp0gzy9\n+XnqjqohULw3dG1/MR88kUf7jsPAPfiftXQWw3bXf6Wyyqbl/USGmqRnUKy1H0tHID04FthkrY0+\nyetVYIYxZri1dn/U9eMI7S6K9jpwPPBAesMUkVToqWbknaoq/rhqBXvKaiAAbtChbXsZbTumc2D3\nM7gl/VcM23P/Fc2iiPSVp0Zt/ayE0GxNtMj3Y4H9Cdw7Npk3DAS8TCwNXZHx0rglTmMW652qKv7v\nTytpaA5SlJ/F5z55DP989S3qm4IUFThcdu0FACy6azmMOY68UW/gZu+j5rk2Rowtw3Ecig6poPbd\nVZQcPqcjsaF2LZdfewHZ2akf5w8PuDj5XZeiPmwmLe/nlT5r3mjckpfqsRoICUpPOs/ddjeXm9Qc\nb3FxgbdohjiNW/I0ZrDurXdYfPcKgqOOw8l32OO6bH3qVX7wzfnMOnJmx31fX7AIxoRmLFreOxKC\nAXJzd9D47jKmTj+cEeMCnPqZs3h+zVvs29/GiGEBrvrW52JeI5VGF+ey50DXGZsxxTmMGjU8Le/Z\nF/qseaNxy5yBkKDsouspySXhv2s6Xa/p5t51ybxhfX0T7e3BZJ4ypAUCWRQXF2jckqAxO+jXv3s4\nlJxELZUERx3Hr3//MD/4zpSO+/bUtxycsWjPAWDYyImMyi/jZ9+7oeO+OR+f0/H1O1VV/Ns3v98x\nM3PZRXOZWV6ekrgv/szZLLpzOW7UUhS1a7no2guoq9vf+wv0E33WvNG4JS8yZqkyEBKUl4EpxphR\n1tq68LUTgXestY1x7p1NeLuzMSaLUF3K/ybzhu3tQdra9IFMlsYteRozqG8Kdt21k+VS3xg7NoV5\nodmVzjMWhXnEHcOYfirhmZnb7lyesi3GMw6bwbfiNF+bcdgMX/5vqs+aNxq3zEl6wcgYs6qb66OM\nMS/3PaRY1to3gJeAXxljRhhjjgJuAn4Vft8qY8zJ4dvvAq42xnzCGDOc0EGGjcCjqY5LRFIjdteO\nS2D8JvKOep7hhbErs/PnzaV1xz9j2sW37vhnt+3iE+2n0heh5mtf5+cLv8HCBTdoi7FICiU8g2KM\nmU6o18lJxpiziBxqcVA5kJ7FXrgYuBvYDtQD/22tvTv82OFAIYC19q/GmBuBPxAqjH0FmKsDDEX8\nK7Jrx5lYTm7Z2wSKQhOlYz82scu9bQcaqbNPkxXIob2tBae9kdt/fS+l40Z39CCJ9CZ5w77P6PKj\nY54fr5+KiPhTMks8JwG3AznAX7u55499jigOa+124LxuHgt0+v5uQsmMiETxS1OxznFcesG5nPO5\nMl6oWw2BUPIwNmcMFx716ZjnLV22koKppzOs0xLPNvs0reNCPUguOetoHnzqDZyS2bRSg6sThEUG\nrISXeKy19xFqytZKbDO2yJ9x1tor0xGkiPSNX5qKdY5ja14Zv3z7Hl6oXwMBl4AT4MSi4wiuzuFn\nP7mfWxbd3hFj7KnEIY7jkBXI6Vi++e39KzqWdYpLZ7J742qdICwyQCVVJGutdY0x46y19ekKSERS\nzy9NxaLjcPI/JO+IF3ECoQLESYUTOKXgRH7z++fjHhTY3anEwfbWjp+pzSnoeLxgxAQAdtlnyKGZ\no82hOkFYZADxsounwBhzK6H288M6P2itPbnrU0QkkxI936Y/43CbhxNsGENWcS3Zm4dz41XXcevi\nX3abSM2fN5cfL1kRs61398bVFJeGSt9c1yXbbYpZ1ikYMYH84lIms46FC26IH5SI+JKXBOUe4Bjg\nGaA5teGISDp0N/vQX/UYkbqTzVu30dRew4gJR1AwYgL160rYv3c32fX7uHXXL9m5pxFnTPxEqqLc\nsODaC1hyzwNUbXiflvYATiCP4SUHl2+u/tz5PPjU2rht8kVkYPGSoJwMHGWt3ZTiWEQkTXo63yYZ\nXgpto/uRjJhxNMWuS231ag401NDa3EBJ2Vk4hzhscV12vv8Q40d/tEsitWXTBr5xy88Jtuxjd1Me\nJUdd0vFz1G1YxXh3PV++5nIqyg3Tpk7t0ptEyzoiA4/T+dTQ3hhj3gemD+Ktu25d3X415klCdnYW\no0YNR+OWuEyMWWWVjf3FneQunpjGZ1FJTqTxWXfJyy2LbmcLs7okHe+//AcO/ciVMdcb927jQK1l\nZNnB83Rq313F8HGGYSMn8kHlU4wvP7PLa2kJp3v69+mNxi154TFL2bSslxmUXwBfAe5IVRAikn6h\npmLeZxJ6KrSdP4+DyUu4uPXH9/2ZWeeOpL61HSe367JNQeGYLrtyho2cSPGB9ZQ6b9LQFGTLpg0M\nLz2JYSNDPVEC2blxd/Kot4nI4JNQgmKM+W2nS+cYY/4F2ADEpJbW2stSFJuI+EhPhbaxyYtL9iGb\nyTl0Hxua68ibUYD7Xtf6l/31tYyJUxdTOm40C7/9dQC+ccvP2VtwsGFbsL01bm8Tt9U/Z9+ISGok\n2gelc8+T9UADob4opZ3+iMggFNuSPiRSaBvpUeLk7Se34iVyp1SFtg8H4ZiyCvZWPxPTj2T3xtUU\nTzyOvdWreuxT0vk9i0tnUlsd29uktno123c393tPFxFJr4RmUKy1c3q/S0QGs54Kbe9f9hgN498j\n59B3O/qaBPcXMbo6j89/fT4v/N/bbLPPkBXIJtjeSnHpTApGTCB756qO5Zx4Ba2d3zO/uJT6ra+w\n/a2/kJtf3PFa+cWl/d7TRUTSK+kaFGPMGYS6ycbTDmy11m7pU1Qi4jsV5Yab4pzeO6VsErmnuuS2\nhGYw3KBD67YyWt+s41++GNolVDpuNK3jQoWyTfu2U7/jHRp2rie/fTc3fPlfui3W7fyexcOyKCgd\nSfOYj3e5V3UoIoOLl108QSDypMhCcPT3LqFD+i6y1m5NRZD9TLt4kqRq9+QNpjFzXZdfvb4EW7eB\nwP4csiqLGdGeG7NLKLIDqDmnlMbd7zFm+ilxdwL1Jjs7i4U//iUbDlRoJ0+CBtNnrT9p3JKX6l08\nXhKU0wjt4LkLWEMoITkB+ALwH4SKZm8Gaqy181MVaD9SgpIk/UNO3kAas0R6n+xuquPlna9x1uRP\nEMgKdPs63/3RLykyn/WcXGRnZ7F122Zu/vH9XZaaEk1yhpqB9FnzE41b8vywzfj7wJXW2jeirr1u\njPknsNhae64x5i3gtZREKCIZE9P7pNPZONGzI5EE5h/5b3TbX6Wi3DB5Shl7+7hNeNaRM1lw7QXc\n96eVasYmMoh5SVCOBariXK8CPhb+ejdQ6DUoEfGH3g4ZTCSBiZaqlvszy8tZ+O0ZffvhRMTXEt1m\nHO09YIExpiO5McY4wNeAD8KX/p3QVmQRGcBC24chMHYrZLUB4RmPZje0ZLPoF10SGCecwMQzf95c\n3Nq1PW4tFhEBbzMoNwN/Bq43xmwhVHMyCRgFXGOMyQFuAS5KWZQikjbRSzTBA3txsnJwcoZTlO/Q\nnrWH3PI1BIr30jasgdbNM3Hd0H2Ll6ygOVBCcRJLNt3tBNLyjIh0lnSCYq191BhzFDAPmEJo585y\n4DFr7SsAxpip1tqdKY1URJLWucD1xGNnsua1d2K+f/CpN3BKZtPcsoMPaz+kpOxkHAcaxm0m59Ad\nBLJDx25lFe7FpQ239nWcvBycktm4u5+O29m1pyWbvrbcF5GhwcsMCtbaKmBRD48rORHJsHj1Ia8+\nePDgvTrXZd2fVpFXYhjmONTveIdx5gyy8hvJmf4WgaK60AsFYdj2Ito2FjAu723mX3M+S+5/DMdx\nKC6dye6Nq7tsG072lGQRkc4SPYtnVaSbrDHmHxzse9KFtfbkFMUmIn0Qr8C15PA57LJPM2zkRBzH\nYWTZwe+zAtnhM3TWR3WDLSavMoeffOummNcuyl9JnetSMGICALvsMzhZAfLba/n+guu1ZCMifZbo\nDMq7UV/H28EjImnUXS+SnnqUdHe4X1YgJ+Z7Jyv0n4FgeyuBUR/gBIK4QYe27WW0bp/GOPetLvFE\nt6AvGDGB/OLScC+Sy5WciEhKJHoWz5eivr4qfeGISGfdbeW95KyjO+pH4m3x7W5Lb7C9Nfb7pl24\nrktx6RHsfHYD4+eMpHXTEQQbC7tdrlGxq4ikW9KdZAGMMZOBq4Ap1tqrw9dOsNa+lOL4MkGdZJOk\njovJ627MKqssv/79fWzaVksgp4DJh4zEDbayb8QnuiQaDVUPU1R+YbddWWMSm3B9SO27B2tQIvUi\nl5x1NGter6ShKUjwwN7QDEv28G67xmaSPmvJ05h5o3FLXsY7yRpjTgH+BmwADgeuNsZMA543xlxi\nrV2RquBEhpLKKsv3br+HxvY8SmaGEo+9rsvud59huLOjo94DQkszbU5BTHISuR7Z4htvluPiS04N\nJyM1MbMecz95Tr/+rCIivfGyi+eHwAJr7R3GmCYAa+17xpgrge8CSlBEPAjVkgQZX35KTGHrmMNP\nZ2fV32ISFNd1yXabet3i23lL767GWs48aw65gdx++IlERLzz0kn2KOB/wl9Hrw89BPhnLlhkgGlo\ndglk58adFckKHujSffXqz52fcFfWoBtk1dYXuO2l23l041/T/8OIiPSRlxmULCAfaOl0vRRo7Xq7\niCSiKN+hva0l7qzI4ZNGUey82aUgddrUqSxd/jg79+ynduc2Ro8ew933PIgbbCUrbyRF+Q6f/PTH\n+MeBl6netwmA57b9gzMnf4IRecUZ+klFRHrnJUF5GviZMeb6yAVjjCE0q/JMqgITGWrmz5tL1e33\nUFu9mpKyg43PWnf8ky995ZJuTwg+8ZhNLPnT84wsv5C2cN1KbfVqCseOpWFqC3/c8RBOIHT/pMIJ\nXDHzUiUnIuJ7XpZ4bgBOAOqBfGPMh8A7QAnwjRTGJjKkVJQbvnfD5ykb207dO39m3/rHGNnwIt/5\nykXd7qSprLL81x+WMbJsTkzdytiZxzBs1pvkTrE4AXDbXYZtLeS8onOYWFjanz+WiIgnXs7i2WqM\nOQY4B5hBqA7FAk9Za5PfsywiHSrKDXcsWpjw/UuXrSSrYFyXupXc6W8TCE+SBPcX0bJxFk2Nhfz0\nfx/lpmuyfLV1WEQkHi/bjF8AVgKPW2ufSH1IIpKohmYXN9jWpW6lZdNMcstfoH3n4bR/MB3cLBwH\nKJnN0mUrWbhACYqI+JuXGpTngE8D3zPG1AJPAI8DT1pr96UyOBHpWVG+Q+7wsWxd+wD5xYfgBtso\nOqSC/bXv4b6dxbiyw2Luj+6TIiLiZ16WeG4GMMYUAZ8A5gA3A380xqyx1n4itSGKSHdOPHYmr777\nPJNmX9pRVLuz8klG59bzYbPTa5+Uns7yERHJJC9FsgBYaxuAJ4G/hP9Y4JQUxSUiPQi6QdqD7ax5\n7R1KDo8tkB1fcTZlZTNY9J3re+yTEmmFv4VZ7C04hi3MYvGSFVRW2Yz9XCIiEV5qUE4GTg//OZHQ\n6cZ/B/6T0PKPiJC+2YldjTXcW/kQh42c3u2JxQ1Nbq8H+i1dtrLjnJ7I81SjIiJ+4aUG5QXgDeDn\nwGettXtTG5LIwNfdCcQ39eHE36Ab5Nn3V/NI9RO0Blt5r34LxaNHU9fY/TJO51b30XpKbkREMs3L\nEs8CoIZwYzZjzE+NMXONMYWpDU1k4Io3O+GEZye82NVYwx2v3sXD7z5Ka7CVgBNg7tQz+dzZn064\n3X1nRfkOnU8z71yjIiKSKV6KZBcDi40xucCpwJnAQuBIY8xr1tqTUxyjyICTqtmJzrMmAGNzxtC6\n1uGpZ9dRlP8ml5x1NGte79oGv7clpvnz5rJ4yQoIJ1Idyc015/d9AERE+sjLEg8A1toWY8wrwDAg\nDygAjktVYCIDWVF+aFmnpx00iXjALuOF7WsACDgBji88mmce2Iwz5uDS0ean1nZZOkpkiam3GhUR\nkUxKeonHGHOuMebHxpiXgVrgF4SSk/8g1O5eZMibP2+u56WXaB+beBJZThaTCidw00e+RvXfduCM\nOb7XpaNEl5hCNSpf5+cLv8HCBTcoORER3/Ayg/Iwod069wFXWGurUhuSyMCX7OxEd8sxk4om8LVj\nvsT0EVMIZAUSXjpSAayIDHReEpTR1trmlEfSDWPMaEIFuecCbcCfga9aaw/EufdK4LdA5DGH0FlB\nH7fWvtI/EYuE9LSDJlpvyzGHj5recW+iS0epWmISEckUL0Wy/ZachP0OGA6UATnAo8Bi4Ovd3P93\na+3p/RSbSNIqqywPLH+cpjaHgmyXvXv34JR8IqF+JIkWtqoAVkQGOs+dZPuDMWYscB5wg7W21lq7\nA/gOcJUxxnOBr0imRGZLNrtHUZN9JNvGF1Fb0kpz/Y6Oe5r2bWeXfZo37Pvcsuj2mM6ukaWjyc6b\njGx6ncmsi9tbJdH7RET8yu+/5I8FWq21b0ZdexUoAgzwdpznTDLG/A2YDWwDFllr70t7pCIJiBSv\nZuU3kjP9LQJFdeRMctj2l7coGDGBpn3b2V+7kXHmDBzHYYvr8sP/+RMlww6QlTeyoz5l4be7m0A8\nKNElJhERP/J7glICdD4heU/477Fx7q8B1hPaUfQOMI/QIYbbrbWrEn3TQMDXE0u+ExkvjVvvGg4E\nyZ6ymZxD1+MEggC4TUVkte/BdV3qd7zTkZxAaLknp/SjrK/6G4dUHEOd6/LjJStYcO0FzCwvz+SP\nkhH6rCVPY+aNxi15qR4rTwmKMeZS4F+BydbasnDTtuuttT/x8FqXA38kVMwaESlu/W4PT+2yHcFa\nuxKI3ke51BgzD7gaSDhBKS4uSPRWiaJx69mOhl24x+0lt3AnAG7QoW17Ga3bp3H4mJcZmV/FXqcl\nprAVQklKIDu342u3ZDZ/euRJbj9pdr//DH6hz1ryNGbeaNwyx8thgV8Abgf+AHw0fHkscJ0xJmCt\n/VEyrxdefom7BGOMORMYaYxxrLWRhCTSa2VXgm/xHqHlnoTV1zfR3h5M5ilDWiCQRXFxgcatB2t2\nvMof336I1sJQN9jg/iJaNs4i2FgItWv54rUXMbO8nP/4wc/ZHGf3TbC9teN7x3HYXd9KXd3+fv85\nMk2fteRpzLzRuCUvMmap4mUG5TrgfGvtKmPMFwGstduMMZ8FlgJJJSi9eJVQIe8sQgcUQugE5b2E\nlnJiGGO+BNRaa/8cfRnYmMybtrcHaWvTBzJZGrfujckbTVuwraMb7MZXPqCpZRMFOS6XXnM+Mw6b\nQVtbkEsvOLfL7pva6tUUl87seC3XdSnMY0iPtT5rydOYeaNxyxwvCcp04Nnw19HLLGuBCX0NKJq1\ndo8x5kHgdmPMfEIda38I3GWtbQcIF8T+2lr7EKFtyL80xlQTKqC9mFD/lBNTGZcMDb2dZZOMqcWT\nuWTGBZSNnMrEwlKyT8pi1Kjh1NXtj/mPX+cGb27rfhoDB8gvLgXQdmERGTK8JCgNwFRCSyfRjic0\ns5Fq1xJq1LYBaAHuBf4z6vHpwCgAa+1/G2NGAMuBMYAlNNvzBiJJSOQsm2R9/NCTErqv8+6byiqr\n83JEZMhxOh+33htjzO3AycD3CHV1/Rih5ORm4GFr7TdSHGN/czv/v1rpWXZ2/NmAgeyWRbezhVld\nakEms46FC27o8+sPxjHrDxq35GnMvNG4JS88ZilrV+1lT9C3gZeBFYROMX4Z+BWhDq83pyowkUxq\naHbj7qZpaI6f0O9qrGHtztf7IzQRkSHBS6v7A8BXjTE3EWo/7wLV1trGVAcnkimJnmUTdIM8+/5q\nHql+AheXiYWlHDJ8fH+HC6S2ZkZEJNOSnkExxuSG+560AlWE6jzawteHpTpAkUyYP28ubu1aIkug\nHcWp8+Z23LOrsYY7Xr2Lh999lNZgK67rsrn+/YzEG6mZ2cIs9hYcwxZmsXjJipg2+SIiA4mXItlm\n4jRJixLwGIuIb3TeTRNdnBo9a9IaDPUnmVQ0kSsqLmFiYWlG4o200E/kwEERkYHAS4JyNbEJShYw\nDbgU+H4qghLxg3hn2exqrOXeygep3rcJgIAT4NypZ3L2lNMIZGUuN29odnEK4tTMNCVXBC8i4hde\nalB+H++6MeYe4CeEtgGLDEr1LQ1s3LcZgEmFE7hi5qUZmzWJlmjNjIjIQJGyk32stRuAoXd6mQwp\nh42cxhmTP855087mxuOv80VyAonVzIiIDCQpO83YGPMxYESqXk/Er+Yd9qlMh9BFTzUzIiIDkZfD\nAnfQtUg2l1A31/9JRVAikrx4NTMiIgOVlxmUu+JcawLettY+1sd4RDIq6AbZ9uEHTCpK6bFSIiKS\npKQSFGNMFvC4tfalNMUjkjG7Gmu4t/IhtjZs4+YTvsHYYWMyHZKIyJCVbJGsC6wKJyoig0LQDfLM\n1ue57aU7qN63iZZgK3/b+vdMhyUiMqQllWhYa13gPuAGY4z2L8qA17kbbMAJcN60c7jk8PMzHZqI\nyJDmpQZlLPBpYIExZhPQEv2gtfbkvoclkl5+7AYrIiIHeUlQ9gJPpDoQkf60uX4rD7/7KOCfbrAi\nInKQl06yV6UjEJH+NG3EFD428aNsrt+qWRMRER9KOEExxjRaa3VasQwaFx52HgEnoFkTEREfSmYG\nRUWxMqBVVlmWLltJQ3PojJr58+aq06qIiE8ls4tHx6LKgNLS3trxdWWVZfGSFWxhFnsLjmELs1i8\nZAWVVTaDEYqISHeSmUHJNsZcQ88zKa61dkkfYxLpk8gOnSc3r+Jbx1/H6PxRLF22Eqdkdsdpv47j\nQMlsli5bycIFmkUREfGbpBIU4Ne93OMCSlAkrv5YYol0g63etwmApXYZXzn6ahqaXZyC2NzacRwa\nmjQxKCLiR8kkKM0qkhWvIkssTslsnAKHOtdl8ZIV3JSiE3fj9jUpnMD5ZecCUJQfes/IDAqA64YS\nJRER8R+1rJd+EW+JxQkvsfRV/G6wZ3Pj8dd1bB+eP28ubu1aXDc0Y+K6Lm7tWubPm9vn9xcRkdTT\nLh7pF+laYqlr3sttL90RM2tyxcxLu/Q1qSg33HTN+Sxd/jgNTcHQElOKZm9ERCT1kklQ/pi2KGTQ\nS9cSy6j8kcwedzQv73yNc6eewdlT5nTb16Si3LDw20pIREQGgoQTFGvtl9IZiAxu8+fNZfGSFRBe\n5ulYYrmm74fyXXj4pzl98qlxu8Gq94mIyMDk5SwekaSlc4llWE4Bw3IKuiQjJx47kwefeiNthbki\nIpI+TqRoUDq4dXX7aWsLZjqOASM7O4tRo4aTyXGL2SUUnqHZue4hxs+6uMuy0mTWsXDBDRmJM8IP\nYzYQadySpzHzRuOWvPCYpaxeVbt4xNd2NdZw5xu/Y++BfT3eF2+XUFbBuJjkJHK9oVlJuYiI3ylB\nEV8KukGe2fo8t710B2/truT+qj/T02xfQ7PbJRlxg21dnqPeJyIiA4NqUMR3OneDDTgBphZPwsXF\n6Wa3e7xdQkWHVLC3ehUjy+akvDBXRETSSwmK+EZ33WDj9TXpLN4uofzWHXz+olNZ8/qb6n0iIjLA\nKEERX2hpb+G/Xv/fmFmT3vqaROtpl9DcT56T5uhFRCTVlKBIRkVvDXaP2Aslic+adKZGbCIig4cS\nFMmYzgcIupsPkF2zhvNOPyfp5ERERAYX7eKRjOmyNbg9j7b6U3lo+RMZjkxERDJNCYpkTLytwepT\nIiIioARF+knQDfL391+koeXDjmtF+Y76lIiISFxKUCTtdjXWcserd/Hg+uU8YJd1XJ8/by5u7dqO\nJKWjT8m8uZkKVUREfEJFspI2kVmTFdWPd/Q1qW3aTVNbEwXZBWk9QFBERAa2AZGgGGOOB+4Haqy1\nJ/dy7/XADcBYYB3wFWvta+mPUqLtaqzl3soHe+1roq3BIiISj+8TFGPMZcAi4C1gVC/3zgNuBT4N\nvAzcCDxmjCmz1jalO1YJLdM8+/7qmFkTr31NRERk6BoINSh5wInASwnc+wXgN9ba56y1TdbaWwEX\n+Ew6A5RY79ZV0xpsJeAEOG/a2dx4/HVKTkREJCm+n0Gx1v4OwJiElgGOI7QUFO114HjggdRGJvE4\njsOl5rMcaG/hs4efp8REREQ88X2CkqQSYE+na3sI1aNIPxmRV8R1x16T6TBERGQAy3iCYoy5HPgj\noaWYCCf8/VXW2nuSeLnuOnwl1fkrEBgIK1/+ERkvjVviNGbeaNySpzHzRuOWvFSPVcYTFGvtfcB9\nKXq5GmBMp2slhHbzJKy4uCBF4QxOOxp2UZQ7nMK84THXNW7J05h5o3FLnsbMG41b5mQ8QUmxl4HZ\nwL0AxpgsQnUp/5vMi9TXN9HeHkx9dANc0A3yzJYXWP7u4xw3/iiuPuoyIJQ1FxcXaNySoDHzRuOW\nPI2ZNxq35EXGLFUGUoISt/+5MaYS+IK19kXgLuBBY8xy4BXgP4FG4NFk3qi9PUhbmz6Q0Tr3NXnl\ngzf45JQzGTespOMejVvyNGbeaNySpzHzRuOWOb5PUIwxVcBkQrFmGWOaCNWUGGvtVmAGUAhgrf2r\nMeZG4A+ECmNfAeZaa1syEvwAVlllWbpsJfXNQXKmNHFg2n7a3HbgYF+T6OREREQklXyfoFhry3t5\nPNDp+7uBu9Ma1CBXWWVZvGQFWRPLyZ35Ni1F9eBCFlnMnXZml26wIiIiqabyZOli6bKVOCWzyZ38\nLoGiOgCC+4soXjeac6edqeRERETSTgmKdNHQ7OI4Di2bK3Bbc2l9/zAOvHMSTXW+n3ATEZFBQr9x\npIuifIc618Vpzaf5jY9DMBvXdSnKj1unLCIiknKaQZEu5s+bi1u7Ftd1O5ITt3Yt8+fNzXRoIiIy\nRChBkS4qyg03XXM+k503Gdn0OpNZx03XnE9FeULnIYmIiPSZlngkropyw8JvKyEREZHM0AyKiIiI\n+MXSYsMAABIMSURBVI4SFBEREfEdJSgiIiLiO0pQRERExHeUoIiIiIjvKEERERER31GCIiIiIr6j\nBEVERER8RwmKiIiI+I4SFBEREfEdJSgiIiLiO0pQRERExHeUoIiIiIjvKEERERER31GCIiIiIr6j\nBEVERER8RwmKiIiI+I4SFBEREfEdJSgiIiLiO0pQRERExHeUoIiIiIjvKEERERER31GCIiIiIr6j\nBEVERER8RwmKiIiI+I4SFBEREfEdJSgiIiLiO0pQRERExHeUoIiIiIjvKEERERER31GCIiIiIr6j\nBEVERER8RwmKiIiI+I4SFBEREfEdJSgiIiLiO9mZDiARxpjjgfuBGmvtyT3cdwvwXaAlfMkBXGCK\ntbYm7YGKiIhISvg+QTHGXAYsAt4CRiXwlHustVenNyoRERFJp4GwxJMHnAi8lOlAREREpH/4fgbF\nWvs7AGNMok852hjzD6AC2AAssNY+labwREREJA18n6Ak6X1CScl3ga3Al4G/GGOOstauT/RFAoGB\nMLHkH5Hx0rglTmPmjcYteRozbzRuyUv1WDmu66b0BZNljLkc+COhYtaISHHrVdbae8L33QKc01OR\nbDevvwZ40lr73RSFLCIiImmW8RkUa+19wH1pfIv3gEPS+PoiIiKSYoNq7soYc7Mx5uOdLwMbMxGP\niIiIeJPxGZQkOPEuGmMqgS9Ya18ktA35V8aYC4DtwFeBMuD3/RWkiIiI9J3vExRjTBUwmVCsWcaY\nJkL1KcZauxWYARSGb19AaFboBWAYsA443Vq7o98DFxEREc8yXiQrIiIi0tmgqkERERGRwUEJioiI\niPiOEhQRERHxHSUoIiIi4jtKUERERMR3lKCIiIiI7/i+D0q6GWOOB+4Hano65yd8FtB3gZbwpch5\nQVOstTVpD9RnEh238L3XAzcAYwn1pvmKtfa19EfpH8aY0cD/AOcCbcCfga9aaw/EufdK4LdA5LHI\nZ+3j1tr/396ZR9tVVHn4e0KIhmCYlDHBMP0AERqZOkDjSsIkMhgQZFBpgoLdIIiADNqykDAJmLSK\nYNowSjO1AZUhDIKyEBYQJgMNP6YEQWZDoCFBIrz+Y9dNbm7ue+9e8l5yk7u/td56t+rUqdpn37qn\n9tm169TkhSPxokHSWsAFwL8AbwMX2z6hi7Jt368qNKq3vI/Ni6SdgUuA220f0EPZ04DRwHLA3cCh\ntqf1uZAtRqM6k3QR8BVgdsnqAGbZXrHRttraQJF0AHAG8CjxFtqeuNT26L6VqvVpRm+SRgE/BHYH\n7geOA26QtI7tWX0tawtxEbAs8WbjfsDvgLOAb3dR/o+2Rywk2VqJ6whjY3ViD62bJb1se1x1oexX\n89GQ3gp5HwMkHUcYHD3udC/paOAgYCdif7dzgWuBzfpSxlajGZ0VTrX9ww/bXrtP8fQHtgbuW9SC\nLGY0o7dDgAm277Q9q3TWTmCPvhSwlZD0CWA34Gjbr5c3G38POFhSWz8kVCNpS2Bj4Ejbb9l+EjgT\nOKxO8bbvVxWa1Fsyl1nAVsAzDZQ9BDjL9hTbbwPHABtJ2rovBWxBmtHZAtPWBorti2y/3MQpm0q6\nR9IMSZMl7dhnwrUwTerts8ADNXkPA1v0rlQtzWbAbNtTqvIeJFzF6uKcwZJuk/SGpEclHdjnUi56\nNgOm2X6zKu9BYH1Jy9aUzX41l2b0BnkfA8D2z2z/X0/lJPUHNiR0Wjn3beBp2qy/NaqzKkZIeqTc\nx+6UtHkz7bW1gdIkLxAd8iBgNeBXwPWS1l+kUrU+KwPTa/KmE3ED7cLKwJs1eRWd1NPDa4QL9TjC\nXT8GuFjS8D6TsDXoqq/A/HrKfjWXZvSW97HmWYmIn8j+1hzPEPex3YDBhMf9lhKP1xBLtHu5PHVe\nRrh+K1SCwg62fWmjddmeAEyoyhonaX/gq0TQ2RJDb+qtpo5G8hdLetBZd/1jPj3YvhG4sSrryhJz\nMRq4Y8GlXSyp1VNb9KteYB59tNN9bCGR/a0LbI+pTkv6LrA/MIp5+2CXLNEGiu3Lgcv7sImpxBPu\nEkUv6+014gmkmpWJgL4lhu50JmkHYHlJHbYrN7SVy/9XG2xiKtCUe3Qx5FXq9xWIflRNW/SrBmlG\nb/VYIu9jvcjrwAfU13Gjv9+2x/YHkp6nib6WUzwNIukkSdvXZgPPLgp5FiPup2pglfQRIn6gnQKT\nHyR+a5tU5W0NzKBONLykQyXtVZvNkt/X7gfWklS9Mmxr4H9tz6xTtt37VYWG9Zb3seax/R4whXn7\n24rAurRnf2sISedK2qgqvTSwNk30tSXag9IEHfUyJT0OHGL7bmI57U8lfRF4ETiCWDJ68cISsgVp\nRG8XAFdLug6YDPwAmEkss20LbE+XdDUwVtJ+wMeA04ALbL8PIOk24Be2ryGWIf9E0jPAY8A+xPtT\nlugVA7YfkXQf8Ts7HBgCHA+cAiDpCWB09qt5aVJveR9rAEmrA78HdrH9HHA+cLKkO4DngJ8A99mu\nDdRuW+robAhxHzsQeAc4FXiXWBLfEG1toJQf7hBCDx+RNIuYU5Tt54H1gYGl+InEU/BdwADClTyi\nLBltK5rRm+2by9r5S4iAssnAruWppJ34N+JFbU8TL8n6FTGoVlib8k4Z2+dJGkT8kFcCDOxp+5GF\nKvGiYR9gPDF4vgWcZ3t8ObYe2a+6oiG9kfexOVTdt/qV9Cig0/aAkrc+8UoFbI+XtCpwC6HL2wmd\ntxXN6IxYmj2O6GNLEd6mkc28p6ijszNjfJIkSZIkaS0yBiVJkiRJkpYjDZQkSZIkSVqONFCSJEmS\nJGk50kBJkiRJkqTlSAMlSZIkSZKWIw2UJEmSJElajjRQkiRJkiRpOdJASZIkSZKk5UgDJUmSJEmS\nliMNlCRZhEgaImmWpJGLWpaekHSPpAsXUlvjy74njZa/Y2HJliTJwqGt9+JJkmaQ9AdgO2IvnWo6\niP0ptrH9cAP1HA5cYXu67b8Qmwf2GZKWBb5p+9y+bKc3sX1ob9dZNi27x3Zb7Nwr6QvAS7YfXNSy\nJMmHIQ2UJGmcTuBq2wd82AokLU9soHUrML23BOuBEcCxwGJjoPQ2kjqAscBXaGK79wVsc2nb/1gY\nbXXBKcQGgh/KQGkB+ZM2Jw2UJOllJI0ATgM2BD4A7ge+TfzeJhNTq49Iugo4GZhKbFF+i6S7gAeA\n2cRuoO8DPwJuAC4ENiZ2Nz7Q9uOlva2AM4F/Irw5fwa+Y/uB4q0ZR+w6PRM4wvaFkrYHTgc2A94A\n7gaOKbtRI2k14JeEx2gGMbh3db0fJYytvW3fVPKOB84AtrN9d8k7Hdje9naSBpc6RxYdTQG+Z/tP\npexFwAa2h5X07kXeocBDwH8QO8ruaPv3VbIcBxwFDCrX9DVgFvAqsdvqbyXdY3t4neu4q+juPeBA\nwiC9ATjc9sxS5quEsTcUmAncARxp+7VyfCpwMbAz8GlgkKQBwI+B3YtcLxG7DY8r5+xA7JI7spTb\nAHgY2A/4OnAYsRvseNsnVsl7GHA0MJjYxfha4Ae235X0EvBJ4GeSTrC9tqT+RD/ZF1iOMNR+antC\nqe8goq8cC5xdvr+zJZ1S9PgJoq9cDRyfxkvS12QMSpL0IpKWJgaKCbaXB9YkDIrxtqcAO5Wim9j+\n1zpVzCYGpvuBlYlB/HRiYBkFrFbKjSnt9QOuB54AVi3HnwV+A2D7vFL2FdsDinEyGLgRuIQYMDch\nBuWbiqeBcmwlYD1ioB1CGEfzYftd4E6getAfCTxCeG8qDAduLG1cTwx2axWZrwNukzSkqnxnucYN\ngInAr4tMRxADaWfRV4WdS3pt4DOEwXai7bcAEcbb7vWMk8JsYH/gUWCVIu8uhIGIpM0I4+Mc2x8H\nNiWM0P+sqWc0cAKwfEmfUWQbZnsg8C3gXEmVvlC5hqOAHYBPEUbHHwjDY7Vy7HhJnymyfIkwgg8B\nBgJfIPrWWADbq5XrPdz22qX+c4FtCKNzEGHcjJX05SrZ+wPbAmvYPrsc+wYwvMg+HPg8cHAXOkyS\nXiM9KEnSHPtK+mKd/Dtt70I8mS5LGXTKk/eRdcp31MmrMNX2VQCSJgKnElNLL5a8W4HdSv2zJQ0F\nZtt+rxy/AviapCElxqWWfwces/1fJT1d0tHAK8D2kh4lBsq9bb9a6jyRGAy7YhLhdUDSMsCw0s7B\nwBhJywGbl7yKd2FYxTMBjJN0SCl/Sk3do4C3gTHlqf0RSRcA59WUe6nilQCmSbqd+Y2q7vQO8Bfb\nvyyfH5N0GWG0HGH7IUkr2Z4BYPsVSTeU49U8aPvOqvQxhHfo7XLeJEkvA/9MeE4qnG/7bwCS/gRs\nafv8kv41cCnhXZlS6pxQ8TgBT0oaA/y3pCNsv199vSUO6VBgT9tTy7E7JF0CfBO4quT1B8bZnlXS\nqxIerr8X2Z8GNupBh0nSK6SBkiTN0W0Miu03yjTDLySdANwGXFc9DdEA06o+Vwbw52vyqgNrRwFH\nSVoH+CgxHUD5XA8Bm5cpnwodhFE1FHiL8E5UBjJs/13Sc93IPImYDhgEbAE8BfwOuKAYLJ8DXi+D\n/JGE9/Z1SdXtdxAelVrWIgyH6imFe5nf2Hi6Jv0uMKAbmevxWE16KrA6gKSlgGMk7QOsQei5H/Ba\nzTnP1KTXAc6QtCXhAeoAlmHe76cTqNbvTGCOcWl7VtFV5XsX8FlJ36ppq5Pwdk2tyV+HuN9PlNRZ\n8ir6e7GmbHWMzkWEMTytGE23Apd3YfgmSa+SBkqS9DK2x5YYip3K30RJE2036hb/oME8JG1DTMcc\nD/zc9kxJwwnDqCs6gUm2d+uizmFV5apZqrZsBdtPSHoe2J6YRrjd9gxJTxBTBsMJI6ZS78wyZdAI\nHcx//bWyUafMh6F22ruD4j0Avkt4w74M3Gr7/RKf8Y2ac2pXef2WiDvZpirGp56xVyt/d9fTCZzU\nxMqsir62s/1AD2XnyF+mx3aUtCHh+doD+L6kvW1P6qqCJOkNMgYlSXqZyjSA7attf514Aj1I0sf7\noLlhwFu2z6maLtmqh3MMbCJpzu9fUoekivfieWJg/lTV8WWp792o5mbCENmBCGAF+CMRhzICuKmq\n/Y+pyn1S2hjaRb0vAoOr4mMgrrGekbKgqCa9DnO9VxXDa1LVFMqW3VYmVeJ4xlYZJ6tTvDILgAlP\nVXVby5dVYvV4BvhHnXPWKB6uukhaRtJA24/bHmd7BHAlMV2UJH1KGihJ0otI2pZwh+8o6SNl5cS2\nwMvlafQdYvDfqEyHLCjTgOUkDSvt7cfcQNxKwOk7xGqSNSQNBM4nphrOkrRciQ/5EXCvpAG2XyBW\nEh0j6ZPFsDqTWFHUHTeXtjcmgmYhDJQ9iGDSSrzFrUQg6s8lrSlpqSL3E2VFUi03ACsUeZaRtAnd\nx8PU453yfwNJK3RTbl1Jh0rqL2lTIq7minJsGrCppFUkDZR0FhFzNKjotR5vAG8CI8v3sx4xbTKV\nud8P9BwbU8uPgb0k7S+pn6Q1gWuAy6vKzATWl7RCMV7HAydJ2rIYpFsA9xABuF1xHrHyaTDMWd21\nAfBkk/ImSdOkgZIkzbGPpJk1f7PK/5NK0OLRxGqKGcBfCa/CruX8h4npl8uJZcMQnoDuvAHdHZtI\nDDzXE0Guw4E9CcPgGkk7lzIvAI8Dh5Un+V0J78tLRKzDxsCIKi/MXsQA9zQRl/EssWy3Xzey3Aas\nCzxUCQglDJVPA/fafhPAdiex5PYNYlnvDGJp676276ut1PZkYhrlMOBvwFnA94lBvSejqVLH68Bl\nxIqaW7opOpEIAv1rKXctsYoKYjXUU4ROHgVeJt6r8irwlKQVqfmubH9ALNH9PBHbcwmxwmcssIek\nCaVoI96gOWVs/w9hWJxMGECTCQOqOj5qHBEA+2fF6rJjiZVQvyEMtiuJacGzu2nzO8R3f6+kd4jY\nn/tKu0nSp3R0dvaFlzRJkqT3kNTP9uyq9EjCgBjaWwGbilfrT7U9ujfqS5Jkwcgg2SRJWhpJqxDT\nZqcA5xDTUycBk3M1SZIsueQUT5IkLY3tV4Avlb/pxJtkXyvpJEmWUHKKJ0mSJEmSliM9KEmSJEmS\ntBxpoCRJkiRJ0nKkgZIkSZIkScuRBkqSJEmSJC1HGihJkiRJkrQcaaAkSZIkSdJypIGSJEmSJEnL\nkQZKkiRJkiQtx/8DPsO9zMkZeaQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40246046d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ESlA+p3g+RLhgIMCZwKPu/r+EjdvGRRVYmnuAWmAEcBAwlrAQ2o6ZHQHcl4yv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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fdcbee668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bwH+4++N5PKeIEJzh8u7HHzC0gud1iEjlyXYE5MyM+y3A2PBfW2mCRmU5cff3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fdcbeea20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = K.eval(model.layers[-1].W).reshape(-1)\n",
    "y = W.reshape(-1)\n",
    "visualize(x, y, 'Estimated weight parameters', 'True weight parameters')\n",
    "\n",
    "x = K.eval(model.layers[-1].b).reshape(-1)\n",
    "y = b.reshape(-1)\n",
    "visualize(x, y, 'Estimated bias parameters', 'True bias parameters')\n",
    "\n",
    "x = K.eval(nb.theta)\n",
    "y = dispersion\n",
    "visualize(x, y, 'Estimated theta params', 'True theta params')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zero-inflated models\n",
    "\n",
    "In some cases, there might be excess number of zeros in the data which can be accounted for using so called [_zero-inflated_ models](https://en.wikipedia.org/wiki/Zero-inflated_model). In such cases, the data can be modeled using zero-inflated negative binomial (ZINB) and the data generation process can be imaged as follows. First a coin, which on average results in tails with probability of $\\pi$, is flipped. If we get tails, then the data that is being generated is  zero (e.g. a point mass at zero), otherwise it is sampled from a negative binomial (or Poisson, if the model is zero-inflated Poisson). If the data is sampled from a negative binomial, we may also end up with a zero. Therefore, there are two sources where zeros in the data may come from.\n",
    "\n",
    "This can be written as a mixture model:\n",
    "\n",
    "$$ \\text{ZINB}(y_i; \\pi_i, \\mu_i, \\theta) =               \\begin{cases}\n",
    "                            \\pi_i + (1-\\pi_i)\\  \\text{NB}(0; \\mu_i, \\theta) & \\text{if } y_i=0\\\\\n",
    "                            (1-\\pi_i)\\  \\text{NB}(y_i; \\mu_i, \\theta) & \\text{if } y_i>0\n",
    "                        \\end{cases}\n",
    "$$\n",
    "\n",
    "Note that the model reduces to negative binomial if $\\pi=0$. Another important thing to note is that the mixture parameter $\\pi$ is sample specific similar to the mean parameter of the negative binomial, $\\mu_i$. It means that it is conditioned on the data. Since it is a value between 0 and 1, it can be computed from the data using a sigmoid function i.e. $\\pi_i = \\text{sigmoid}(\\textbf{X}_i \\mathbf{\\alpha})$ just like a logistic regression, where the coefficients are different than the coefficients of the negative binomial mean parameter. This can be easily implemented with a neural network with multiple outputs e.g. one output with an exponential activationo function which estimates the mean parameter of the negative binomial and the second output with a sigmoid activation which estimates the corresponding $\\pi_i$ probabilities of the samples from the data.\n",
    "\n",
    "Negative log likelihood can be written as:\n",
    "\n",
    "\n",
    "$$ \\text{NLL}_\\text{ZINB}(y_i; \\pi_i, \\mu_i, \\theta) =               \\begin{cases}\n",
    "                            -\\log\\left(\\pi_i + (1-\\pi_i)\\ \\left(\\frac{\\theta}{\\theta+\\mu_i}\\right)^\\theta\\right) & \\text{if } y_i=0\\\\\n",
    "                            -\\log(1-\\pi_i) + \\text{NLL}_\\text{NB}(y_i; \\mu_i, \\theta) & \\text{if } y_i>0\n",
    "                        \\end{cases}\n",
    "$$\n",
    "\n",
    "Now let's implement it in TensorFlow using the `NB` class we defined previously:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class ZINB(NB):\n",
    "    def __init__(self, pi, scope='zinb_loss/',\n",
    "                 **kwargs):\n",
    "        super().__init__(scope=scope, **kwargs)\n",
    "        self.pi = pi\n",
    "    \n",
    "    def loss(self, y_true, y_pred):\n",
    "        scale_factor = self.scale_factor\n",
    "        eps = self.eps\n",
    "        \n",
    "        with tf.name_scope(self.scope):\n",
    "            # reuse existing NB neg.log.lik.\n",
    "            nb_case = super().loss(y_true, y_pred, reduce=False) \\\n",
    "                      - tf.log(1.0-self.pi+eps)\n",
    "                \n",
    "            y_true = tf.cast(y_true, tf.float32)\n",
    "            y_pred = tf.cast(y_pred, tf.float32) * scale_factor\n",
    "            theta = 1.0/(self.theta+eps)\n",
    "            \n",
    "            zero_nb = tf.pow(theta/(theta+y_pred+eps), theta)\n",
    "            zero_case = -tf.log(self.pi + ((1.0-self.pi)*zero_nb)+eps)\n",
    "            result = tf.select(tf.less(y_true, 1e-8), zero_case, nb_case)\n",
    "            result = tf.reduce_mean(result)\n",
    "            \n",
    "            if self.debug:\n",
    "                tf.summary.histogram('nb_case', nb_case)\n",
    "                tf.summary.histogram('zero_nb', zero_nb)\n",
    "                tf.summary.histogram('zero_case', zero_case)\n",
    "        \n",
    "        return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can implement the regression model using the `ZINB` loss function with TensorFlow slim:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Summary name fc/weights:gradient is illegal; using fc/weights_gradient instead.\n",
      "INFO:tensorflow:Summary name fc/weights:gradient_norm is illegal; using fc/weights_gradient_norm instead.\n",
      "INFO:tensorflow:Summary name fc/biases:gradient is illegal; using fc/biases_gradient instead.\n",
      "INFO:tensorflow:Summary name fc/biases:gradient_norm is illegal; using fc/biases_gradient_norm instead.\n",
      "INFO:tensorflow:Summary name pilayer/weights:gradient is illegal; using pilayer/weights_gradient instead.\n",
      "INFO:tensorflow:Summary name pilayer/weights:gradient_norm is illegal; using pilayer/weights_gradient_norm instead.\n",
      "INFO:tensorflow:Summary name pilayer/biases:gradient is illegal; using pilayer/biases_gradient instead.\n",
      "INFO:tensorflow:Summary name pilayer/biases:gradient_norm is illegal; using pilayer/biases_gradient_norm instead.\n",
      "INFO:tensorflow:Summary name zinb_loss/theta:gradient is illegal; using zinb_loss/theta_gradient instead.\n",
      "INFO:tensorflow:Summary name zinb_loss/theta:gradient_norm is illegal; using zinb_loss/theta_gradient_norm instead.\n",
      "Step 0 - zinb loss = 1.843, (0.035 sec/step)\n",
      "Step 200 - zinb loss = 1.357, (0.011 sec/step)\n",
      "Step 400 - zinb loss = 1.353, (0.026 sec/step)\n",
      "Step 600 - zinb loss = 1.351, (0.009 sec/step)\n"
     ]
    },
    {
     "data": {
      "image/png": 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DElmSqShdR17hrLbnvdaQ9GYpSmQg8VIkO7W7rxljRvUuHBGR5Eu0CHXn3o/4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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fd7c49d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hvHHlrOnUPPQYDY2t4VU8s6brKh6RmMimQOnVbg2cU4Hrkvd3AGr3KCK7GNCn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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4028e896d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9PRasWES2JkPPmpIGTytCEvZNW8qnciUpF4g+j1I+RQ4HDizmC78T9cCQnGVD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\nKMGX9r9X0IRnzKyJ4P3fM7w/Cci6e59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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fd7f80c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4024519940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tf.reset_default_graph()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    predictions = slim.fully_connected(X, num_out,\n",
    "                                       activation_fn=tf.exp,\n",
    "                                       scope='fc')\n",
    "\n",
    "    pi = slim.fully_connected(X, num_out,\n",
    "                              activation_fn=tf.nn.sigmoid,\n",
    "                              scope='pilayer')\n",
    "\n",
    "    zinb = ZINB(pi, theta_init=tf.zeros([1, num_out]),\n",
    "                debug=True)\n",
    "\n",
    "    zinb_loss, zinb_theta = zinb.loss, zinb.theta\n",
    "    loss = zinb_loss(Y, predictions)\n",
    "    slim.losses.add_loss(loss)\n",
    "    tf.summary.scalar('loss', loss)\n",
    "\n",
    "    optimizer = tf.train.RMSPropOptimizer(5e-2)\n",
    "    train_op = slim.learning.create_train_op(loss, optimizer,\n",
    "                                            summarize_gradients=True)\n",
    "\n",
    "    for var in slim.get_model_variables():\n",
    "        tf.summary.histogram(var.name.replace(':', '_'), var) \n",
    "        \n",
    "    summary_ops = tf.summary.merge_all()\n",
    "\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    swriter = tf.summary.FileWriter('logs_zinb', sess.graph)\n",
    "\n",
    "    for i in range(800):\n",
    "        start_time = time.time()\n",
    "        step_loss, summaries = sess.run([train_op, summary_ops])\n",
    "        swriter.add_summary(summaries)\n",
    "\n",
    "        duration = time.time() - start_time\n",
    "\n",
    "        if i % 200 == 0:\n",
    "            print('Step {:d} - zinb loss = {:.3f}, ({:.3f} sec/step)'\n",
    "                  .format(i, step_loss, duration))\n",
    "    swriter.close()\n",
    "\n",
    "    x = slim.get_variables_by_name('fc/weights')[0].eval().reshape(-1)\n",
    "    y = W.reshape(-1)\n",
    "    visualize(x, y, 'Estimated weight parameters', 'True weight parameters')\n",
    "\n",
    "    x = slim.get_variables_by_name('fc/biases')[0].eval().reshape(-1)\n",
    "    y = b.reshape(-1)\n",
    "    visualize(x, y, 'Estimated bias parameters', 'True bias parameters')\n",
    "\n",
    "    x = zinb_theta.eval().reshape(-1)\n",
    "    y = dispersion.reshape(-1)\n",
    "    visualize(x, y, 'Estimated theta params', 'True theta params')\n",
    "\n",
    "    sns.distplot(sess.run(pi).reshape(-1), kde=False)\n",
    "    _ = plt.xlabel('$\\pi_i$ distribution of the data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here comes the Keras code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:525 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:507 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n",
      "WARNING:tensorflow:From /home/gokcen/miniconda3/lib/python3.5/site-packages/keras/callbacks.py:525 in _set_model.: histogram_summary (from tensorflow.python.ops.logging_ops) is deprecated and will be removed after 2016-11-30.\n",
      "Instructions for updating:\n",
      "Please switch to tf.summary.histogram. Note that tf.summary.histogram uses the node name instead of the tag. This means that TensorFlow will automatically de-duplicate summary names based on their scope.\n"
     ]
    },
    {
     "data": {
      "image/png": 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nmMw1d2nxYpy1roUqt53pQCR13bZ9o3z/gR1ccvYKVrXXnfQxItEYT7w8yC+f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\nIjYvO+X2x3WxSlVPvsJBLBb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6Ih2cpFeQfzuntD3VyLYZJJ8xaRv3mAyukQsJ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\nxv8B7lNvFhFWEVkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fdcc07d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K.clear_session()\n",
    "\n",
    "inputs = Input(shape=(num_feat,))\n",
    "predictions = Dense(num_out, activation=tf.exp)(inputs)\n",
    "model = Model(input=inputs, output=predictions)\n",
    "\n",
    "pi_layer = Dense(num_out, activation='sigmoid')\n",
    "pi = pi_layer(inputs)\n",
    "zinb = ZINB(pi, theta_init=tf.zeros([1, num_out]))\n",
    "\n",
    "model.layers[-1].trainable_weights.extend([zinb.theta_variable,\n",
    "                                           *pi_layer.trainable_weights])\n",
    "\n",
    "opt = RMSprop(lr=5e-2)\n",
    "model.compile(optimizer=opt,\n",
    "              loss=zinb.loss) #zinb loss function\n",
    "\n",
    "early_stop = EarlyStopping(monitor='val_loss', patience=20)\n",
    "tb = TensorBoard(log_dir='./logs_zinb', histogram_freq=1)\n",
    "\n",
    "losses = model.fit(X, Y,\n",
    "                   callbacks=[early_stop, tb],\n",
    "                   batch_size=128,\n",
    "                   validation_split=0.2,\n",
    "                   nb_epoch=10000, verbose=0)\n",
    "\n",
    "val_hist = losses.history['val_loss']\n",
    "train_hist = losses.history['loss']\n",
    "\n",
    "plt.plot(range(len(val_hist)), val_hist, 'b.-',\n",
    "         range(len(train_hist)), train_hist, 'g.-')\n",
    "plt.ylabel('Loss')\n",
    "_ = plt.xlabel('Steps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XWE/B5HeJlGwH2vY1ieRFUj6mqzN0vCQz6lci/Z2fItnJ6X5mjBnevXBERDrq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fd7fd54e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tZmcBLxQ6wC4EXdzvanuHqqvzOfMVPak8lE/0xCWXhW8s5YGVc3aPmgypHcxF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\nRo0bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4024637ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0rVakdGVSgOwinIorIpI1f1v72u7io1tlV6YeNknTakVKWKanYD4FPJjdUESk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4024637400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vpFLOrLWMiGGq89H3AX57oCNa/u5U84i4L9U5//svzHD2CzN/zlcAn83Mf6m/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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3fd6c96b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = K.eval(model.layers[-1].W).reshape(-1)\n",
    "y = W.reshape(-1)\n",
    "visualize(x, y, 'Estimated weight parameters', 'True weight parameters')\n",
    "\n",
    "x = K.eval(model.layers[-1].b).reshape(-1)\n",
    "y = b.reshape(-1)\n",
    "visualize(x, y, 'Estimated bias parameters', 'True bias parameters')\n",
    "\n",
    "x = K.eval(zinb.theta)\n",
    "y = dispersion\n",
    "visualize(x, y, 'Estimated theta params', 'True theta params')\n",
    "\n",
    "pi_model = Model(input=inputs, output=pi)\n",
    "sns.distplot(pi_model.predict(X).reshape(-1), kde=False)\n",
    "_ = plt.xlabel('$\\pi_i$ distribution of the data')"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}