14. Uncertainty_and_Probabilistic_Layers.ipynb

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        "# Deep Learning, uncertainty and probabilistic models.\n",
        "\n",
        "\n",
        "> **Certainty** is perfect knowledge that has total security from error, or the mental state of being without doubt. (*Wikipedia*)\n",
        "\n",
        "> **Uncertainty** has been called *an unintelligible expression without a straightforward description*. It describes a situation involving insecurity and/or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. (*Wikipedia*)\n",
        "\n",
        "A common understanding of the term **uncertainty** in scientific works is that of a measure that reflects the amount of dispersion of a random variable. In other words, it is a scalar measure of how \"random\" a random variable is. But this a reduction of the term.  \n",
        "\n",
        "> There is **no single formula for uncertainty** because there are many different ways to measure dispersion: standard deviation, variance, and entropy are all appropriate measures. However, it's important to keep in mind that a single scalar number cannot paint a full picture of \"randomness'', as that would require communicating the entire random variable itself!  *Eric Jang*.\n",
        "\n",
        "When working with predictive systems, measuring uncertainty is **important for dealing with the risk associated to decisions**. If we can measure risk, we can define policies related to making use of predictions.\n",
        "\n",
        "Regarding uncertainty, we can be in several **states**:\n",
        "\n",
        "+ Complete certainty. This is the case of macroscopic mechanics, where given an input there is no uncertainty about the output.\n",
        "+ Uncertainty with risk. This is the case of a game with an uncertain output, but where we exactly know the probability distribution over outcomes.\n",
        "+ Fully reducible uncertainty. This is the case of a game where by gathering sufficient data and/or using the right model we can get complete certainty.\n",
        "+ Partially reducible uncertainty. This is the case of games where we have no full knowledge about the probability distribution over outcomes. By gathering sufficient data we can know the probability distribution over outcomes.\n",
        "+ Etc.\n",
        "\n",
        "Uncertainty in predictive systems $y = f_w(x)$ can be **caused** by several factors (see next). Different  types  of  uncertainty  must  be  measured in different ways.   \n",
        "\n",
        "## Epistemic uncertainty\n",
        "\n",
        "Epistemic uncertainty corresponds to the uncertainty originated by the lack of knowledge about the model.  It can be explained as to which extent is our model able to describe the distribution that generated the data.  \n",
        "\n",
        "In this case we can talk of two different types of uncertainties caused by whether the model has been **trained with enough data**, so it’s been able to learn the full distributionof the data, or whether the **expressiveness of the model is able to capture the complexity of the distribution**.  \n",
        "\n",
        "When using a expressive enough model, this type of uncertainty *can be reduced* by providing more samples during the training phase.\n",
        "\n",
        "##  Aleatoric uncertainty\n",
        "\n",
        " In this case the uncertainty measured belongs to the data.   This uncertainty is inherent to the data and *can’t be reduced* by adding more data to the training process. Its cause can be the lack of information in $x$ to determine $y$ or the lack of precision when measuring $x$ or $y$.\n",
        "\n",
        "**Aleatoric uncertainty propagates from the inputs to the model predictions**. Consider a simple model $y=5x$, which takes in normally-distributed input $x  \\sim N(0,1)$. In this case, $y \\sim N(0,5)$, so the aleatoric uncertainty of the predictive distribution can be described by $\\sigma=5$. \n",
        "\n",
        "There are two types of aleatoric uncertainty: \n",
        "\n",
        "+ **Homoscedastic**:  Uncertainty remains constant for all the data. For example:   $y \\sim N(0,5)$.\n",
        "+ **Heteroscedastic**: Uncertainty depends on the input. For example:   $y \\sim N(0,f(x))$.    \n",
        "    \n",
        "## Out of Distribution (OoD) \n",
        "\n",
        "Determining whether inputs are \"valid'' is a serious problem for deploying ML in the wild, and is known as the Out of Distribution (OoD) problem. \n",
        "\n",
        "There are two ways to handle OoD inputs for a machine learning model: 1) Model the bad inputs and detect them before we even put them through the model 2) Let the \"weirdness'' of model predictions imply to us that the input was probably malformed.\n",
        "\n",
        "Modeling bad inputs is a difficult task. Training a discriminator is not completely robust because it can give arbitrary predictions for an input that lies in neither distribution. Instead of a discriminator, we could build a density model of the in-distribution data, such as a kernel density estimator.\n",
        "\n",
        "The second approach to OoD detection involves using the predictive (epistemic) uncertainty of the task model to tell us when inputs are OoD. Ideally, malformed inputs to a model ought to generate \"weird'' predictive distribution $p(y|x)$. For instance, it has been showed that the maximum softmax probability (the predicted class) for OoD inputs tends to be lower than that of in-distribution inputs. \n",
        "\n",
        "## Example\n",
        "\n",
        "Uncertainty can be understood from a **simple machine learning model** that attempts to predict daily rainfall from a sequence of barometer readings. Aleatoric uncertainty is irreducible randomness that arises from the data collection process. Epistemic uncertainty reflects confidence that our model is making the correct predictions. Finally, out-of-distribution errors arise when the model sees an input that differs from its training data (e.g. temperature of the sun, other anomalies). *Eric Jang*.\n",
        "\n",
        "<img src=\"https://2.bp.blogspot.com/-cAmhDaGEHTA/XCZZ-_pfJTI/AAAAAAAANjY/niymrKAYmUMV0fEjUhm95StzV7VBvLncgCLcBGAs/s1600/barometer_uncertainty.jpg\">\n",
        "\n",
        "## Calibration\n",
        "\n",
        "Just because a model is able to output a \"confidence interval\" for a prediction doesn't mean that the confidence interval actually reflects the actual probabilities of outcomes in reality! \n",
        "\n",
        "Suppose our rainfall model tells us that there will be $N(4,1)$ inches of rain today. If our model is **calibrated**, then if we were to repeat this experiment over and over again under identical conditions (possibly re-training the model each time), we really would observe empirical rainfall to be distributed exactly $N(4,1)$.\n",
        "\n",
        "Machine Learning models mostly optimize for test accuracy or some fitness function. Researchers are not performing model selection by deploying the model in repeated identical experiments and measuring calibration error, so unsurprisingly, this **models tend to be poorly calibrated**.\n",
        "\n"
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        "## Uncertainty and Neural Networks\n",
        "\n",
        "A trained neural network $f$ can be viewed as the instantiation of a specific probabilistic model $p(y|x,D)$. \n",
        "\n",
        "For classification, $y$ is a set of classes and $p(y|x,D)$ is a **categorical distribution**. \n",
        "\n",
        "For regression, $y$ is a continuous variable and $p(y|x,D)$ can be modelled with a **Gaussian (or Laplacian) distribution**.  \n",
        "\n",
        "Our training goal  can be  to  **find  the  most probable network instance** (represented by parameters $w$)  that  generated the outputs:\n",
        "\n",
        "$$\n",
        "p(y | x, D) = \\int_w p(y | x, w)p(w|D)dw\n",
        "$$\n",
        "\n",
        "We can observe that the distribution of the output depends on two terms: one that depends on the application of the **model to the input data**, and a second one that is measuring **how the model may  vary  depending  on  the  training  data**.   \n",
        "\n",
        "From this definition we can say that the first term is modeling the **aleatoric uncertainty**, as it is measuring  how  the  output  is distributed when the input is $x$,  and the second term is modeling the **epistemic uncertainty** as it is measuring the uncertainty induced by the parameters of the model."
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        "## Epistemic Uncertainty \n",
        "\n",
        "In  the  case  of  the epistemic uncertainty, let’s assume that we want to train a model with parameters $w$ that produces an output $y = f_w(x)$.\n",
        "\n",
        "To capture epistemic uncertainty in a neural network we will adopt a Bayesian point of view and we will put a prior distribution over its weights, for example a Gaussian prior distribution: $w ∼ \\mathcal{N} (0, I)$. Such a model is referred to as a  **Bayesian neural network**. Bayesian neural networks replace the deterministic network’s weight parameters with distributions over these parameters.\n",
        "\n",
        "In the case of regression, we suppose the model likelihood is $p(y | x,w) ∼ \\mathcal{N} (f_w(x), \\sigma^2)$. \n",
        "\n",
        "For classification tasks, we assume a softmax likelihood:\n",
        "\n",
        "$$\n",
        "p(y = d | x, w) = \\frac{\\exp(f^d_w(x))}{\\sum_{d'}\\exp(f^{d'}_w(x))}\n",
        "$$\n",
        "\n",
        "Given a dataset $D = (X,Y)$  we then look for the posterior distribution over the space of parameters by invoking Bayes’ theorem:\n",
        "\n",
        "$$\n",
        "p(w|X,Y) = \\frac{p(Y|X,w) p(w)}{p(Y|X)}\n",
        "$$\n",
        "\n",
        "The true posterior $p(w|X, Y)$ cannot usually be evaluated analytically, but we can use indirect methods such as variational inference or MC-dropout. \n",
        "\n",
        "This distribution captures the most probable function parameters given our observed data. With it we can predict an output for a new input point $x$ by integrating:\n",
        "\n",
        "$$\n",
        "p(y|x,X,Y) = \\int p(y|x,w)p(w|X,Y)dw\n",
        "$$\n",
        "\n",
        "This integral can be computed by Monte Carlos method:\n",
        "\n",
        "$$\n",
        "\\mathop{\\mathbb{E}}(y|x, X,Y) \\approx \\frac{1}{M}\\sum_{j=1}^{M} f_{{w_{j}}}(x)\n",
        "$$\n",
        "\n",
        "Finaly we can calculate the corresponding variance:\n",
        "$$\n",
        "\\mathop{\\mathbb{Var}} (y) \\approx \\frac{1}{M}\\sum_{j=1}^{M} f_{w_{j}}(x)^2 - \\mathop{\\mathbb{E}}(y|x, X,Y)^2\n",
        "$$\n",
        "\n",
        "\n",
        "Which can be used as a measure of the **epistemic uncertainty**."
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        "## Aleatoric Uncertainty\n",
        "\n",
        "For obtaining the heteroscedastic uncertainty, we follow the same approach as in the epistemic case: we consider that we have a **fixed model**  $f_w(x)$ and we want to observe the variability of the term $p(y|f_w(x))$. \n",
        "\n",
        "In **regression tasks**, , we can assume that $y \\sim \\mathcal{N}(f_{{w}}(x), \\sigma(x)^2)$, where $f_{w}(x)$ is the predicted value of $x$ and $\\sigma_(x)$ is the unknown variance of this value. How do we estimate this value? \n",
        "\n",
        "In the same way we use a deep learning model to estimate $f_w(x)$, we can use a deep learning model to estimate variance: $\\sigma_w(x)$, and then $y \\sim \\mathcal{N}(f_{{w}}(x), \\sigma_w(x)^2)$.\n",
        "\n",
        "Applying this approximation to the log-likelihood adds an additional term to the loss that depends on $\\sigma_w(x)$:\n",
        "\n",
        "$$\n",
        "\\mathcal L = - \\frac{1}{N} \\sum_{i=1}^N \\log p(y|f_w(x_i))\n",
        "$$\n",
        "\n",
        "$$\n",
        "= \\frac{1}{2 \\sigma(x)^2} ( y - f_w(x))^2 + \\frac{1}{2} \\log \\sigma_w(x)^2\n",
        "$$\n",
        "\n",
        "We can easily optimiza a model that outputs $(f_{{w}}(x), \\sigma_w(x))$ by using the reparametrization trick in the last layer of the network.\n",
        "\n",
        "In **classification tasks**, this approximation is not as straightforward as in regression, as for classification there is already an uncertainty component due to the distribution of the probabilities when applying the softmax to the logits. \n",
        "\n",
        "In this scenario, we can apply the same assumption but to the logits space instead of the output directly:\n",
        "\n",
        "$$\\begin{split}\n",
        "logits \\sim \\mathcal{N}(f_{w}(x), diag(\\sigma_w(x)^2))  \\\\\n",
        "p = softmax(logits) \\\\\n",
        "y \\sim Categorical(p)\n",
        "\\end{split}\n",
        "$$\n",
        "\n",
        "Here we can apply the reparametrization trick for computing the logits, $u$:\n",
        "\n",
        "$$\n",
        "\\begin{split}\n",
        "u \\sim \\mathcal{N}(f_{w}(x), diag(\\sigma_w(x)^2))  \\\\\n",
        "u = f_{w}(x) + \\sqrt{diag(\\sigma_w(x)^2)}* \\epsilon\\\\\n",
        "u = f_{w}(x) + diag(\\sigma_w(x))* \\epsilon, \\epsilon\\sim\\mathcal{N}(0,1)\n",
        "\\end{split}\n",
        "$$\n",
        "\n",
        "And then apply Monte Carlo sampling to obtain the expectation of the probability:\n",
        "\n",
        "$$\n",
        "\\mathop{\\mathbb{E}}[p] = \\frac{1}{M}\\sum^{M}_{m=1}softmax(u^{m})\n",
        "$$\n",
        "\n",
        "When applied to a crossentropy loss we have that:\n",
        "\n",
        "$$\n",
        "\\begin{align}\n",
        "\\ell(W) & = -\\frac{1} {C}\\sum^{C}_{c=1}y_{i,c}\\log{(p_{i,c})}  \\\\\n",
        "& = -\\frac{1}{C}\\sum^{C}_{c=1}y_{i,c}\\log{\\frac{1}{M}\\sum^{M}_{m=1}softmax(u^{m})}\\\\\n",
        "& = -\\frac{1}{C}\\sum^{C}_{c=1}y_{i,c}\\log{\\frac{1}{M}\\sum^{M}_{m=1}\\frac{\\exp{u^{m}_{i,c,m}}}{\\sum^{C}_{c{}'=1}\\exp{u^{m}_{i,c{}',m}}}} \\\\\n",
        "& =  -\\frac{1}{C}\\sum^{C}_{c=1}y_{i,c}\\log{\\sum^{M}_{m=1}\\exp({u^{m}_{i,c,m}}} - \\log{\\sum^{C}_{c'=1}\\exp{u^{m}_{i,c',m}})}-\\log{M} \\\\\n",
        "\\end{align} \n",
        "$$\n",
        "\n",
        "Where $C$ is the number of classes and $M$ is the number of Monte Carlo samples taken.\n",
        "\n",
        "Once trained, the sigmas can be used to obtain a measure of the aleatoric uncertainty associated to the input by calculating the mean variance of the logits:\n",
        "\n",
        "$$\n",
        "\\begin{align}\n",
        "\\mathop{\\mathbb{U}} & = \\frac{1}{C}\\sum^{C}_{c=1}var[p_{c}] \\\\\n",
        "&= \\frac{1}{C}\\sum^{C}_{c=1}var(softmax(u^{m}_{c})), m \\in \\left \\{1,M\\right \\}\\end{align} \n",
        "$$\n"
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        "## Total uncertainty\n",
        "\n",
        "Epistemic and aleatoric uncertinty can be combined in a model. Then, the predictive uncertainty for $y$ can be approaximated by:\n",
        "\n",
        "$$\n",
        "Var(y) \\approx \\frac{1}{T} \\sum_{t=1}^{T} y_t^2 - (\\frac{1}{T} \\sum_{t=1}^{T} y)^2 + \\frac{1}{T} \\sum_{t=1}^{T} \\sigma_t(x)^2\n",
        "$$\n",
        "\n",
        "with ${y_t,\\sigma_t(x)}$ a set of $T$ sampled outputs: $y_t, \\sigma_t (x) = f_{w_t} (x)$ for random weights $w_t \\sim p(w)$. \n"
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      "source": [
        "# Predicting probability distributions"
      ]
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        "#### Regression with a pre-defined homoscedastic noise model\n",
        "\n",
        "A network can now be trained with a Gaussian negative log likelihood function (`neg_log_likelihood`) as loss function assuming a **fixed standard deviation** (`noise`). \n",
        "\n",
        "\n",
        "This is equivalent to consider the following loss function:\n",
        "\n",
        "$$\n",
        "LogLoss = \\sum_i \\frac{(y_i - f(x_i))^2}{2 \\sigma^2}+\\frac{1}{2} \\log \\sigma^2\n",
        "$$\n",
        "\n",
        "where the model predicts a mean $f(x_i)$. \n",
        "\n"
      ]
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      "source": [
        "import tensorflow\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "def f(x, sigma):\n",
        "    epsilon = np.random.randn(*x.shape) * sigma\n",
        "    return 10 * np.sin(2 * np.pi * (x)) + epsilon\n",
        "\n",
        "train_size = 320\n",
        "noise = 1.0\n",
        "\n",
        "plt.figure(figsize=(8,4))\n",
        "X = np.linspace(-0.8, 0.8, train_size).reshape(-1, 1)\n",
        "y = f(X, sigma=noise)\n",
        "y_true = f(X, sigma=0.0)\n",
        "\n",
        "plt.scatter(X, y, marker='+', label='Training data')\n",
        "plt.plot(X, y_true, label='Truth', color='r')\n",
        "plt.title('Noisy training data and ground truth')\n",
        "plt.legend();\n",
        "\n",
        "print(X[0],y[0],y_true[0])"
      ],
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k+719ddoPTHq/O/nz54KDByFHDpfE46y5+hPbv5n187UObmVI+Dssa92Ljms/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\nmbWAG7aZmVkL/B9ctKz/zRYp/gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zFiwFNxCN9aa",
        "colab_type": "code",
        "outputId": "93d92c15-e791-4498-cf36-cbd6c9e95248",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 474
        }
      },
      "source": [
        "from tensorflow.keras import backend as K\n",
        "from tensorflow.keras import activations, initializers\n",
        "from tensorflow.keras.layers import Input, Dense\n",
        "from tensorflow.keras.models import Model\n",
        "from tensorflow.keras import callbacks, optimizers\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "\n",
        "x_in = Input(shape=(1,))\n",
        "x    = Dense(20, activation='relu')(x_in)\n",
        "x    = Dense(20, activation='relu')(x)\n",
        "x    = Dense(1)(x)\n",
        "\n",
        "model = Model(x_in, x)\n",
        "model.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "WARNING: The TensorFlow contrib module will not be included in TensorFlow 2.0.\n",
            "For more information, please see:\n",
            "  * https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md\n",
            "  * https://github.com/tensorflow/addons\n",
            "If you depend on functionality not listed there, please file an issue.\n",
            "\n",
            "WARNING:tensorflow:From /usr/local/lib/python2.7/dist-packages/tensorflow/python/ops/resource_variable_ops.py:435: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Colocations handled automatically by placer.\n",
            "_________________________________________________________________\n",
            "Layer (type)                 Output Shape              Param #   \n",
            "=================================================================\n",
            "input_1 (InputLayer)         (None, 1)                 0         \n",
            "_________________________________________________________________\n",
            "dense (Dense)                (None, 20)                40        \n",
            "_________________________________________________________________\n",
            "dense_1 (Dense)              (None, 20)                420       \n",
            "_________________________________________________________________\n",
            "dense_2 (Dense)              (None, 1)                 21        \n",
            "=================================================================\n",
            "Total params: 481\n",
            "Trainable params: 481\n",
            "Non-trainable params: 0\n",
            "_________________________________________________________________\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eCpz6-ENN-pu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def neg_log_likelihood(y_true, y_pred, sigma=1.0):\n",
        "    dist = tfp.distributions.Normal(loc=y_pred, scale=sigma)\n",
        "    return K.sum(-dist.log_prob(y_true))\n",
        "\n",
        "model.compile(loss=neg_log_likelihood, optimizer=optimizers.Adam(lr=0.01), metrics=['mse'])\n",
        "model.fit(X, y, batch_size=10, epochs=150, verbose=0);"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xZHbbb4mOJbf",
        "colab_type": "code",
        "outputId": "6bbdb018-082d-4606-9f98-8528304ac0c2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "from tqdm import tqdm_notebook\n",
        "\n",
        "X_test = np.linspace(-0.8, 0.8, 1000).reshape(-1, 1)\n",
        "y_pred_list = []\n",
        "\n",
        "y_pred = model.predict(X_test)\n",
        "    \n",
        "y_mean = np.mean(y_pred, axis=1)\n",
        "y_sigma = noise\n",
        "\n",
        "plt.figure(figsize=(8,4))\n",
        "plt.plot(X_test, y_mean, 'r-', label='Predictive mean');\n",
        "plt.scatter(X, y, marker='+', label='Training data')\n",
        "plt.fill_between(X_test.ravel(), \n",
        "                 y_mean + 2 * y_sigma, \n",
        "                 y_mean - 2 * y_sigma, \n",
        "                 alpha=0.2, label='Uncertainty (Confidence Interval)')\n",
        "plt.title('Prediction')\n",
        "plt.legend();"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GLQitbbgWfHY8xXVZUqsgNGus5TUPHTrE0qVL+e6779i/fz833HADxcXFlc7x8Dgn6elM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\n/gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i53ozVbmNkjL",
        "colab_type": "text"
      },
      "source": [
        "#### Regression with an heteroscedastic noise model\n",
        "\n",
        "This is equivalent to consider the following loss function:\n",
        "\n",
        "$$\n",
        "LogLoss = \\sum_i \\frac{(y_i - f(x_i))^2}{2 \\sigma^2(x_i)}+\\frac{1}{2} \\log \\sigma^2(x_i)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9lBh0pVPXyiV",
        "colab_type": "code",
        "outputId": "997f4a6c-1da5-493d-b720-372171652db9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 609
        }
      },
      "source": [
        "# https://engineering.taboola.com/predicting-probability-distributions/\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.utils import shuffle\n",
        "def f(x):\n",
        "    return x**2-6*x+9\n",
        "\n",
        "def data_generator(x,sigma_0,samples):\n",
        "    return np.random.normal(f(x),sigma_0*x,samples)\n",
        "\n",
        "sigma_0 = 0.1\n",
        "x_vals = np.arange(1,5.2,0.2)\n",
        "x_arr = np.array([])\n",
        "y_arr = np.array([])\n",
        "samples = 50\n",
        "for x in x_vals:\n",
        "    x_arr = np.append(x_arr, np.full(samples,x))\n",
        "    y_arr = np.append(y_arr, data_generator(x,sigma_0,samples))\n",
        "x_arr, y_arr = shuffle(x_arr, y_arr)\n",
        "x_test = np.arange(1.1,5.1,0.2)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10,10))\n",
        "plt.grid(True)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('g(x)')\n",
        "ax.scatter(x_arr,y_arr,label='sampled data')\n",
        "ax.plot(x_vals,list(map(f,x_vals)),c='m',label='f(x)')\n",
        "ax.legend(loc='upper center',fontsize='large',shadow=True)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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GtEvsfXbvsMcC7TBMREQUyZSmWg+N256wQRgEsn82esf9ofyZl6Y2FmNBljgz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\neCaoWmYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TVcfJ4p7X9qF",
        "colab_type": "code",
        "outputId": "ed9ae895-724f-4adc-e12d-c6a34b0a4a6b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 926
        }
      },
      "source": [
        "epochs = 500\n",
        "batch_size = 50\n",
        "learning_rate = 0.0003\n",
        "display_step = 50\n",
        "batch_num = int(len(x_arr) / batch_size)\n",
        "\n",
        "tf.reset_default_graph()\n",
        "x = tf.placeholder(name='x',shape=(None,1),dtype=tf.float32)\n",
        "y = tf.placeholder(name='y',shape=(None,1),dtype=tf.float32)\n",
        "\n",
        "layer = x\n",
        "for _ in range(3):\n",
        "    layer = tf.layers.dense(inputs=layer, units=12, activation=tf.nn.tanh)\n",
        "\n",
        "output = tf.layers.dense(inputs=layer, units=1)\n",
        "\n",
        "# cot function\n",
        "cost = tf.reduce_mean(tf.losses.mean_squared_error(labels=y,predictions=output))\n",
        "\n",
        "optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost)\n",
        "x_batches = np.array_split(x_arr, batch_num)\n",
        "y_batches = np.array_split(y_arr, batch_num)\n",
        "\n",
        "with tf.Session() as sess:\n",
        "    sess.run(tf.global_variables_initializer())\n",
        "    for epoch in range(epochs):\n",
        "        avg_cost = 0.0\n",
        "        x_batches, y_batches = shuffle(x_batches, y_batches)\n",
        "        for i in range(batch_num):\n",
        "            x_batch = np.expand_dims(x_batches[i],axis=1)\n",
        "            y_batch = np.expand_dims(y_batches[i],axis=1)\n",
        "            _, c = sess.run([optimizer,cost], feed_dict={x:x_batch, y:y_batch})\n",
        "            avg_cost += c/batch_num\n",
        "        if epoch % display_step == 0:\n",
        "            print('Epoch {0} | cost = {1:.4f}'.format(epoch,avg_cost))\n",
        "    y_pred = sess.run(output,feed_dict={x:np.expand_dims(x_test,axis=1)})\n",
        "    print('Final cost: {0:.4f}'.format(avg_cost))\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10,10))\n",
        "plt.grid(True)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "ax.scatter(x_arr,y_arr,c='b',label='sampled data')\n",
        "ax.scatter(x_test,y_pred,c='r',label='predicted values')\n",
        "ax.plot(x_vals,list(map(f,x_vals)),c='m',label='f(x)')\n",
        "ax.legend(loc='upper center',fontsize='large',shadow=True)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From <ipython-input-6-95eb9bdd72d8>:13: dense (from tensorflow.python.layers.core) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use keras.layers.dense instead.\n",
            "WARNING:tensorflow:From /usr/local/lib/python2.7/dist-packages/tensorflow/python/ops/losses/losses_impl.py:667: to_float (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.cast instead.\n",
            "Epoch 0 | cost = 5.5742\n",
            "Epoch 50 | cost = 1.7065\n",
            "Epoch 100 | cost = 0.5422\n",
            "Epoch 150 | cost = 0.1754\n",
            "Epoch 200 | cost = 0.1384\n",
            "Epoch 250 | cost = 0.1219\n",
            "Epoch 300 | cost = 0.1158\n",
            "Epoch 350 | cost = 0.1100\n",
            "Epoch 400 | cost = 0.1095\n",
            "Epoch 450 | cost = 0.1077\n",
            "Final cost: 0.1101\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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XXuGEE04gJyeHI4880qfr+Nq1aznooIPIzs5m2rRpVMVCwyWRBKRiTESGV1UFZWXgcHhf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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ml0_uM6xYFUA",
        "colab_type": "code",
        "outputId": "6cd688bc-4b74-481d-ccd6-45a796766abb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 926
        }
      },
      "source": [
        "\n",
        "#new cost function\n",
        "def mdn_cost(mu, sigma, y):\n",
        "    dist = tf.distributions.Normal(loc=mu, scale=sigma)\n",
        "    return tf.reduce_mean(-dist.log_prob(y))\n",
        "\n",
        "epochs = 500\n",
        "batch_size = 50\n",
        "learning_rate = 0.0003\n",
        "display_step = 50\n",
        "batch_num = int(len(x_arr) / batch_size)\n",
        "\n",
        "tf.reset_default_graph()\n",
        "x = tf.placeholder(name='x',shape=(None,1),dtype=tf.float32)\n",
        "y = tf.placeholder(name='y',shape=(None,1),dtype=tf.float32)\n",
        "\n",
        "layer = x\n",
        "for _ in range(3):\n",
        "    layer = tf.layers.dense(inputs=layer, units=12, activation=tf.nn.tanh)\n",
        "    \n",
        "# now we have two different outputs\n",
        "mu = tf.layers.dense(inputs=layer, units=1)\n",
        "sigma = tf.layers.dense(inputs=layer, units=1, activation=lambda x: tf.nn.elu(x) + 1)\n",
        "\n",
        "cost = mdn_cost(mu, sigma, y)\n",
        "\n",
        "optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost)\n",
        "x_batches = np.array_split(x_arr, batch_num)\n",
        "y_batches = np.array_split(y_arr, batch_num)\n",
        "with tf.Session() as sess:\n",
        "    sess.run(tf.global_variables_initializer())\n",
        "    for epoch in range(epochs):\n",
        "        avg_cost = 0.0\n",
        "        x_batches, y_batches = shuffle(x_batches, y_batches)\n",
        "        for i in range(batch_num):\n",
        "            x_batch = np.expand_dims(x_batches[i],axis=1)\n",
        "            y_batch = np.expand_dims(y_batches[i],axis=1)\n",
        "            _, c = sess.run([optimizer,cost], feed_dict={x:x_batch, y:y_batch})\n",
        "            avg_cost += c/batch_num\n",
        "        if epoch % display_step == 0:\n",
        "            print('Epoch {0} | cost = {1:.4f}'.format(epoch,avg_cost))\n",
        "    mu_pred, sigma_pred = sess.run([mu,sigma],feed_dict={x:np.expand_dims(x_test,axis=1)})\n",
        "    print('Final cost: {0:.4f}'.format(avg_cost))\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(10,10))\n",
        "plt.grid(True)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "ax.errorbar(x_test,mu_pred,yerr=np.absolute(sigma_pred),c='r',ls='None',marker='.',ms=10,label='predicted distributions')\n",
        "ax.scatter(x_arr,y_arr,c='b',alpha=0.05,label='sampled data')\n",
        "ax.errorbar(x_vals,list(map(f,x_vals)),yerr=list(map(lambda x: sigma_0*x,x_vals)),c='b',lw=2,ls='None',marker='.',ms=10,label='true distributions')\n",
        "ax.plot(x_vals,list(map(f,x_vals)),c='m',label='f(x)')\n",
        "ax.legend(loc='upper center',fontsize='large',shadow=True)\n",
        "plt.show()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From <ipython-input-7-ca41b9ba3966>:2: __init__ (from tensorflow.python.ops.distributions.normal) is deprecated and will be removed after 2019-01-01.\n",
            "Instructions for updating:\n",
            "The TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use `tfp.distributions` instead of `tf.distributions`.\n",
            "WARNING:tensorflow:From /usr/local/lib/python2.7/dist-packages/tensorflow/python/ops/distributions/normal.py:160: __init__ (from tensorflow.python.ops.distributions.distribution) is deprecated and will be removed after 2019-01-01.\n",
            "Instructions for updating:\n",
            "The TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use `tfp.distributions` instead of `tf.distributions`.\n",
            "Epoch 0 | cost = 2.5419\n",
            "Epoch 50 | cost = 1.6657\n",
            "Epoch 100 | cost = 0.4186\n",
            "Epoch 150 | cost = 0.2715\n",
            "Epoch 200 | cost = 0.2184\n",
            "Epoch 250 | cost = 0.1774\n",
            "Epoch 300 | cost = 0.1528\n",
            "Epoch 350 | cost = 0.1351\n",
            "Epoch 400 | cost = 0.1277\n",
            "Epoch 450 | cost = 0.1341\n",
            "Final cost: 0.1197\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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OO++EyWTCmjVret0nMzMTjz32GH7605+ioKAAer0+6s7D66+/Hueddx7mzJkD\no9GIWbNmYXvkhLcIc+fOxcqVKzF79myMHz8es2fP7rNtX331Fc4880wYDAacfPLJ+NnPfoYzzjhj\nwO3uzaJFi7B48WLk5+ejo6MDa9euHdA1XnTRRQCA7OxsTJ06tcdxr7rqKixatAinnXYaxowZg7S0\nNDzyyCMDatObb76JSZMmwWAw4Prrr8eLL744oLl6RKOJVit6wtRq8ZxIiRgASLIsK92GAZs+fbq8\nc+fOuJ2vvLwcZWVlcTtfIuG1lyndDABARUUFpk2bNuj3h0bHRtA/c0piFRUV+Oijj7Bo0SJkZWUp\n2pZE+nceb7z2sridT5KkClmWp/e3H3vGiIiIiBTEZIwoickye8WIiEJV+AOBxKu+DzAZIyIioiTG\n5ZCIiIiIFOTxABpNdAV+jUZsTxRMxogSXF/lEIhGEv4ek1L8/p53kqvVYnui6L+IDREpJiUlBR6P\nBwaDQemmEA2Jx+NhQkaK0GiAjg4gLw8AylBVBaSmivUpEwV7xogSWEFBAQ4cOACXy8UPMhqRgsEg\nXC4X9u/fj7q6OgCAOtYF74iOQqsFmpvDsd8v4kSqNcaeMaIEZjab0dnZiT179kClUvW7rA5RIgoG\ng6irq4PdbkdaWhr03dfqIhpGPh9gNodjjUYsD5dIE/iZjBElOKvVikAggL/+9a8IhFa6HQZ1dXVR\ni1GPJrz2+Fx7SkoKLrjgAvaMUVz5/UBaWjgOrUnp9SrTnt4wGSMaAQoLC7F48WI4HI5hG67csWMH\nZsyYMSzHTnS89uG/drVaDZPJxKWaKO5Cc8ZCHI7EmzPGZIxohNDr9cM6vHPgwIGo9RRHE1776Lx2\nGh20WqCqKhw3NwMqFTB2rHJt6o4T+ImIiChpheqMhbDOGBEREVEcOZ3RQ5JqtYidTuXa1B2TMSIi\nIkpafj/Q1haOZVnEiVT0lckYERERJS2NRiwQHikQiB66VFoCNYWIiIgotnS66GQsGASMRrE9UTAZ\nIyIioqSVni4SsBBJEkVfE6nKCocpiYiIKGmNhOWQmIwRERFR0vJ4xKT97jFLWxARERHFQXNz9NJH\nKpWII3vLlMY5Y0RERJS0nM7ommJut+gZi+wtUxp7xoiIiChpBQIiAQuRZRF3L3ehJCZjRERElLRU\nKsBgCMeSJGJVAmVAHKYkIiIixfh8YjK93y8Ksep0sb3TMTNTJGAher1IxDIyYneOoUqgvDBxeDxA\nZSXQ2SmeE+mOCyIiomTh8wEOhxg6TEkRzw6H2B4rZnN0z5heL2KzOXbnGCr2jHXj8QDffCMKxMky\n0NoqJv6NHZtY1XqJiIhGOo9CTOUDAAAgAElEQVRH9Iap1SIOPXs8okcrFjIzo5M7g0EkfrE6fiyw\nZ6ybujpxy6tWK7o1tVoR19Up3TIiIqLk4veHE7AQtTq2i3hrtUBOTjg2mUScSEVf2TPWTUuL6AGL\nzNLT08V2IiIiip3QIt6RCdlwLOIdmXglUo9YCHvGulGre1/dvXvmTkREREOj04lesNDnbiAg4tE2\nLYjJWDcWC9DeHq7W6/WK2GJRtl1ERETJRqsN3+3o9YrnzMzYDyFGzhmL9Q0CscBhym5ycsJ3dwQC\nYhK/xRI93kxERESxEUrIhovPBzQ2huPWVnGDQCLNG2PPWDdaLWC1AsXFQGqqeLZaE+cvjIiIiAbO\n4YguUaVSidjhUK5N3TEZ60WoZ8zvT8zuTCIiIhoYpzO66KvbLeLI9SqVxmHKbjwe4PPPxWrunZ3A\nnj2iMNyJJ46+CYVEREQjnd8v5n6HyDLQ1iYqJSQK9ox18803QHW1uHsy9KiuFtuJiIhoZAmVz4g0\nHOUzhoLJWDcHD4psORAIP9LTxXYiIiIaWXQ6IC0tHDscIk6k0a4EygsTQ2enuL22s1MsmdDSIiby\np6Qo3TIiIiI6VhqNmLQfYjSKmD1jCSzUC9bWFh5XDvWWERER0cgTWREhIyPxKiQwGesmLU30gl13\nHbBgQRncbhFHdnESERHRyCBJYqQrpK1NxJF3WCqNyVg3sizqioWo1SKWZeXaRERERIMjy9HrS4fi\nRPpcZzLWjdcb/ZdmNos4tDwSERERjRw+X/TnutMp4kSqIcpkrBtZjk68GhtFnEgZNBEREQ1M96Kv\nHk/iFX1VPBmTJEktSdIuSZI2K90WAAgGoxOvjg4RB4PKtYmIiIgGp60tuuirSiXitjbl2tSd4skY\ngOsB7FW6ESHt7dFrWH31lYgj/yKJiIhoZPD7xeLgIf/8p4j9fuXa1J2iyZgkSYUA5gF4Ssl2ROrs\nBJ58MhTJ2LRJxJ2dSraKiIiIBkOSgDvuAAAx7HXnnSLm3ZRhfwDwKwAJMwj40UeA3R6KJPj9Iv7o\nIyVbRURERIOxcyfw5ZcyAJF9dXQAX34pticKxerPSpI0H0C9LMsVkiSVHWW/pQCWAoDFYkF5efmw\ntquxsQSBQClCf2kAEAjIaGo6iPLyQ8N67kTicrmG/WedqEbrtY/W6wZ47aPx2kfrdQPJce1TVq4E\nAOz+wx/63XfHjhJ0dpRGbevslPHxx4nzua7kYgDfB3CeJEnnAEgDkCFJ0rOyLF8euZMsy+sBrAeA\n6dOny2VlZcPaqIceEpP7IhcVVakkdHSMQVnZmGE9dyIpLy/HcP+sE9VovfbRet0Ar300XvtovW4g\nSa7dZAKAAV1HVRXwv88G0B5Ud21LT5fwn/+ZOJ/rig1TyrL8G1mWC2VZLgVwCYB3uydiSsjLE0sl\nCDLS4IfJEERenpKtIiIiSk4+n1i8u6lJPMe6/td/jndjYtABzZEZUTodMHUqMG9ebM8zFErPGUs4\nGg3w3e+KP5vgw++xFz81VyfUgqJERETJwOcT9TxbW0WpidZWEccyIXM8a8f9ms+QCjHktXYt8MQT\nibXMYUIkY7Isl8uyPF/pdgBiQfDUVPHnVqTAlunHjDo70tNY9ZWIiCiWHA5RPkqlEutAq1Qidjhi\nc/yAJ4DG5w4jY24u3BCrg594IqDXswJ/QsvIADIzw/EnJTaY2ztQ0tjS95uIiIjomDmdIglTH5nO\npVaLOFbV8es31SPg8CN4rq1rm14vet9YgT+BmUyIGpJsPCEX7alalH5i7/tNREREdMz6qvUVqxpg\n9sftUI/TIfV74V6WlBTxOR+r3rdYYDLWjU4HlJaG48wcFWpPykfmF43oqO5QrF1ERETJxmgU6z+H\nKhgEAiI2God+7LaKNrR93Ib0i21QqyPLVYnhUFUCZUAJ1JTEkJMDmM3AffcBL75YjqIiwHW66N6s\nfapW4dYRERElj8xM0QkSDIokLBgUceR0ocGyr7NDpVMh+xJL1GR9SRKT9w2GoZ8jVpiMdZOXB+Tn\nizFlQDxnTUqHNMOM2idrEfQlzGIBREREI5pWKzpBTCbRG2YyiVirHdpx/Q4/Dj9/GHkL82AZp4XL\nFX6tqQlwucR5EgWTsW7y8sQEwowM8cuQkSHirJ/Y4LV70bS5SekmEhERJQ2tVvSEZWeL56EmYgBQ\n9+c6BD1B2JaLka3uc9ASaV1KgMlYD1otkJsrJvcFg+I5NxcwnGlGamEq7I9zIj8REVGseDxAZSXw\n1Vfi2eMZ2vFkWYb9cTuM043ImJ6Bxsaugv0AgDFjRNzYOLTzxBKTsW7a20VCNnasGLceO1bEHT4V\nrEutaHm7BZ4DQ/xNISIiIng8YrmiYFBMCwoGRTyUhMzxoQOePR7YrhG9Yp2d4g7KSCkpYnuiYDLW\njc8nukk1GkCWxXNmpthuvdoKqIHaJziRn4iIaKgaG0Wh9VCylJIi4qH0Wtkft0OdqUbexWIdw9TU\n6OTO6RRxqMB7ImAy1o1OJ2531elEIhYZp9pSkXN+DmqfrkWgI9D/wYiIiKhPse618tZ70fByA/Kv\nyIdaLyrJZmZGJ3ednSKOxR2bscJkrBuzWWTLwaDoGQsGRWw2i9dty23wN/nR8HKDsg0lIiIa4UK9\nVk4n0Nw89F6ruqfrIPtk2JbZorYXF4f/rNVGx4mAyVg3mZniYTCIHjGDIbwNALJmZyH9O+mcyE9E\nRDREoV6rUA/ZUHqt5KAM+xN2ZJ6eCf0J+q7tfn90EdmiIhH7/TG4gBhhMtZNZM0TtbpnzRNJJcG2\nzAbnP51wfeo6+sGIiIjoqIqLxWesyzW0Xqvmt5rR8W1HVzmLEI0G6IhYQMfhEHHk0odKYzLWi1DN\nE7W695on+YvzIaVKsK9j7xgREdFg+f2iGn5GhpgOlJEh4sH0Wtkft0Obq0XuBblR27VaMQQaec7m\n5tjUM4sVJmODoM3WIm9BHg7/+TD8bQnUz0lERDSCyDJQXy96q1wu8VxfL7Yfi46qDjRtboL1aitU\nKdGpjc8XnvcNiB4xs1lsTxRMxgbJdo0NAVcA9c/XK90UIiKiEcnnAxoagJoawG4Xzw0Nx54o1T5Z\nC8iAdZm1x2uh3reQzMzB974NFyZjg5QxKwP6yXrUPF4D+VhTeCIiIkJzs+gR83gAt1s8u1zRw4r9\nCfqCqH2qFua5ZqSXpvd4XaMBAt2qUQUCnDOWFCRJgm25De5P3HBudyrdHCIiohGnoUEMSf74x8AF\nF4ib5mRZbB+opr81wVvr7TFxP0SnE6vrhDQ3i1inG2LjY4jJ2BBYLrNAbVCHy1yUlYkHERER9cvn\nE2WkQiRJxMcyTFnzeA1Si1KRfU72Uc8T4nQm1nwxgMnYkGiMGlgut6B+Uz18zQn2N0tERJTgQoXW\nQ7oXWu+PZ78Hre+0wrrUCkkt9bqPwxG9HJJKJWKHYwgNjzEmY0NkW26D3CmjbmOd0k0hIiIaUWy2\n6GQsLU3Ett5HHHuwP2GHpJHE2tF9aGoS89BCXC7xaGoaZKOHQQJNXxuZDJMNyDg5A/Z1dhRaRRcr\nERER9S8nJ3rIMLTqTU5O/+8NBDSo21iHnPNzkGrte/2ktrboGwLq6xNrkXCAPWMxYbvGhvav2tHa\nOkbpphAREY0YoVVvQkKJ2EAKsjY0TIK/2Q/bNUfvRmtvj74hIBgUceSkfqUxGYuB3ItyocmS4DyY\nChw6BGze3PM+WiIiIori80XP58rIEPFAJtjba6cj/bh0mM4wHXW/7mtTajRcmzIpqbXAVONvUOD8\nE+SDB4GFC4Gzz2ZCRkREdBQeT3S9L7VaxJEJWm9cLgucziLYltsg9TM/KD09euFxnU7E6T1LkimG\nyVgsbNmC9MZPoUE7JEDMDNy+HdiyRemWERERJSy/XyRgkdTq/nutauzfg0rlQ/4V+f2eIzc3ugK/\nXi/i3Ny+3xNvTMZiYdcuSO3d0ni3G9i9W5n2EBERjQCDqY7vb/Ojvv67yM39Alpz/5PLrFaRgIWk\npYnY2vcNmHHHZCwWTjop+m8aEPGUKcq0h4iIaAQYTHX8w88eRiCQigLbxwM+x9ix4dhkEjEr8Ceb\nuXOBmTMhq1SQISGgTgdmzhTbiYiIKCZkWYb9cTsMhloYjTUDfl9k4lVcnFiJGMBkLDbUamDrVkgn\nnIDWzDLsCdyK9nWv9RwIJyIioi4eT/REerNZxH1N4Hf+ywn3Z27YrDuTqq4nk7FYUauB7GykTzCg\nSXUyajfUK90iIiKihOb3i7pfIQ6HiPuawG9fZ4faAFi07yZVKSkmYzGWluZE9rnZqN1Qi2BnsP83\nEBERjVKyDLS09Ixluee+viYf6jfVYmrmb6H+8lMgiUpJMRkbBgXXFMDX4EPDqw197uPziW8ATU3i\nOdFWkCciIoqHyM8/p7Pvz8Pap2th9m6HruXTcHfaAEtJRR4zET9zmYwNg6yzspA2Ng32dfZeXw8l\nYrIMpKSI50T85SAiIhpOA60zJgdl1D5Ri+ziymMuJRX6zO06VgJ+5jIZGwaSSoJtmQ2Ofzjg/sLd\n43WPR/wyhFaNd7lE3F/FYSIiomTi9UavQ5mVJWKvN3q/lnda0H6gHekXnXLMpaRCn7khifiZy2Qs\nlsrLxQNA/pX5kFIk2J/o2TvW3h7+ZQj1jLlcibVoKRER0XBLSYnuoWppEXFKSvR+9nV2aLI1yLj9\nYlE6SnUkfTEY+i0lFfrMrawE3nqrPCE/c5mMDZOU3BTkXpiLumfqEHBHTyz0esVcQ7dbFLhzu0Xc\n/ZsAERFRMtNogLa2cGy3iziyAn9nTSca/9oI61VWqPUpwNatwAknAKWlwAsviPgopaS8XqCjA6it\nBTo7xXNHR2J95jIZG0a25TYEnAHUvxhd5kKSxHi13y+yf79fxMlUM4WIiKg/Hg9w+HA4DgZFHDmE\nWLuhFggA1qVH1i86UkoKJSXA/Pn91vT0+0UVjNBdmi0tIu5v/ct4YjI2jDJ/kAndJB1qHo+uEizL\n4SUgDh8OL/3Q2628REREyaq+HkhNDccpKSKuP9KHEfQHYV9vR9acLOjGD65svtMpetpCQ58pKSJ2\nOofY+BhiMjaMJElCwTUFcFW44NzpjNgerjpssYSrDbNnjIiIRhOXK3o+fmamiF0uETe/0QxvjRe2\na2yDPkdnp+jwMBpFJ5rRKOLOziE2PoaYjA0zy+UWqHQq2B8PT+SX5XACVl8fTszYM0ZERKOJwRA9\ndysYFLHBIOKax2uQUpCC7PnZgz5Haqr4jJUk8TkrSSKO7JFTGpOxYabJ1MBymQX1L9TD1yJuGZEk\nMUExEBC38AYCImbPGBERjSYFBdGT9X0+ERcUAO1ft6NlawtsS2xQaQafrlgsYn5Yaqo4dmqqiC2W\nGFxAjDAZiwPbchuC7UEc/rOYpejziV8Ej0dM3Pd4RJxIBeiIiIiGW06OSLxCDAYR5+QA9vV2QA1Y\nf2od8jksFtErFgiIZ4tFbE8UTMbiwDjVCOMMI+zr7JBlGe3tIvEyGMQvg8Eg4kSqeUJERDTctNro\npCgzU8TqYBB1f6xDznk5SC0Y2niiVgtYrUBxsegVKy4WcWSxWaUxGYsT23IbPHs9cPzDAb9f/MJp\nNOEu2czMxLrNloiIaLj5fNFlLDIyRFy3qQG+Rh9sywc/cX8kYTIWJ3kX50Fj0qDm8RqkpYmu0lDy\n5feLOC1N2TYSERENWVmZeAxAX0sV1ayzI21cGrLOzBpycyLXgw5N4ufalKOUWqeG5QoLGl9thK7T\nC4cDmDVLPGpqxC9GRobSrSQiIoqf9naxCk2ILAMt/3bB/S8HbMtskFRDv7PN4xEjUKHasGq1iLk2\n5ShlW26D7JPR/Fxt1ArybnfiZelEREShXqWmpuH5nPJ6o+dL19UBLX+yQ0qVkH9lfkzO4ff3LNKv\nVifW1CAmY3Gkn6CH6QwTWv5kR9AX7pfVaERtlZqao7yZiIgojiKH91JShmd4z++P/uzzOvzwvHYY\n6XPzkJKT0vcbj4FGI6YCRQoEoktqKI3JWJzZltuAuk5gZ3PXNq9XVAKOXJ+LiIhISfEY3vN4AJMp\nHKveq4fkCUB7Qewm7ut0omfvs8/ESNRnn4lYN7jVlYYFk7E4yzk/B4FMLbT/F67IHwwCDQ2JtTQD\nERGNbvEY3lOpIs8hw/uKHarxeqRMjd0kao8HsNvFZ61KJZ7tds4ZG9VUKSr4zrQiY28TLOgAAFRX\ni+7fRFqagYiIRrd4DO+lpobnjE1AG+R9Lkg/siEtLXZL0lRViRvk8vJE2/PyRFxVFbNTDBmTMSXM\nF92v8yB6x/x+cTsvkzEiIkoUOp1IlJqbxbBec7OIYzm8p9WGFwU/D3YgXYX271tiWpA1tP5zpND6\n0ImCyZgCvOY0NIwzw4IOSAhi2zYxIZJ3UxIR0WgSCAD5+UAa/KhFGv45aSzyx2l69MgNRSipjBTr\npHKoEuhegtGjoQG4s2kCDkMFGRLefVdMKCwpUbplREREQqhHyWAIbwsExPbMzNico70duPpqwAcV\nnkUJUj8D/nI18MwzsTk+ABQVAXv3Rp+zvR2YODF25xgq9owp4J13gBqXFu3QAJDg9wONjWI7ERFR\nIojHBP733gM+/0xG4EjnREenhM8+E9tjJTMTGD9eJJFer3gePz52CWUsMBlTQE0N4PNFT070+cTd\nHURERIkgHhP4P/mkZyUBrxf49NPYnSM0BWjiRECvD/eIJdLUICZjCigp6fnLrNGIleSJiIgSgU4X\nXjsZCK+pHMu5VmPGAGmqYNS2tDSgtDR25+BySNSrsjIgJycUyUiDH5aswEDXVSUiIhp2Wq0YypMk\n0VslSSKO5Z2Op1nbMDHogAYiIUtPB044ATjjjNidg8shUa8yMoDFi8Wf9fDjd9iLO8Z8y4XCiYgo\noYQSsuzs2CdiAJD2WhXuT/8CaoglAu+4A3j44dje0MblkKhXfr/ohgUAN7QoOV6N4t21CDgTKE0n\nIiIaRu0H29G2uR7GS6zohOi6+u53gdzcyNGjoYvHcOtQMRlTgNcbLnIHAJUnF0HjDSBlK2fwExHR\n6FD9cDUkSULqpYVd26xWkSjFcnJ95HCrLA/PcOtQMRlTQHt7dN2W4DgjWsaYYNhajaA32PcbiYiI\nkoCv2Yfap2qhPy8PmePTurbn5IjPx8ZGBRunACZjCtDpopc+8niAutOLoHV4cfj5w8o1jIiIKILP\nBzgcYjkkhyN2PVb2x+0IeoLQLS6Kms9VUyOGEbuXuxiK0DWEesVkObbXEgtMxhSg14uhyhBZBhpK\nzfAX61G1pgqyLCvXOCIiIkQnMSkpsUtiAh0BVD9Sjayzs6A+zoBvvw2/FgwC334rnmOFpS2oV+np\n0Vm/0Qh0eiUELyqC5wsPmt9sVq5xREREEMmKLIs5zk1N4lmWh57EHH72MHyHfSi+qRiyHF1iwukU\ncSz7JEZCaYsEurFz9AgExB0jDz4ofrnT0oCxYwFvah4ML36DqgeqkD03W+lmEhHRKBZaw1GjET1j\ngYD4zEpPH/xSQnJQRtWaKhhOMsA024TavYDZHH5dpRLHjmXPWKi0RWRCxtIWBI1G/KLZbMCECeI5\nGAQ06SoUrixE63utaKtoU7qZREQ0ioUKvUYO74UKwA5W0+YmtO9rR9FNRZAkCcGgSMBCTCYRxzIZ\nY2kL6lVmpujmdbuBtjbx7PGI7bYlNqiNalQ+UKl0M4mIaBRLSRHzw1pagOZm8ezzie2DVfVAFVKL\nU5F7YS4AMYe6OWJmTlOTiPX6ITY+AktbUK/S00XvWFubmAzZ1ibi9HRAk6mBbZkNDf/bgPZv25Vu\nKhERjVKxrlzv2OaA40MHCm8ohEor0g9Zjq4u0N4u4ljfxxZKyNTqxEvEACZjimhvF1m/xQLk54tn\nvV5sB4CC6wsgqSRUP1ytbEOJiGhU02rFEn5ms3geShJT9UAVNCYNrD+1dm1rb4++ISB0g0D7KOuL\nYDKmgM5OkflnZIQfqanhOyzTCtOQd2keajfUwteUQIVQiIho1JAkICsreqHwUHysPF950PiXRtiu\nsUFjCHettbUBHR3h/VQqEbeNsmnTiiVjkiSlSZK0Q5KkTyRJ+kKSpNuVaku8abUi+4+cTCjL0d84\nim4sQtAThH0dl0giIqL4i+UwZfXD1ZC0Egp+XhC13eOJHqYMdU70Wz6jvFw8BihUMy0QSLyCr4Cy\nPWOdAGbLsjwZwBQAP5QkaZaC7YmbUAV+SRK/EJIk4sg7OwzfNcD8QzOqH6lGoCPQ98GIiIiGgVYr\nJtP7/WLSvt8v4mMdqvQ2eFH3dB0siyxItaZGvabXR0/WDwZ7bhsqVuA/ClkILZetPfIYFaXnQ/VZ\nUlLEn0N3pnSv21J0UxF8h304/GcukURERPHl84m5YmPGAAUFokfMbD72JKbmf2oQ7Aii6JdFPV7L\nzY3uaQsGRZybO8TGR2AF/n5IkqSWJGk3gHoAb8uyvF3J9sSLRgMUF4ux95QU8Vxc3LPr13SGCYap\nBlQ9WAU5eCRPLSsTDyIiomHk90fX+3I6RXwslesDngBqHq1B9rnZ0E/s2d2VnR1dt8znE3F2DOue\nj4QK/FIirIMoSZIJwF8A/FyW5c+7vbYUwFIAsFgs01588cW4tcvlcsFgMMT8uKFf8MhJkLIsJi72\nGIt/F8DqI48fAFNWrgQA7P7DH2LerkjDde0jwWi99tF63QCvfTRe+2i9bmDg1+7zice8eWUAgC1b\nyhEMimHKow1VRn1OvQbgv488/qPnvn6/OMc554hz/O1v5dBoxPFjVSE/NO9NkgC32wW93tBVOqN7\nkhZrZ5xxRoUsy9P72y8hkjEAkCTp9wA8siyv6Wuf6dOnyzt37oxbm8rLy1E2DL1QDofI/Ds7xS+i\nRiPmjIWGLSMF/UFsH78dqYWpmPrh1HCv2DFMXByM4br2kWC0XvtovW6A1z4ar320Xjcw8Gv/+mvx\neTVtmoj37BElJzIzgXHjjvLGI8eW33kP24/fDm22FlO3TYXUy22Y+/eLY06ZEj6H1yvqbh533LFd\nV19Cc8Y0GuDf/y7H1Kll8PvjU29MkqQBJWNK3k2Ze6RHDJIkpQM4C8CXSrUnnnQ6kaEbDKIr1mAQ\ncW9LM6g0KhTdUATnR044/uWIf2OJiGhUCgajhwslScQDXaqo8bVGdHzd0bX0UW9Ci5F3j2M5n4sV\n+I/OCuA9SZI+BfAxxJyxzQq2J24ifzFCtVuO9ouRf3U+NFkaVK2pim9DiYho1OpeCT8jo2fF/L7I\nMlD5QCXSxqUh98d9z8bXaoGGhnDc0iLiWCdKiV6BX7E1y2VZ/hTASUqdX2mhX4yB0Bg0sF1jQ+U9\nlfBMN0Ona+7/TURElNR8PtGDFJruotPFNsnIyQGqIvoAQtNrinreFBkWCABNTehoVCOl7i3kP3IZ\nJHXfVWLV6t5rmQ33XK5Ewwr8I0TBzwsgaSVUV5+sdFOIiEhhkbWzUlKGp3aWThedeKlUIu5tSg0A\nkUWdfTawZw/S6j7BCVgN2ytX9sy2IqhUIukLMRpFrBpl2ckou9yRKzU/FfmX58Jb1wH/N3Zg8+aj\n/oITEVHyilftrMietn6H97ZsAbZvB4JBSADUaIe0c4fYfpTjR85Ly8wUcaINIw43JmMjRSCAcXuu\nxQT5HqirvgIWLhTfQJiQERGNOvGonRXqfQvpt/dt1y7A7Y7e5nYDu3f3eQ6jMfqGAL1exEbj4Ns9\nEjEZGym2bIHm853QoB0SALhc4hvIUb5xEBFRcorlupF9CfW+hfTb+3bSSZC7j2Hq9eG6Fb3IzIwe\n9gwGRTzQOdXJgsnYSDGIbxxERJScdDrRCxZKyAIBEfc5n2sQjrn3be5ctOdMhh9pYm1DgwGYOROY\nO7fPc2i10XPGTCYRc5iSEtNJJ/VYOVXWHf0bBxERJadjLZE0GMfa++Zvl/Fvx92oyVgMqbQUeOEF\nYOvWfm+NPKZ5aUmKydhIMXeu+IahUkEG4EcavGNOOuo3DiIiSl6hhCw7e3iSmFDvW0h/vW91G+rg\nb5VhGtcGlJQA8+ePvhoVg6RYnTE6Rmq1+IYxZQrQ5sLX3hVwpZ+KqSoV+qrgMtw1aIiIKHl1r4d5\ntN63oD+IqoerkPmDTGSqq+PXyCTBnrGRRK0GsrMhlZbAcOslaPvYA8cHvS+RFI8aNERElNwGOoTY\n8L8N6DzUiaKbjlYRlvrCZGyEyl+cD22OFlUP9L5EUmh9L5cLaGoSz7Fe74uIiJJb5Bf4vr7Qy7KM\nqgeqoJugQ/b87J47UL+YjI1Q6nQ1ClYUoGlzE9x73D1eb28XN1tG9oy53WI7ERFRf3w+oLExHLe2\nirh7Qtb6bitcu1wo/GUhJFXfSx9R35iMjWC2a21QpalQ9VDP3jGvVzxHVmeO3E5ERHQ0Dkd00VeX\nq+c2AKhaUwWtRQvL5Zb4NjCJMBkbwVJyUpB/ZT4O//kwOms7o1870hsWWYMm1EtGRETUn+ZmsTB4\niEol4ubm8DbXZy40v9mMwp8XQp3GOycHi8nYCFf4i0LIPhk1j9REbU9PF/X2ImvQGAxiOxERjVJl\nZZiycuWAdvV4oitTqNXiETn3uGpNFVR6FWzX2GLc0NGFydhIU14uHkfoxuuQc0EO7I/b4W8LF4TR\n6cT8sJYW8S2mpUXEsazOTEREyUuniy76GgiIR+hzpKO6A/XP18N6tRVa89DqJsmyeIxWTMaSQPFN\nxfC3+lG7obZrm88nkjCnU0zcdzpFzNIWRETJIVTCqKlpeEoXmc1iaDLE4RCx2Szimv+ugSzLKLyh\nMLYnHoWYjCWBjJkZyDw1E9UPVyPoCwIA6urEgqtmM2CxiOdgUGwnIqKRLR61JHU6McWle6zTAX6H\nH/Yn7Mi7KA/ppUOb/zLcSeVIwGQsSRTdVITOyk40/G8DADEsqdGIsf2WFvGs0Yg/ExHRyBb6Pz3y\njvnQ//mx4vMBRmP0OcfJKfMAACAASURBVI1Gsd2+3o5AW2DIRV5D5TNaW4G2tr7LZyQ7JmNJInte\nNnQTdKhaUwVZliHL4hfa4RDDlA6HiEfzmDwRUbLw+3su+6hWR68lOVROJ1Bd3TN2NAZR/d/VMM02\nwTjV2PcBBsDhEEmeSiV6+FQqEXcvn5HsmIwlCUkloejGIrh2udD6bivS0oDDh4H//E/xqK0VcVqa\n0i0lIqKh0miiJ9cDItbEcMXp2lqgoSH6nA0NQPWf6+Gt8cZk6SOnUwx9ut1iXrPbLWKnc8iHHlGY\njCWRvMvyoLVoUflAJfz+6G9Ibjd6bCMiopFJpxP/n0fWkvT7Y3vHvNMZndy1twMatYzOP1VBf6Ie\n5rPNQz6H3y+SsMhRnObm0fdZxWQsiajT1Ci8rhAtW1vQWuGK6gXTakWvWGurcu0jIqLY0GrFwt2R\ntSSPtpD3YEndVjfS7GqG9K0bRTcWQer+4iCEbjwAwm0P3ZgwmjAZSzK2a2xQ6VXwPVcVtaZYMCjm\njLlcyrWNiIhiJ5SQZWcPTyKWmRndQ5WeDmheroKUl4K8hXkxOUcoiZQkMWk/Mh5NmIwlGW2WFtaf\nWqH5Rz3kwx1d21tbxben0XaHChERDU5+PmAyhWPXv9ug+awVWT8thColNumDViuSyYwMQK8Xz9nZ\nsU8sEx2TsSRUdEMRIMswvRu+DSYQEOP9o+3bBhERDU56ukiOQvRvVAF6NSxXx27pI6NRjNzo9aIe\npl4vYuPQbtIccZiMJaG0kjT4vp8Hy45a6CH6mDs6xDeN0TYOT0REg+PzhUdTLGiH+oN6aM63IZge\nu1s2MzPFTQfBoBi9CQZFnJkZs1OMCEzGklTn+UVQdwYwH3YAoqtZltkzRkREA9PRER6mvBDVACRk\nLy1AR8dR33ZMtFogJ0ecx2gUzzk5HKakJCEdZ0TbBBNK4YYKQXz5pfimEcsaNERElLx8PnHTVxr8\ncECLndPHot2QFvO5x8N9I8JIwI/mJKXTAT93nYBvoUIQEjZsAMaMAR57TOmWERFRLPh8olq93y++\naOt0sU9kli0D/FDhOZTgld3ApmXAc8/F9hzEnrGktWMHcKBei3ZoAEjweoFvvxXbiYhoZIvHQuEf\nfQR88YUMP1SQIaG9U8IXX4jtFFtMxpLUnj2A1xs9QczrBfbuVahBREQUM/FYKPzTT4GO9uhtHR3A\nZ5/F7hwkMBlLUllZPeeHaTRyVM0YIiIameKxUPhxYwJIQzBqW1oacPzxsTsHCUzGkpROF1msT0Ya\n/LCleWO6bhkRESlDoxG9VA4H0NQknjs6YnuT1oyqGkyEAxJETSSdDjjpJGD27NidgwQmY0mqsRGY\nMSMcX5f+LR4K7EJTfbDvNxER0Yig1YYX1E5JCS+4HasJ/H6HH56nKvHfp1ZDhpjycv/9wPr1YuSF\nYovJWJKSZUQsFC7BO9mM7PYOjN1Xp2SziIgoBnw+UZfL4wEOHxbPRmPsJvBXPVyFQKsfhhVjurad\neqr4bOEIS+wxGUtSOTnR/yjrSsywZ2Vg8qeHEOgIKNcwIiIasvZ2wO0WyVFodRW3W2wfKl+TD9UP\nVcN0Xg7yfhBel0ijEUsWcY3j2GMylqSOOy56TTGHU8KuqWOQ3taJ2vW1yjWMiCjJhcpOhOZyDUfy\n4vEAbW2ASiWGKVUqEcfibsrK+ysRcAWQ9YsxaG0Nb3c6gdbW2CR8FI3JWJLKygJSU8Ox1ws0l2TB\nd6IJh+4+hICbvWNERLEWj/pfofP0djflUM/TWdeJmkdqYLnMgo58PWojvrtLElBbK66HYovJWJKq\nr4/+B2OxiNg+dwx8h32oebRGucYRESWpeNT/AkSiZzSKBMnrFc9Go9g+FJV3VyLoDaLkthI4ndHH\nC/XCOZ1DOwf1xGQsSR08KBKwkNxcEX+pzoT5HDMq76uE3xHDgjRERBSX+l+ASLxkGdDrxTwuvV7E\nRmP/7+1LR2UH7E/YYb3KCt14HVQqsVZkiCSJWNVf5lBeLh40YEzGklQgIBZdDTGbRRwIAGNWj4G/\nxY+qh6uUayARURLSaMT/s5ECgdjW/wLCSVJVFbBvn3iO3D4Yh1YfAgCU/K4EgJjuEplE6vUiZmmL\n2GMylqRKS8V/AHfeCdx7r/hmFgiI7capRuT8Vw6qH6qGr4m3xRARxYpOJxKWUEIWCIg41uUgfD4x\nkd5gECMfBoOIBztnzHPAg9qna2FbbkNasaiLlJ8fPUzp84k4Pz8GF0BRmIwlqdNOE99iAgHRtRwI\niPi008TrY24fg4ArgMr7K5VtKBFREtFqRe9U5FyuzMzYFWMNaWwUCVhOjhj5yMkRcWPj4I53cNVB\nqFJUKP5Ncdc2nQ4YOza8j8kkYtYZiz0mY0nq+OOBs84S32BkWTyfdVZ4TTH9JD0sl1lQ80gNOus6\nlW0sEVESCSVk2f/P3pnHx3VWd/93586+aF8tS5a3eEvsOHFwApSapQRDaFhK27C0NBR42UoKNBCW\nsgQIa1iSFgikBAgk0OYtLS5pCCGGN5DYITjEtmxH8iLJ1mZtM5p95t77/nH8+N6r0TKSnrkaSef7\n+cxnfMYzc2c0M/f+7nnO+Z3a0ggxAMhkKEvV0kIXgOLMPHbniaMJDP1oCC3vaYGvyWf7P6vwamtj\nIVYqJK9iM+XE6tVAQwOJMUUp7LJZ8/E1GLxvED239WDj1zYuzotkGIZh5ozPR5k3K9ms3dKoWE5/\n/DTUsIq2m9tmvzNTEjgztkxJJoFAwCzcr6mh2NpeHdwQRPONzej7Zh/SPenFe7EMwzDMnKirs2fB\nslmK6+rm9jwTf5jA8APDWP2+1fDUliCFxxQFi7FlSrHt1aJrpvvT3eaNe/bg8ptuKvErZBiGYeZL\nMAi0tpqxy0XxXJcRT3/sNNw1brT+Y+uU/29tCCjVNAGGxdiypdj2an+bH6vevgr9/9aPZJdkV0KG\nYRimZMy5nkvTgJER+AYHgX37EP1/oxj9+Sjabm6Du7KwaklMExCUapoAw2Js2TKX9uq2D7fB5XWh\n+5Pdhf85C07MYGMYhmEKsQqlI0dmGVOkacC11wIdHfAPDAA33ADX9XvhaXCh5d0tUz4kmSQBJojH\nKZY9TYBhMbZsmUt7ta/Jh5b3tGDwh4NIHE0UvQ2nZrAxDMMwdqJR4NgxM9Y0iqcVZA8+CBw4AOg6\nFACIxxEYewabrj8FNaRO+ZBUCrZB4dEoDwovFSzGljFzaa9uu7kNaljF6Y+fLvr5nZrBxjAMw9jp\n7aWmLEEgQJfe6QarHDoEJOwn2yoyqFk1vddkMglMTJixy0Ux7+Plw2KMAQB4aj1Y/b7VGH5gGBMT\nzUU9xqkZbAzDMIwd0TFvZXLHvI2dO8n524LhC8C164ppt8H7eOdgMcZcpPUfW+GuceP0mRcWdX+n\nZrAxDMMwdoLBwuXCVGqGIv69e4Hdu2G4XDCgQFMCUJ57Nd0+DW63ffC4olDM+3j5sBhjLuKudKPt\n5jaMjl6CRKJ91vs7NYONYRiGsdPaahdjqRRdWqd2qKCU1kMPIdpyLc7g7xD7x29BefgXhakvCxUV\n9gL+UIjiigo574ExYTHG2Gh5RxMa1F8BPQawb19h6suCx0PCKxYDBgboOhgszegPhmEYxqSyEtiy\nxYxVleLKyukfY8CFZ0f+DgO+P0PVF944oxAT27CeXOs6xTNtg5kfLMYYE02D+pqXY7P+OazK/gzG\nX/41tUJPI8is3ZQeD3dTMgzDOIlVKBVj+Dr4o0Ekk/VobnoQiqrM+vyiCUxQqqHnDIsxxsqF1meX\nkYMCA0oqAePAAbp9CqJRKhZ1ucjawuWieEavG4ZhmEVEnERq2tI+eczlgB5LI+TRoxRP9370nI4z\nnziDcLgflZXPFL0NNn11BhZjjMkUrc9IJICnn57y7hMTJMASCWB0lK5F6zPDMEy5Yc3mK8rSFhf9\n/cCJE2Y8MUFxf//U9x/47gDSp9JY2/4rKIox9Z0mIU64BXzCXTpYjDEmU7Q+64ofxvYdU96dTV8Z\nhllKOOWN6MRkklOn7BYT+TxdTp0qvK+W1tB9azcqrqlATU1n0duIxWjfLlBVimOxBbxwZkpmFWOK\norxHUZRqJ14Ms8hcaH2GywUDgO4LIqpvwfnUrinvrqpU0GlF12etCWUYhlkUnPDNWtBJ6p49dCmC\nkREaTyQ4f57ikZHC+/Z/qx+Zsxms/fRaKLOXil1EUex/m1iM4rk8B1McxWTGGgE8qSjKTxRFeZmi\n8MewbLnQ+oytW5FuaoLy4/vRteVOnPlkLwytMK0dCgF+P+1ohobo2u8vSK4xDMOUBU54IzqVfdN1\noK/PjBMJiiefIGsJDd2f7UbVi6pQ/aK55VX8fhJ5gnyeYr9/AS+cmZJZxZhhGB8FsBHA3QDeDKBT\nUZTPKoqyvsSvjVkMVBWorUWmsRHK9a/E2ls3IHksicEfDRbc1bpjE140bPrKMEy54oQ3olOu9T6f\nPduWSFDs89nvd/aOs8gN5bD21rVz3obHY/cUUxSKuZtSPkXVjBmGYQAYuHDJA6gG8B+KonyhhK+N\nKQPqXl2H8M4wznziDPSc/ZQrl6O0uDUdH49zzRjDMOWJsGoQxfulsGpwajKJzwfU1Zmxy0WxVYzl\no3n0fqEXNS+vQeVz524OpihAQ4MZV1ZSLHt9zIkau3KnmJqx9yqK8hSALwD4LYDLDMN4B4ArAby2\nxK+PWWQUl4K1n16L9Kk0Br47YPu/WIx2Yq4L3yKXi2Iu7mQYplwRgkxVS+OZJYywz5wBOjvpWhhi\ny8TlsmfgamspdlmO6r239yI/lp9XVgwgAWl9vspKimUKS24EI4rJjNUAeI1hGNcahvHvhmHkAMAw\nDB3AdSV9dUxZULO3BhXXVKD71m5oafOUL52m2oHqavPi99PtDMMwK5FcjsSXVVzEYvLFhd9vrw/T\nNIpFPVd2OIuzXzmLutfWIXJFZOonmYXJ8y9HR2eZfzkPnKqxK3eKqRn7uGEY3dP83zH5L4kpNxSF\nsmOZsxn0f8s0sQkESHiNjZmXdJpuZxiGWYkMDwPhMC0Z1tTQdThMt8vE4wGqqsw4FKJYZPp6v9AL\nLa5h7afmlxVzCqdq7Mod9hljiqL6RdWoelEVuj/bDS1B2bFIhM72rr6aLrpOcWR+J2EMwzBLnkyG\naqpiMcokxWIUZzJyt+N220cVhcMUu91Apj+Dc3eeQ+MbGhHaOv/2dpG1EpQia+VUjV25w2KMKZq1\nn16L3FAO5+48B4DOwMJh8/8VhWLutGEYZqXiclEhunWZcmTEXnslg0DAXkgv4kAA6LmtB3pWR/sn\n2he0jVSKujR7eoBz5+i9JBL2pcuF4kSH61KAxRhTyP79ePqrXy24ufKaStS8ogY9n+9BPprn9DLD\nMMwknBIXgYDddqKi4oLtxFgafd/qQ/ONzQisX1jNSDZLr9068i6fp9tlYe1wzWZX7jByFmPMnFh7\n61rkx/Lo/Uovkkn7HEpFoXilFV4yDMMIvF5gzRpzbq/LRbF1rJAMgkFqmhKEQhQnvkEl3ms+umbB\n2xDLrfk8vf583lx2lYkQZLW1K1OIAcAKW5VlFkpkZwT1f1GPs7efRdWfrcZEyvzVCGFmXbpkGIZZ\nSbjdVD9bUUHiRdhDyK6BCgTs3ZSKAngGk4j+uB8t72qBv23hNvmGQduZmADGx0mQRSKmyTcjD86M\nMXOm/ZPt0OIaYnf12Oag/eEPVBshs56AYRhmKeHxAIODtKwXj9P14KD8bI/HQ2PoBGNjwLnbzsDl\ndaHtljYp2xCZMU2j7WlaaTJjzCKKMUVRWhVFeVRRlA5FUY4qivLexXotzNwIbQ2h8Q2NyP74HLoO\nmC1CXi/Q0WGfZcYwDLOScMo3Kxqly8XtHo0j9+AQqm5sga/JN/0D54DwRrMae1tvZ+SxmMuUeQDv\nNwzjD4qiRAA8pSjKw4ZhdCzia2KKpP0T7Rj40SAu+X0PaHSpWaBqHV7LMAyzkojFqH7L2twkMkrW\n8UULpa9vUiH9PWdgBFRkXy0nKwbQMqvfTyfaqkrvQxT1M3JZNDFmGEY/gP4L/55QFOUYgBYALMaW\nAIH1AcSe14y6x/vQgFYMwY94nOokuJ6AYZiViqJQqUY0St5iPl9pitLPn8fFMpFLMAHP48OIvXoN\nMjl5G3K7SYxFoyTCvF7Ty4yRi2KUwZFTUZR2AL8BcKlhGLFJ//c2AG8DgMbGxivvv/9+x15XPB5H\neIVWoxfz3qNdQMU7gP/JN+PL2IT7798Pw6Afr9UZeqmxUj/3lfq+AX7vK/G9l+p9Z7M0iURVzYHk\nmmZmmGbi8ptuAoAprYUmMz5OGarXvW4PbsMzeE54FGN3AmrlzPvfy2+6CZqm4fAdd8y6jVxuahsL\nr3fpdjw6/X1/4Qtf+JRhGLtmu9+i61tFUcIAHgBw02QhBgCGYdwF4C4A2LVrl7Fnzx7HXtv+/fvh\n5PbKiWLe+++8QNfOTlQ/mUYEWezbtwdr1wIvexnw3Oc68zpLwUr93Ffq+wb4va/E916q933yJI0+\nEkJMXNfVAevXz/LgCyqqmNf14IPUINCGBJ5FBMkrmnCJ2oBaHzDjw6uqMD4+XtQ2+vtp0DlA9WKi\ne7O9HWhunvXhZUm5ft8XVYwpiuIBCbEfGobxfxfztTDz44uxdeiCgTRU/OQnwMaNJMYYhmFWIroO\nNDXRUqWwtggE5BqlAuTJ9eEPGxiAH/egHb6DwOYY8K1vydtGKkXzNScvU3LHvHwWs5tSAXA3gGOG\nYdy+WK+DmT+PPAJ0nlGRhhuAgmwW6Oqi2xmGYVYiPl9ht2EuR7fL5Phx4EQHkIUKAwrSaQUnTtDt\nssjnack1EgEaGug6neYC/lKwmD5jzwPwJgAvUhTl6QuXly/i62HmSFdX4fDbTMbAyZOL83oYhmEW\nm8pKWt4bHiYH/uFhiq1DvWVwslNHelK2LZ0GTp+Wtw0e4u0ci9lN+RgAto5bwqxbR0Wc1rNAn2pg\n7Vr+WBmGWZnkclT6lUjQv91usrqQ7c3VenoYftQgZTmMBwLAjh3ythEMksCLRun1ezzUMb/Shng7\nAetbZt60tgKNjcDZswBgwK/o2GxMYE1tCMASbbVhGIZZABMTJMZqa83bNI1ul+Uzlu5JY90Dx7Gt\n5gr8fpQ6A4NBEmLXXCNnG4A5ykmMQFKU0ox2YngcErMAhoeB17xGRApe/YIMvqg/Df/9ZxbxVTEM\nwywehkFZpFiMRiHFYhTLdJHqel8XVADff8BURV/6EvC971FGTiYiG1ZTQ9elsLTI5Sj7NjJiZuFW\nGizGmHmTy9nT1fU7gujbuQqNvzuH+DPxxXthDMMw0yAO/JpWmgN/IECiIp+n7sN8nuJAQM7zjz48\niuEHhhF+exuSEXMY+JVXkvCTWVyvKEB1NV1ns/ZYFuLzMAz6exnGyhRkLMaYeVNRAdugcFUFDl66\nFlrQjc53daIcDIUZhmEE1gO/8P+SfeD3eGhZzypgIhE5GSU9q6PzPZ3wr/cjdGOrbQ5wLEau/DJ3\nu2KZsrKSll0rK+UvUzo1y7PcYTHGzJv6etrJCFIpwFfvQeL16xB9LIqhHw0t3otjGIaZhBMH/lJm\nk85+9SxSJ1LY+PWN0KzDL0EGsIDczFgwSM8nOio1jWKZBfz5vH2OJ0DxSrPPYDHGzJtwGFi1yoyb\nmihWr2tG5KoITn7gJPKxFfaLYhimbHHiwG8YJIwiEdonRiIULzRjlT6bxplPnUHtn9ei9uW1SKXs\nAk+MX5rVkHX//qLGLQGUzaustAtL2XM22T6DYDHGzBufj+atWfH7AV9AwcZ/2YjsYBZnPnlmUV4b\nwzDMZJw88Le1AS0t8p7v5AdOwsgb2PDVDQBIQFpd/UMhipdaRsmJ7NtSgMUYsyDGx81/+/1mXHFV\nBZr/vhlnv3YWiaOS23sYhmHmgRMHfkWhVQPBxATFC1mmHHt0DOd/fB5tH2pDYC11Arjd9pPhRIJi\nmcIyl6Ou+fFxeh/j4xTLrrErdfZtKcBijJk38Th1vwiiUYpF7cLaz66Fu9KNzndzMT/DMIuP9cAv\nivhlH/gNAxiylMvGYhTPdxeo53R0vrsT/rV+tH2w7eLtgYBd4IlYVtcmQPv0ZJKK9r1euk4m6XaZ\niM9FNAmsNCEGsBhjFkA8bk+TV1dTLMSYt86LtZ9Zi/H94xj68aRi/j176MIwDOMg4sCvqqU58CeT\nNP5IoOsUz7dJ4Nwd55DsSGLDVzdADZgFb4GAXeCJTkqZYmxiggRYIkGeaYkExRMT8rbBECzGmHmT\ny9nT5CJtbk1hr3rrKoSvCOPk+08iH19ixQwMwzBzZGyMTkwFmQzFY2OzPFDTyCuouxvYtw/QNGT6\nMzjziTOoeXkNal9Za7t7Pk8CSeD1UiyzZow9wJxjhfUrMDKpqqIdzNe/bs6ozGbpdoGiKth450Yc\neu4hdN/ajfWfX794L5hhGKbEpNP2JoFIhPaLuj7DgzQNuPZaoKOD7njDDcDu3TjZ8BXoGR0bvrYB\nyqSis5ERoKHBjOvrTT0nC1UtfN26XtiRyiwczowx86a+nqwsQiGqVQiFKK6vt9+v8ppKNP1dE87e\nfhaJ41zMzzDM8sXrtZdvABRb62sLePBB4MABU/nE4zB+9wS0+/ah7eY2BDcUdhhMXpIMBAqXLhdK\nKERiUtdNQRmJ0O2MXFiMMfOmpYVc+CsraWB4ZSXFU7Vzr/vcOqhhFV3v6eJifoZhli11dfaOxtFR\nimccEn7oUOFQyVQSlZWn0XZL25QPqaiwx6JWd/LtCyEQoJWOykrqCK2spFhmXRpDsBhj5k1FBe1g\nVJWMBlWV4ql2Bt4GL9pvbcfYL8dw/oHzhXdgGIZZBgQCdqsMRaF4RgGzc2dBukmDD5Xv/FOowanX\nBJua7HVobjfFTU0LePGTCAZNq47aWtOiY6V5gDkBizFm3uRylLZubATWraNrXZ++uHPV/1mF0I4Q\nTr7vJDSt+BYmUUQ6MsLFowzDlDe5nL2IvrmZ4hn3W3v3Art3Ay4XDAAaAkjVbEfFp/5q2od4PMDW\nrWbs9VIsszuUPcCcg8UYM29iMfpRWue8eTx0+1S43C5svHMjMr0ZdPf8SVHbcMJ0kGEYRhbptD3J\nNThIcTo9w4NUFXjoIWDrVpwP7UWH+jGoj/0SygwOrvk8UFNjxlu3UizbgZ89wJyBuymZeZNOk5WF\ntTA1m515p1P1/Co0vqkRvfc+F02NT2O2bHc0ShdNM00aheibsQaDYRhmEUgm7aav4TDF1s7HKVFV\nRN2XoyPxFrR9qA3BLZEZ7+522/e10SiNqJuxUYApWzgzxsybQIBEknW0iKbNXty57gvr4HLl0dW1\nd9Zi/tFR8umxOkBnMnZ/HYZhmJJTpFG1WM4TuFzmMt9MGJqBzq6Xw+eLYs1H18y6HY/Hvh8UvmOc\nuVqasBhj5k1NDZ2JWduefT576nwqfPVubK7/DiJjjyP20R8VTu61kExSJsy6FKqq83ezZhhmZSNq\nUDWtNDWoPp+9wD0apdjnm/lxfd/qQzzejPXrfgE1NLuRVy5n39e63RRzCcfShMUYM28qK2knI4r2\ndZ3iysoZHnTB3LBu6D/RjnsQvu2tMF7y0mkFWTBImbDxceoUGh+nmLt5GIaZK1ZHeTGfUrYgmyy6\nRHf5TGIsez6L0x85jaqqU6ivP1rUdvJ5+wSUykqKZdeMMc7AYoxZEB4P7Wyqq+l61hT5BXNDRdeh\nwIBqpGD89gm6fQoiEbLfiUZJiEWjFEdmLqdgGIYpIJmkDJI10+52y820B4N2QaRpFM90AnnqllPQ\n4ho2bvg5JhntT4vbXXgOq2l2jzNm6cBijJk3ySTVh9XUUKdNTQ3FM+7YpjA3VHIp5H715LQP8Xio\nCLaqiq65JoJhmPmQzxeO8lFVudkkMY1EEI+bU0qmInYghoG7B7D6ptUIhYaL3s58RB9TvrAYY+bN\nvHZsU5gb6vDj3GP1U949nSb/supqelh1NcUztokzDMNMgehAjEZpPxWNUiwzm5RMmm74ABXwx+NT\nn6QamoFn3/UsvKu8WPPPsxftW/F47MIrFqOYT1aXJizGmHkzrzS5xdwQABAOI7vhCpx5cguG9xWe\nFRoG1XPEYrRMGYtRzBOVGIaZK6IDMZ+nTFUpOhBjMWBgwIwnJiieyn+x/+5+xJ+KY/2X1sMdmZsi\nzOXsAq+igmIu4F+asBhj5o1Ik1utLWZNk1vMDdHeDtx3H3yHH0VwSwRd7+2ClrarO7cb6O4m/fYn\nf0LP393NdREMw8wd0YHodtMJXSk6EMfH7eLO7aZ4fHzSaxnJ4dQtp1D5p5Vo+OvZTMgKEfVvglLU\nvwE8AcUpWIwx82beozJUlYrM1qwBrrsOLr8HG+/YiPSpNHq/0Gu76+Sl0O5u+TUeDMOsDEQHYmUl\nCZdSdCDmcnbj1UiE4ski5tRHTiEfzWPjnRuhFFu1b8GJ+jdr96nXW5ruU4ZgMcYsCFmjMqpfXI36\n19Wj57YepE6nLt4+OmpP7/v9FLPpK8Mwc8WJDsTqaruNhfBfrK42b4v9Pob+u/qx+j2rEb40PK/t\nOPFenOg+ZQgWY0zZsP7L6wEXcPJ9Jy/eNjpqPwubmKCYxRjDMHNlXqUVc6SlxS7G/H6KW1ooNnQD\nne/uhKfBg/ZPtM97O050U+bzJCaty5S6zisTpYDFGFM2+Fv9WPOxNRj+6TBG/ncEAP3oe3rM+4yN\nUcw7A4Zh5oq1tEIYv8oefl1XB6xebcbhMMVilu7AdwcwcWAC67+4Hu7K+aexnOimNAza51qXKUXM\nyIXFGFNWtL6vFYFLAuh6Txf0jI5Ewj7r0uuleJJVGcMwTFEIQaaq8oWYeP7mZjNua6PY4wFyYzmc\n+tApVD6/Eo1vbFzQdribcnnBYowpK1xeFzbesRGprhR6v9wLn89epCqKVmeb88YwDLNYWAWeVfCd\n/thp5EZz8y7aKDzagQAAIABJREFUt+JEN6WiUK2btUlLxIxcWIwxZUfNS2tQ9+o6dH+6G4GJtO2H\nn0rRjsCaLWMYhiknrNkp0X048fQE+r7Rh5Z3tiC8Y35F+1ac6KZ0u8kS0tqk5XKxtVApYDHGlCUb\nvrIBAOD5dpdt57J6deGAXIZhmHIhlwP6+824pwfoO2fg2Xd2wlPrQfut7VK2I7opYzGz41x2N6UT\nDQ8MwWKMWRz276fLNPjX+NH24Tbg18NoGzJbJ8+eBVatsvv4MAxTetj8sziGh+0O/IoCnPvuICYe\nj2Hd59fBUyWnSM0JoTRvL0lmzrAYY8qW1g+0Ai1++O7qhBs6AMqMjY/TjoFhGGdg88/iGRy0CyJ3\nJo/cnSehXlaBpr9tkrYdp4SSLC9JZmZYjDFli+pXob9rI7wDKfwFzgKgjiGfrzQHAXHA0TQ+0DCM\nFTb/LB5Ns9dyTXz9NIyxHHwf3AjFJbfynYXS8oHFGFPW+F5Qi8xzarEJMQSRw759QCgkv5vSeuYv\nPIhYkDEM4USxOODMUmipT7qqqoB4/MK/kcEv703D9epVqL06IndD4KXj5QSLMaas0XXgfSNb8Xls\nRhJu3HMPcMstdLtM+MyfYabHidE7TiyFOnHS1dAAvOc9AGBgHF7cqm/FP3VvQMPcZ4HPCC8dLy9Y\njDFlzYEDwMmzKtJwA1CQyQCnTtHtMnHqzJ9hliJOFIs7cUKUTFJ9VV8fkMnQdTYrdxu//jVw5AgA\nKAAUpKDi6HEXfv1redsA+ARyucFijClrTpwoLNbPZg2cOCF3O06c+TPMUsWJYnEnTohiMbKd0HXy\ny9J1ioU1hAwOHQKSSfu8oGQSePppedsA+ARyucFijClrNmworA/zKTrWr5c7HI39dBhmZkpdLO7E\nCVE0Ss8nrHG8XoqjUXnb2LFdh1+x11EEg8Dll8vbBsAnkMsNFmNMWfO859FsN4HfrWOrHsU1I/3T\nP2geODFAmGGY6XHihMjloot1G+I2WWw+2I0tehSuC3Y8oRBwxRXAS14ibxuAcyeQ3CTgDCzGmLLG\nMIDPfc6M//ZGBZ/d3gvjzi4kn+XiCIZZLjixFBoO03Nv3Qq87GV70NlJcXjh04kAANHHo+j7XDe+\n+dpB6BcOr1/4AvDDH1KNmkyc+Htxk4BzsBhjyhpdB8bGzHjXVQoG/mYz4HXh2BuOQc/JaatkawuG\nWXxKvRTq8QCdnWbsdlMsYzv5iTyOvfEY3C1+aO/cePH2nTupUUBmXZqg1H8vbhJwDhZjTFmTyZie\nPQCQTgNRjw+5f7gEE7+fwJlPnpGynWSSBFg8Tqn+eJxi3ukwzPJhZARoaTFjTaN4ZGThz9313i6k\nz6Th/+RmpF1m4ZbHA6RScrbhNNwk4BwsxpiyJpu1F/AHAhRndjeg6c1N6LmtB+OPjS94O6kUkEjY\nM2OJBN3OMMzyIBq1Z4+amyleaAH/+QfOY+C7A2i7pQ3a1ipbDdrEBNWkyV6mdAJuEnAOFmNM2VNT\nY/47mzXjDV/fAH+7H8ffdBz56BSnanv20KUIhH2GNR1vvZ1hmKWPy2UvPRDxQgr4M+cyOPG2E4js\niqD94+1TZo6myjAtBbjL3DlYjDFlTThM9RYCt5vicBhwR9zYcu8WpHvS6HxP5/RPUgSiONW60xFF\nqwzDLA8aG+0ZqnSa4sbG+T2foRs4/ubj0NM6tvxwC1weF8Jhu+DTNIplNQk4iVPDyBkWY0yZ4/Xa\nzyiHhykWIqnymkqs+egaDP5gEEM/Hpr3dgIBOjs+d4520OfOURwILPANMAxTNtTWAhvN2nq4XBTX\n1s7yQE2joq/ubmDfvotnbWe/fhZjvxzDhq9sQPASSheFQoDfbz50YoLiUKiIF7h/P13KCB5G7gws\nxpiyJpezC6JwmGLrmeeaj61BZHcEz/6fZ5HuTc97W/399NxeL133y7UyYxhmkQkG7aJo82aKZ1x2\n0zTg2muBjg7gzBnghhuAa69F/OkoTn3oFGr/vBbNb22+ePds1i7GWloo5pIHZiZYjDFlTSxGqXGB\nqlJsbRN3uV3Ycu8W6Dkdx//2OAx97u780ShQV0fNAYZB13V1cp25GYZZXESWR1DUstuDD9IwXP2C\njU48DuOJJ9B3/d1wV7mx6TuboFh2UppmbzqKRCieXAjPMFZYjDFljaYB58+b8cQExZN3bMENQWz8\n2kaMPzqO3tt757ydTIbOjisqSPBVVFC8FDugGGbFMYdmHavwKmrZ7dAhaq22kkjC03MUm7+7Gd56\ne2Gpx2PPtE1MULxUl/fYgd8ZWIwxZU0uZ+9MymQonmqH0HRjE+peXYfTHz6N+B/jhXeYAZ9vqoHk\nhXMxGYZZ2lj3HUWJi507Cwq+NPjgfcVzULu3sNjM77d7iolyM+vS5VKBHfidg8UYU9bk81S/dccd\nwDe+QbYWgcDUpoOKouCSuy6Bp86Djtd3QNOKN8OpqyOj1+Fh2nkOD1NcVyfxzTAMs6jkcvTbFoyP\nUzyjuNi7F9i9G3C5YADQlAASwUvRdP/fTfsQw5g5XiqwA79zsBhjyppQiASYqlJWTFUpnq4zyVvn\nxeZ7NiPZkcSp039W9HY8Hrr099N2+vvN2xiGWR5Eo3Yh4XJRPGNtqKoCDz0EY8tWDAWvQ4frY3D9\n+mGo4al9b9JpMpMVVFdTnJ5/b9GiwQ78zsFijClramooU+XxUCGsx0Ox1Qi24DEvrUHLe1tw7txu\njIxuKGo7w8O0QxadTy0tFFvPohmGWdpMbghKJAobgqZEVTGQfzGOJd+Pys++AZFdVdPe1TDsDvUV\nFRQvxewYO/A7B4sxpqypqqLi10CARFIgQHHV9PtCAMC629YhGBzCiRPXI3t+9p7ywUF6XuFf5vVS\nPDgo4U0wDFMW5PPAkMWO8OxZimfL9KROptDVtRdVlafR+v7WGe9bUWGv9x8bo7iiYgEvfBpKXVzP\nDvzOwWKMKWu8XnLHdrloTqTLRfFszviqF7is+Q40Zx9A/59/G8Yse1tNmzodz+3oDLN8yGaBnh4z\nnpigeCYPMD2v49ibjgEwsHnzT6GoyvR3hilgBKUSME4U17MDv3NwspEpa3I52pnV15MQ03VzvMi0\nXDBpDJz+HdrxGLQnfoLsZffDd2T/tAPiqqpoSfLqqwFgD554gm7nAn6GWT7EJzVZZzK0X5l8u5We\nz/Qg9ngMW7bsg98/u/FgLmcfr1RTQ13ZsrNWUxXXi9utXmoLZbI3G1MaODPGlDXZrLkzqKoyz8pm\ndLO2mDQqANxIQT3+FNJ3/3Tah9TV2Z8zl6OYxRjDLB/icXvzTyRC8XRiLPpEFGduPYPGNzaiseFI\nUdtwquidi+uXFyzGmLLG56M6MVFMH41SPKP/1xQmjSrSGPnUL6Hn9Gkf1tZm/tvjsccMw5SeUtdA\niQkegnCY4qkS5vmJPI698Rh8q33YeOfGwjtMg2HY69KiUYplF/Bzcf3ygsUYU9ZMNUZk8riRAqYw\naTR8QYyea0P3rd1TPiSVsu8sV62iOJWa5wtnGGZOOFED1dBgrzfN5ShuaCi8b9c/diF9Ko0tP9gC\nd2XxCieXs3dnGgbFXFzPzASLMaas8XhoCSEYpCXDYJDiGQtILSaNAIBwGK7nXw33m16J7s90I/q7\nwrqPbNae3k8kKObhvgzjDMkk/d76+oDOTrrOZuUajDY22uu5wuHC2wDg/H+ex8DdA2j7UBuq/mSW\n1u1JpNNU4ypwuymW7TPGxfXLCxZjTFmjaUB7O+1gEgm6bm+fpcvxgkkjtm6lO993H/DQQ9h452b4\n1/hx7I3HkI/ZCysUxW5j0dNDsTJz49Sc4TlvTClYDt+rWAwYGKAmnXCYrgcGivAAmwOVlfakua5T\nbC1Qz/RlcOLvTyB8ZRjtn2if8zac9BkTgqy2loXYUofFGFPWGAbViLW0AOvX03UgUMSOTVVpD7Vm\nDXDddYCqwl3hxpYfbEG6O43Of+i03T2ZpDZ3gaJQLPOsnOe8rUxKLZSWy/cqGqWfrdXrT1Vnccef\nI7mc/TcdDlMs/laGbuD4m49DT+nYcu8WuLxzP0RWVNgz6ppGcSl8xpjlA4sxpqwROzZrXcRCdmyV\nz6vEmo+sweD3BjH072aV7cSEXeCNjFBsFWgLhee8rTycEErL5XvlctHF+lsXt8lieNherJ9OUywm\nbZy74xzGHh7D+tvXI7R5mplrs1BZaa/b0nWK2R6CmQnuu2DKmspK02ZC0yhjtdAd25qPrcHoQ6N4\n9u3PouKaCvhX+xGP25cp43HaUQcCC38PgnyeXn88Tv92u+m9LMUxKUxxOOEFtVy+V+GwWbuZzdL7\nCARmN3ieC2NjhcX1w8O0vZpoHCc/eBK119Vi1dtXzXsbHo/dEkdMEeElRGYmODPGlDXWItVcTk6R\nqsvjwpZ7t0DP6jj+5uMwdAOxmL1zUlUpllmvYhh0MLBmSUTMLE+c8IJaLt+rujo64fL7ySjV76dY\nptefdUkSoBOuXA5IjGk49oZjcFe6senuTVAWWCxq3T9xLRdTDCzGmLJG1HhUVABNTXQ9eYc6H4Ib\ng9jw1Q0Yf2QcZ796FoC96FbX2a+HWTjsBVU8wSD9xuNxmhkZj1Ms06rB67UbvGazFBvfOY3E4QQ2\n/9tmeBskpuIYpkhYjDFlTSnrYZrf0oza62tx6pZT8PbGUV1t/p+qAtXVcs9oFYWe09qKLmJmeeKE\nF9Ry+V7lcnRZvRrYsoWuxW2y8PnsNhYeD1DXM4bcD89i1TtWofYVtfI2xjBzgMUYU9aUcplHURRs\n+s4meGo8CNzegeE+M4UxNgacPy93icTtpmJkayu6y8VZkuWME15Qy+V7lUzS0mo8Tg008TjFMhsR\nJtfpeTM5ZD91DJ4NQaz/0np5G2KYObKoYkxRlH9TFGVIUZTihn4xK45SL/N467zY9N1NME4lUfXv\npy7efuAA+ZpNM1d8XrBj9sqk1F5QTn2vkkny3+vspGvZ3ZqpFDA+Tt2m8Thdj4/LnYJhH6Vm4Df/\n1AdtNIe2b26BGpT4Y2eYObLYmbF7ALxskV8DU8Y4caCpfVkt0te14IuP1cIFqnr+z/8Evv1t4Nw5\nedvxeOh1C3PLWIy7rJiF40T2LZkEentNk1Rdp1imIBNefy4X1Xa5XPK9/jQNeOc7zfhTh1vw4Zbn\nwHtpRN5GYH/NpRCuzPJjUcWYYRi/ATC6mK+BKW+cGvnx8Np16FAqoYMKbbJZoLsbePRRedsoVTMC\nw5Q6+zY8TBklqyGrz2f6c8lAlCRs3Qps2kS3ye48feQR4JlnRKQgBTeOjvjxyCPytpFMAqdOAX/8\nI3D4MGX3Tp1iQcbMTNlXFSiK8jYAbwOAxsZG7N+/37Ftx+NxR7dXTiyL9/6JT9B1Ee/j3NAaZIx2\n223ZrIH+/jPYv3/q4eJzRWT3rIXVwn5A5nLofFkWn/k84fe+f8b7ZDJTm6/qOgkNGWSz4vewBwBw\n+vR+qCr9Xvr6Zn7s5ePjAICnZ3kfDz+8BslkOwDzR5hMAg8/fBqrVs38Oy92G8IrzeWi124Y9Hfq\n65PrmQaYzy0Q25wN/r7vX+yXUUDZizHDMO4CcBcA7Nq1y9izZ49j296/fz+c3F45sdLe+69+BXi8\n9jEmHg+wceNa7NmzVso2RkZoR5lMFppz1pZBE9dK+8yt8HvfM+N9enrooG8VE9ksHfzb2uS8jv5+\nsrQQtLXtQSpFXZXNzbM8uIqGec/2PsaGdfz4+zpShnn2EwwquP76In7nRW7jqafod209wdI0+t1f\neeXMm5gLYrqD6DYXJRzFZEb5+75nsV9GAYtdM8YwZcGLX0wzxQkDfuRxSTiFF794lgfu2UOXIjAM\nqkE7e9a8nDu39Mw5mZVHXR1lx8TJSjZLscxuY48HiFhKtxSFYllLroZhYON/ncAWPQoVlE4KBoGr\nrgJe+Uo52wCc85ZbLmOwGILFGMOA3L4/9SkzvnnHAL46ehDuh2ZZH5kDohstGqWDWTRamuLeUg+m\nZlYewSDQ2kqZsESCrltb5fulNTSYcWUlxbL80rpv7cbwvYO45+YYtAuHvrvvBu6/377Ut1AaGqgD\n1CpcUyn7e5OBE9MdGOdYbGuL+wA8DmCToihnFUV5y2K+HmbloqrWnaWCPV9aBddV1ch94VmMPiyn\nx2RwkFrrxZm+x0OxdSbmQnFiMDVTfjghwINBWpLcuJGuZVtnlDKjNHDvAM58/AxqbmhE4/vXXLz9\n+c8nYSnzhKiujoxlhWeaYVAsM4sIOJeB45M7Z1jsbsobDMNoNgzDYxjGasMw7l7M18OsXCIR+1Bw\nXXHBf9s2uNeHcPQvjiJ+JD79g4skkSCBJHaWbjfFicSCn/oivHSx8lguAtzjsZ+YjI5SvNBlyvHf\njOPEjSdQ9cIq1H9uE6JRM9VWCi8zj4dq3NragDVr6Lq5eWn6yy2X79ZSgJcpGQZkM2Et3tc0IOdx\no+2Hl0ENqTj8isPI9GcWtA2/n5z983naMefzFPv9C3zxFnjpYuXhlACfd4akyLpK4cA/OV7I+0ie\nSOLIq44gsD6AbQ9sQyrvwsSE+f+l8DJzCqf85fjkzhlYjDHMBaw7mKEhij0tfly27zLkRnI4/MrD\n0BLa9E8wC9XVtDOLxeiAFouZMzBlwYOpVx5OCPBcjjzFxsdJvIyPUywzQzI6aj8hcrkoHp1nlUD2\nfBbPvPwZKG4Fl/3PZfBUe5DL2bfR10exzPfhZDap1P5yfHLnHCzGGAa0HGJdLgyFKB4cBCJXRLD1\n/q2IH4qj4/UdMLT5tT8Gg3TRdToA6Lp5myx45NLKwwkBHo3SyYnVHT+ZpNtlEYvZT4jENmKxWR6o\naXR2090N7NsHaBq0lIYj1x9Bti+Ly352GQLrqAYhn6eZs4KBAYpliotkkn7ffX1AV5cp+JZiNolP\n7pyDxRjDgHaY5sw6c4adMJusu64OG762ASP/PYKTHzg5r21ks/S8LS1US9LSQrH1TH2hODWxgCkf\nnBDgExMkwqzLVV4vbEt+MkinzX/39dnjKdE04NprgY4O4MwZ4IYbYLz0pTj+N0cReyKGLfduQcXu\niot3j8Uo6y1QFIpnFXxzIBYjzzTr6Kj+frnbcAo+uXMO1rcMc4ELBtsATLfsmhrzttXvXo30yTTO\nfvUs/Ov9WP3u1XN6fk2jg5iu09KFotDZ/+Qzz4UiBBmzMhCft8jIuN3yBfh0XngyPfLcbnsBv+g+\nrq+f4UEPPggcOGB6U8TjMP7fE9Bz/4N1X3wD6l9rf3A0am/UUVWKZWb4hBGrdXSUptHtra3ytuME\nTny3GILFGMOAdi7WOXtieaSx0X6/9V9aj9TpFLre2wV/ux9z7VbP54FrrqF///KXdObMMAul1AK8\nooKyO4mEOT0iFCrCGX8OiAO+IBSizNiMy3uHDhW0Iyu5FJquGkTd+wuVTz5vN5ZVVTP7IwuXi+rD\nxsfNky6PZ+kKGD65cwZepmQYmONEBPG4mcmyoqgKtv5wKyJXRNDxVx2YmCj+aGQY9uNGOEyxbAd+\nYS7b2VkaU1lm5eHxUGbH2gkcjcoVGIkEiT5BJkPxjNYvO3cWnNHoqh+1H3kRlCncYquq7A0BokHg\nwqSjmdm/v6g5t36/dc4mXWezcrummeUHizGGAZ3JWs/+RDp+qg4oNaTi0p9dCk+dB4ePvB7pdEXh\nnabBug1RzyWTZBLo7bXXq/T2Lk1BxmaT5UM0ahqXhkKmsanM5T3R2CIQ9ZQzuuPv3Qvs3g3DpcKA\nAs0VgPL8q+G67hVT3r2qyj5fU8zbLEqMFUkgQNmxUIg6pUMhiq3LowwzGRZjDAMyfbRmxmprKZ7O\nDNLX5MNl/3MZNM2Dw0fegHxs9nWOyTVoFRUUWw8OC2V4mBoPrPUqPp99CXYpwGaT5UUmQ6JCfGcr\nKijOLMx6z4bHY/+9JRIUz5h9U1Vk7vlvHHd9CL3q66HdfS9cjzxcmNK+gNcLNDWZsctFsczfoNdL\nRq8uF2XYxTB1mdtglh8sxhgGlAmzLhcaBl1mauEObwng8tVfRl3if9Gz5xvQ0zMrhUjEvuQyPk6x\ntYZloWQyhTt9r1fuQdMJ2GxybpQ6i+jzFXb9ZrP2DuSFImxfBPG4af8yHVpCw+FXdeC8/gJU78jD\n++bXTCvEAPq7WDs0RV2azL+X201/l9ZWGh3V2kox20EwM8FfD4YB7ZQbGmhosMezH7ncHlRVzVBg\nf6GlPtL7KMLQoR36MVLrf4Rg9/+DMs1e1+Oxd2zm8xS3tcl7Hz4fCTzRgi4EjcyDphPk84WiUlXl\n2oAsF4QQEx18onNPZtdbXR0tdwO0jWyWBL7M7sBczr5c2NRkFsNPhaEZ6LihA/FDcVy29d8RiQzM\nuo1EolDQJ5NyR5IFg+byrahFzee5CJ6ZGc6MMQxIiAlvMZeLrgMB6/DwSVha6hUAbqTg63sa59/6\ng2m3EY3ahwV7vRTLrLuprKTsiMiQZTIUL7UDAZtNFo8YGxSP02cthlPLzCIGgyS8XC4SLi4XxTL9\npkSdlaC+3qy3moqu93dh5Gcj2Pj1jait7SxqG5Nr0BKJwlq1hcJef8x8YDHGMKA6GFU1uyjjcYqt\nNV42pmipV5FB4p7HMPQfQ1M+JB63L5EYBsXxhc8gt9HWRjv+RIKuZWbenILNJosnlaIMazRK36VS\nDL8G6G/f1kZLb21t8j8L0RggUBSzYWAyZ+84i3NfO4fVN61Gy7tait5GLmfPuFZWUix7WbfUY4qY\n5QeLMYYB7YwzGcqGCSPITGaGnfQULfUIBaFtvgzH33Qc0ScK012ZjD0L5nJRLLOeS/gotbYCGzbQ\ndSSy9GbJcXaheBIJcsK3jiqamJC79OYEjY30OQvq6yme7PU3/LNhdN3Uhdrra7H+S+vntI1AwJ5x\n1TS6cKcjs9iwGGMY0EiUUMjMkNXUUDw0dZLrYkv9xTWUcBjK1Vejbf/b4W3x4sifH0HqlD01IboC\nBcKJX2aXlVPLe07YTnB2oTg0rXAprxSTHUqNsMsQGIZppyGYeGoCHX/dQfNif7gVilroJTYT4bD9\n9xaPUxwOL/DFM8wCYTHGMDB3yuKgJrIM0y4hqirw0EPA1q1Aeztw333AQw/B2xjA9p9vh5E38MzL\nn0FuzFQpwaC9Bi0ep3ipDQpn24nywqksYqkFuMdjd/Rva6NYvI90TxqHrzsMT50Hl/7sUqih6bsm\nZ9qGVbgGgxSz0GcWGxZjDANyxx4dJfGiKHQ9OjqLa7aqUtpmzRrguusuttQHLwni0p9eivTpNI6+\n5ij0rH5xG9ZlStF1JdOZ24kDM9tOlBeRiGnyKzK6ui7XMiWXI6+68XFaAh0fp7gUgkxg/d7mY3kc\nvu4wtKSG7T/fDl/T/NqDxQQBQThsThRgmMWExRjDgJyyfT5z6VDXKa6unt/zVb2gCpv/bTPG94/j\nxN+fgHFhfdJawD8wYI9lUerlvXy+0MpJVfmANh2lzihVVpoeXaJbMBiU20EbjZLYbm8H1q6lbFIy\nKbcTeDr0nI6jrzuK5LEktj2wDaFt8x/oms/bB49XV1PM311msWExxjCgA1drK50pKwpdt7Yu7IDW\n+IZGtH+qHYM/GET3p7oxMmLPHqVSFI+MLPz1OwnbThSPE0u61mxoLleabGgsZi+uTyQojsXkbQOw\ni7sjR4DxcQOd7+rE2C/GcMm3LkHNS6Zrby4Ov98uvPJ5uvDcSGax4d0nw4C6qerracxLLAasXm0f\nKzRf1nx0DVInUzjziTPIJ/2YuNycxVJRQUs+/f3ApZfO8CR79tB1EUOKnSAYpCUqMQxZUUzPNMaO\n1QNMmPD6fHS7rMxVLkfPV1FhmowmkyTGZAmyfN5ulWEY9N2V2YUYjQLPPGPG4+PAyL/0wvh2P9o+\n3IbmG5unf3CRVFTYB4XrOl0qih8vyzAlgTNjDAMSGCIj5nabGbKFFr4rioJNd21C1QuroN5+AupR\n04L/scfkm3My5UUqZZqwisxYPC7XA8wJ01cnsqGnT9vNV5/49jjy3zwFz0vrsfbWtVK24fHYOyfF\nb54L+JnFhsUYw4B2xsEgZcVyOboOBuXspF1eF7Y9sA35pgA+d5sBBVQ/9pWvALfeOuMovbIkmaSM\nSE0N1aXV1FDMorKQbJZESyJBGRkxqkqm4/uCBN+ePbj8pptmvVswaF/KE40nMrt0h4aAW24RkYF/\n/n4YN4evQOI9m6G45mZhMR2TlyQjkcKlS4ZZDFiMMQzsSz0eD10nk/JqezzVHjz5VztwTK+AATqw\nZLPAqVP2pRkZlLpgPJ+npR3rNnSdD2hToSj0NxobIyE2NkaxIkdbADC7Zq3draKbVhZut73ZZGKC\nYpmZsUOHqE6MUJCCGx35CA4dlXe2Iv5WglL8rRhmPrAYYxg4Y9dw4rwPmUk/uVwOePZZedtwwoLA\nMEhUWDMxImbs5HJmDZfoSNQ0uZ+HqGu0estZb5dBMkndvwJdp1jm72NgAEin7F+iTEbB4KC8bSiK\nvUkgn6dYpjhmmPnABfwMA9opTz54qarcM+b16wGfX7FlGHweA+vWyTsSRKN00TSzuF5VKdvHBfbO\nIzpmARL3uk6xzJoxMbqrr4+eOxgEmprkFtcPDdmfT/xWhobkzT7d4o3DjwBSMDNhPh9w+eVynh+g\n34R1aTWZpKVKPpFgFhvOjDEMnClQvuYaYN06ERnwQ8OW3Diu8Y3O9LA5MTpKy0fWOYXptL2DbKEo\nCvkzWY1lRczYEZmwZJLqEK2xTHp6KNsWDNJ1T4/c54/H7SJGeJvJGnI/eP8g1t/+FLb4E8CFmkq/\nH9i2Ddi1S842APqOWv/2wSDF/N1lFhsWYwwDs3j/zBkSL2fOmEX8sqiqAt75ThEp+NsbdNz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Gbtz1ldbdbxTYumAddeC3R0wD8wANxwA4yXvhR93+zFwS0HMfq/o1j3+XW44sAViOyMIJejJXXB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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CKVhs1N-Ot2R",
        "colab_type": "text"
      },
      "source": [
        "## Epistemic and Total Uncertainty"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ZrwVQsM9TiUw"
      },
      "source": [
        "##### Copyright 2019 The TensorFlow Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "CpDUTVKYTowI",
        "colab": {}
      },
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ltPJCG6pAUoc"
      },
      "source": [
        "# TFP Probabilistic Layers: Regression\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_Layers_Regression.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_Layers_Regression.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "WRVR-tGTR31S"
      },
      "source": [
        "In this example we show how to fit regression models using TFP's \"probabilistic layers.\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "uiR4-VOt9NFX"
      },
      "source": [
        "### Dependencies & Prerequisites\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gcJrUr0pF6qM",
        "outputId": "7d6447ca-79c2-445f-b640-e92793367ac5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 139
        }
      },
      "source": [
        "#@title Install { display-mode: \"form\" }\n",
        "TF_Installation = 'TF2 Nightly (GPU)' #@param ['TF2 Nightly (GPU)', 'TF2 Stable (GPU)', 'TF1 Nightly (GPU)', 'TF1 Stable (GPU)','System']\n",
        "\n",
        "if TF_Installation == 'TF2 Nightly (GPU)':\n",
        "  !pip install -q --upgrade tf-nightly-gpu-2.0-preview\n",
        "  print('Installation of `tf-nightly-gpu-2.0-preview` complete.')\n",
        "elif TF_Installation == 'TF2 Stable (GPU)':\n",
        "  !pip install -q --upgrade tensorflow-gpu==2.0.0-alpha0\n",
        "  print('Installation of `tensorflow-gpu==2.0.0-alpha0` complete.')\n",
        "elif TF_Installation == 'TF1 Nightly (GPU)':\n",
        "  !pip install -q --upgrade tf-nightly-gpu\n",
        "  print('Installation of `tf-nightly-gpu` complete.')\n",
        "elif TF_Installation == 'TF1 Stable (GPU)':\n",
        "  !pip install -q --upgrade tensorflow-gpu\n",
        "  print('Installation of `tensorflow-gpu` complete.')\n",
        "elif TF_Installation == 'System':\n",
        "  pass\n",
        "else:\n",
        "  raise ValueError('Selection Error: Please select a valid '\n",
        "                   'installation option.')"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[K     |████████████████████████████████| 349.2MB 52kB/s \n",
            "\u001b[K     |████████████████████████████████| 3.1MB 38.7MB/s \n",
            "\u001b[K     |████████████████████████████████| 61kB 26.3MB/s \n",
            "\u001b[K     |████████████████████████████████| 430kB 59.4MB/s \n",
            "\u001b[?25h  Building wheel for wrapt (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[31mERROR: thinc 6.12.1 has requirement wrapt<1.11.0,>=1.10.0, but you'll have wrapt 1.11.1 which is incompatible.\u001b[0m\n",
            "Installation of `tf-nightly-gpu-2.0-preview` complete.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "9clSiUTiT3G1",
        "outputId": "a9ed9fdc-0a4e-48fd-a5eb-79b55bc4042a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "#@title Install { display-mode: \"form\" }\n",
        "TFP_Installation = \"Nightly\" #@param [\"Nightly\", \"Stable\", \"System\"]\n",
        "\n",
        "if TFP_Installation == \"Nightly\":\n",
        "  !pip install -q tfp-nightly\n",
        "  print(\"Installation of `tfp-nightly` complete.\")\n",
        "elif TFP_Installation == \"Stable\":\n",
        "  !pip install -q --upgrade tensorflow-probability\n",
        "  print(\"Installation of `tensorflow-probability` complete.\")\n",
        "elif TFP_Installation == \"System\":\n",
        "  pass\n",
        "else:\n",
        "  raise ValueError(\"Selection Error: Please select a valid \"\n",
        "                   \"installation option.\")"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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            "\u001b[?25hInstallation of `tfp-nightly` complete.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "kZ0MdF1j8WJf",
        "colab": {}
      },
      "source": [
        "#@title Import { display-mode: \"form\" }\n",
        "\n",
        "from __future__ import absolute_import\n",
        "from __future__ import division\n",
        "from __future__ import print_function\n",
        "\n",
        "from pprint import pprint\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "\n",
        "import tensorflow as tf\n",
        "from tensorflow.python import tf2\n",
        "if not tf2.enabled():\n",
        "  import tensorflow.compat.v2 as tf\n",
        "  tf.enable_v2_behavior()\n",
        "  assert tf2.enabled()\n",
        "\n",
        "import tensorflow_probability as tfp\n",
        "\n",
        "sns.reset_defaults()\n",
        "#sns.set_style('whitegrid')\n",
        "#sns.set_context('talk')\n",
        "sns.set_context(context='talk',font_scale=0.7)\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "tfd = tfp.distributions"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "7nnwjUdVoWN2"
      },
      "source": [
        "### Make things Fast!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "2CK9RaDcoYPG"
      },
      "source": [
        "Before we dive in, let's make sure we're using a GPU for this demo.  \n",
        "\n",
        "To do this, select \"Runtime\" -> \"Change runtime type\" -> \"Hardware accelerator\" -> \"GPU\".\n",
        "\n",
        "The following snippet will verify that we have access to a GPU."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "qP_4Xr8vpA42",
        "outputId": "77de58bf-824c-4de9-ff15-5cab6a2047ae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "if tf.test.gpu_device_name() != '/device:GPU:0':\n",
        "  print('WARNING: GPU device not found.')\n",
        "else:\n",
        "  print('SUCCESS: Found GPU: {}'.format(tf.test.gpu_device_name()))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "SUCCESS: Found GPU: /device:GPU:0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "FJRBc_S0ppfE"
      },
      "source": [
        "Note: if for some reason you cannot access a GPU, this colab will still work. (Training will just take longer.)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "xuqxMmryiduM"
      },
      "source": [
        "## Motivation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "RtBLNF-tin2L"
      },
      "source": [
        "Wouldn't it be great if we could use TFP to specify a probabilistic model then simply minimize the negative log-likelihood, i.e.,"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "3PFfNeJzifo7",
        "colab": {}
      },
      "source": [
        "negloglik = lambda y, rv_y: -rv_y.log_prob(y)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "cN4IP8n_jIvT"
      },
      "source": [
        "Well not only is it possible, but this colab shows how! (In context of linear regression problems.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "both",
        "colab_type": "code",
        "id": "5zCEYpzu7bDX",
        "colab": {}
      },
      "source": [
        "#@title Synthesize dataset.\n",
        "w0 = 0.125\n",
        "b0 = 5.\n",
        "x_range = [-20, 60]\n",
        "\n",
        "def load_dataset(n=150, n_tst=150):\n",
        "  np.random.seed(43)\n",
        "  def s(x):\n",
        "    g = (x - x_range[0]) / (x_range[1] - x_range[0])\n",
        "    return 3 * (0.25 + g**2.)\n",
        "  x = (x_range[1] - x_range[0]) * np.random.rand(n) + x_range[0]\n",
        "  eps = np.random.randn(n) * s(x)\n",
        "  y = (w0 * x * (1. + np.sin(x)) + b0) + eps\n",
        "  x = x[..., np.newaxis]\n",
        "  x_tst = np.linspace(*x_range, num=n_tst).astype(np.float32)\n",
        "  x_tst = x_tst[..., np.newaxis]\n",
        "  return y, x, x_tst\n",
        "\n",
        "y, x, x_tst = load_dataset()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "N8Shtn_e99XC"
      },
      "source": [
        "### Case 1: No Uncertainty"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "RxKJ_RPI0K4N",
        "outputId": "40645ac0-5571-41d2-8b33-fe76c66da0cf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# Build model.\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1),\n",
        "  tfp.layers.DistributionLambda(lambda t: tfd.Normal(loc=t, scale=1)),\n",
        "])\n",
        "\n",
        "# Do inference.\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01), loss=negloglik)\n",
        "model.fit(x, y, epochs=1000, verbose=False);\n",
        "\n",
        "# Profit.\n",
        "[print(np.squeeze(w.numpy())) for w in model.weights];\n",
        "yhat = model(x_tst)\n",
        "assert isinstance(yhat, tfd.Distribution)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.13275796\n",
            "5.1289654\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "1AE9ElaKI6Er",
        "outputId": "fa7f95d6-ef76-479b-bd06-8a2d8f32dad5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 147
        }
      },
      "source": [
        "#@title Figure 1: No uncertainty.\n",
        "w = np.squeeze(model.layers[-2].kernel.numpy())\n",
        "b = np.squeeze(model.layers[-2].bias.numpy())\n",
        "\n",
        "plt.figure(figsize=[6, 1.5])  # inches\n",
        "#plt.figure(figsize=[8, 5])  # inches\n",
        "plt.plot(x, y, 'b.', label='observed');\n",
        "plt.plot(x_tst, yhat.mean(),'r', label='mean', linewidth=4);\n",
        "plt.ylim(-0.,17);\n",
        "plt.yticks(np.linspace(0, 15, 4)[1:]);\n",
        "plt.xticks(np.linspace(*x_range, num=9));\n",
        "\n",
        "ax=plt.gca();\n",
        "ax.xaxis.set_ticks_position('bottom')\n",
        "ax.yaxis.set_ticks_position('left')\n",
        "ax.spines['left'].set_position(('data', 0))\n",
        "ax.spines['top'].set_visible(False)\n",
        "ax.spines['right'].set_visible(False)\n",
        "#ax.spines['left'].set_smart_bounds(True)\n",
        "#ax.spines['bottom'].set_smart_bounds(True)\n",
        "plt.legend(loc='center left', fancybox=True, framealpha=0., bbox_to_anchor=(1.05, 0.5))\n",
        "\n",
        "plt.savefig('/tmp/fig1.png', bbox_inches='tight', dpi=300)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8chkiJX1WU1LSGbAVJdqdecoplTQ3Qyi0rddFxOPlRnZzzTU2ACUXukczwQCa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\niqIois+o2CqKoiiKz/x/QMp3YT7CGhQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x108 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "91kwRqs4O5Yv"
      },
      "source": [
        "### Case 2: Aleatoric Uncertainty"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "TLZ97_V4PP-f",
        "outputId": "9ac2cc59-3f31-4216-c58c-ced3cb213bcb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# Build model.\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1 + 1),\n",
        "  tfp.layers.DistributionLambda(\n",
        "      lambda t: tfd.Normal(loc=t[..., :1],\n",
        "                           scale=1e-3 + tf.math.softplus(0.05 * t[...,1:]))),\n",
        "])\n",
        "\n",
        "# Do inference.\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01), loss=negloglik)\n",
        "model.fit(x, y, epochs=1000, verbose=False);\n",
        "\n",
        "# Profit.\n",
        "[print(np.squeeze(w.numpy())) for w in model.weights];\n",
        "yhat = model(x_tst)\n",
        "assert isinstance(yhat, tfd.Distribution)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.13226233 0.41329   ]\n",
            "[5.1153    1.2915019]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "JSSWw2-FPCiG",
        "outputId": "4b211095-ecc8-480a-c1f6-95df60eadee0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 147
        }
      },
      "source": [
        "#@title Figure 2: Aleatoric Uncertainty\n",
        "plt.figure(figsize=[6, 1.5])  # inches\n",
        "plt.plot(x, y, 'b.', label='observed');\n",
        "\n",
        "m = yhat.mean()\n",
        "s = yhat.stddev()\n",
        "\n",
        "plt.plot(x_tst, m, 'r', linewidth=4, label='mean');\n",
        "plt.plot(x_tst, m + 2 * s, 'g', linewidth=2, label=r'mean + 2 stddev');\n",
        "plt.plot(x_tst, m - 2 * s, 'g', linewidth=2, label=r'mean - 2 stddev');\n",
        "\n",
        "plt.ylim(-0.,17);\n",
        "plt.yticks(np.linspace(0, 15, 4)[1:]);\n",
        "plt.xticks(np.linspace(*x_range, num=9));\n",
        "\n",
        "ax=plt.gca();\n",
        "ax.xaxis.set_ticks_position('bottom')\n",
        "ax.yaxis.set_ticks_position('left')\n",
        "ax.spines['left'].set_position(('data', 0))\n",
        "ax.spines['top'].set_visible(False)\n",
        "ax.spines['right'].set_visible(False)\n",
        "#ax.spines['left'].set_smart_bounds(True)\n",
        "#ax.spines['bottom'].set_smart_bounds(True)\n",
        "plt.legend(loc='center left', fancybox=True, framealpha=0., bbox_to_anchor=(1.05, 0.5))\n",
        "\n",
        "plt.savefig('/tmp/fig2.png', bbox_inches='tight', dpi=300)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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u5tEbG1gg9Zw8WM/HCxqYsb/Bt770BBhMSSf2VCMGDIZwY8INUwgTbog+/NcNeHCViyUf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\ny0kEAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x108 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "xEvTd7ZJYvDx"
      },
      "source": [
        "### Case 3: Epistemic Uncertainty"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "both",
        "colab_type": "code",
        "id": "VwzbWw3_CQ2z",
        "colab": {}
      },
      "source": [
        "# Specify the surrogate posterior over `keras.layers.Dense` `kernel` and `bias`.\n",
        "def posterior_mean_field(kernel_size, bias_size=0, dtype=None):\n",
        "  n = kernel_size + bias_size\n",
        "  c = np.log(np.expm1(1.))\n",
        "  return tf.keras.Sequential([\n",
        "      tfp.layers.VariableLayer(2 * n, dtype=dtype),\n",
        "      tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
        "          tfd.Normal(loc=t[..., :n],\n",
        "                     scale=1e-5 + tf.nn.softplus(c + t[..., n:])),\n",
        "          reinterpreted_batch_ndims=1)),\n",
        "  ])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "both",
        "colab_type": "code",
        "id": "aAQhyK9Y_lm1",
        "colab": {}
      },
      "source": [
        "# Specify the surrogate posterior over `keras.layers.Dense` `kernel` and `bias`.\n",
        "def prior_trainable(kernel_size, bias_size=0, dtype=None):\n",
        "  n = kernel_size + bias_size\n",
        "  return tf.keras.Sequential([\n",
        "      tfp.layers.VariableLayer(n, dtype=dtype),\n",
        "      tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
        "          tfd.Normal(loc=t, scale=1),\n",
        "          reinterpreted_batch_ndims=1)),\n",
        "  ])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "XI7ZCFzSnrWN",
        "outputId": "cbef410d-8408-4496-f868-2ee400ea76aa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "# Build model.\n",
        "model = tf.keras.Sequential([\n",
        "  tfp.layers.DenseVariational(1, posterior_mean_field, prior_trainable),\n",
        "  tfp.layers.DistributionLambda(lambda t: tfd.Normal(loc=t, scale=1)),\n",
        "])\n",
        "\n",
        "# Do inference.\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01), loss=negloglik)\n",
        "model.fit(x, y, epochs=1000, verbose=False);\n",
        "\n",
        "# Profit.\n",
        "[print(np.squeeze(w.numpy())) for w in model.weights];\n",
        "yhat = model(x_tst)\n",
        "assert isinstance(yhat, tfd.Distribution)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 0.1374202  5.1056857 -3.7132006 -0.5256554]\n",
            "[0.1592448 5.12206  ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "Y4Bypix9UvTO",
        "outputId": "e3202845-5cda-417c-c718-2a4bf579a381",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 147
        }
      },
      "source": [
        "#@title Figure 3: Epistemic Uncertainty\n",
        "plt.figure(figsize=[6, 1.5])  # inches\n",
        "plt.clf();\n",
        "plt.plot(x, y, 'b.', label='observed');\n",
        "\n",
        "yhats = [model(x_tst) for _ in range(100)]\n",
        "avgm = np.zeros_like(x_tst[..., 0])\n",
        "for i, yhat in enumerate(yhats):\n",
        "  m = np.squeeze(yhat.mean())\n",
        "  s = np.squeeze(yhat.stddev())\n",
        "  if i < 25:\n",
        "    plt.plot(x_tst, m, 'r', label='ensemble means' if i == 0 else None, linewidth=0.5)\n",
        "  avgm += m\n",
        "plt.plot(x_tst, avgm/len(yhats), 'r', label='overall mean', linewidth=4)\n",
        "\n",
        "plt.ylim(-0.,17);\n",
        "plt.yticks(np.linspace(0, 15, 4)[1:]);\n",
        "plt.xticks(np.linspace(*x_range, num=9));\n",
        "\n",
        "ax=plt.gca();\n",
        "ax.xaxis.set_ticks_position('bottom')\n",
        "ax.yaxis.set_ticks_position('left')\n",
        "ax.spines['left'].set_position(('data', 0))\n",
        "ax.spines['top'].set_visible(False)\n",
        "ax.spines['right'].set_visible(False)\n",
        "#ax.spines['left'].set_smart_bounds(True)\n",
        "#ax.spines['bottom'].set_smart_bounds(True)\n",
        "plt.legend(loc='center left', fancybox=True, framealpha=0., bbox_to_anchor=(1.05, 0.5))\n",
        "\n",
        "plt.savefig('/tmp/fig3.png', bbox_inches='tight', dpi=300)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ooIrJLPq+4rIrR69Bl8GhRyl1HfB5rfW5Q7yvkb4Qo148aqxjCISDjNPppDu+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\n",
            "text/plain": [
              "<Figure size 432x108 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "H_3At7s2fel0"
      },
      "source": [
        "### Case 4: Aleatoric & Epistemic Uncertainty"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "GcRC3uwcft6l",
        "outputId": "62b321a9-2ab3-4e18-e164-e10f0ed6f871",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "source": [
        "# Build model.\n",
        "model = tf.keras.Sequential([\n",
        "  tfp.layers.DenseVariational(1 + 1, posterior_mean_field, prior_trainable),\n",
        "  tfp.layers.DistributionLambda(\n",
        "      lambda t: tfd.Normal(loc=t[..., :1],\n",
        "                           scale=1e-3 + tf.math.softplus(0.01 * t[...,1:]))),\n",
        "])\n",
        "\n",
        "# Do inference.\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01), loss=negloglik)\n",
        "model.fit(x, y, epochs=1000, verbose=False);\n",
        "\n",
        "# Profit.\n",
        "[print(np.squeeze(w.numpy())) for w in model.weights];\n",
        "yhat = model(x_tst)\n",
        "assert isinstance(yhat, tfd.Distribution)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 0.13091448  2.8183267   5.1185093   2.954348   -3.344546   -0.684905\n",
            " -0.5135757   0.05770317]\n",
            "[0.13267924 2.7312424  5.191225   2.9794762 ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "cWhfYYzcgFak",
        "outputId": "99edee12-f4f1-409c-de4e-424dac645d0b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 147
        }
      },
      "source": [
        "#@title Figure 4: Both Aleatoric & Epistemic Uncertainty\n",
        "plt.figure(figsize=[6, 1.5])  # inches\n",
        "plt.plot(x, y, 'b.', label='observed');\n",
        "\n",
        "yhats = [model(x_tst) for _ in range(100)]\n",
        "avgm = np.zeros_like(x_tst[..., 0])\n",
        "for i, yhat in enumerate(yhats):\n",
        "  m = np.squeeze(yhat.mean())\n",
        "  s = np.squeeze(yhat.stddev())\n",
        "  if i < 15:\n",
        "    plt.plot(x_tst, m, 'r', label='ensemble means' if i == 0 else None, linewidth=1.)\n",
        "    plt.plot(x_tst, m + 2 * s, 'g', linewidth=0.5, label='ensemble means + 2 ensemble stdev' if i == 0 else None);\n",
        "    plt.plot(x_tst, m - 2 * s, 'g', linewidth=0.5, label='ensemble means - 2 ensemble stdev' if i == 0 else None);\n",
        "  avgm += m\n",
        "plt.plot(x_tst, avgm/len(yhats), 'r', label='overall mean', linewidth=4)\n",
        "\n",
        "plt.ylim(-0.,17);\n",
        "plt.yticks(np.linspace(0, 15, 4)[1:]);\n",
        "plt.xticks(np.linspace(*x_range, num=9));\n",
        "\n",
        "ax=plt.gca();\n",
        "ax.xaxis.set_ticks_position('bottom')\n",
        "ax.yaxis.set_ticks_position('left')\n",
        "ax.spines['left'].set_position(('data', 0))\n",
        "ax.spines['top'].set_visible(False)\n",
        "ax.spines['right'].set_visible(False)\n",
        "#ax.spines['left'].set_smart_bounds(True)\n",
        "#ax.spines['bottom'].set_smart_bounds(True)\n",
        "plt.legend(loc='center left', fancybox=True, framealpha=0., bbox_to_anchor=(1.05, 0.5))\n",
        "\n",
        "plt.savefig('/tmp/fig4.png', bbox_inches='tight', dpi=300)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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U0iOEKEYRhFlSyjEhRAYwBCSgWP3edm/eYi8ngRVSys64APy9lPJH8XNPAo1S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\ni8VisZxi/H8o/RXaKjbF3gAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x108 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}