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udlbook/Notebooks/Chap05/5_2_Binary_Cross_Entropy_Loss.ipynb
2023-12-24 10:12:00 -05:00

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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyNUzNhNIdP8kIZAUo43Yz99",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/github/udlbook/udlbook/blob/main/Notebooks/Chap05/5_2_Binary_Cross_Entropy_Loss.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"# **Notebook 5.2 Binary Cross-Entropy Loss**\n",
"\n",
"This notebook investigates the binary cross-entropy loss. It follows from applying the formula in section 5.2 to a loss function based on the Bernoulli distribution.\n",
"\n",
"Work through the cells below, running each cell in turn. In various places you will see the words \"TO DO\". Follow the instructions at these places and make predictions about what is going to happen or write code to complete the functions.\n",
"\n",
"Contact me at udlbookmail@gmail.com if you find any mistakes or have any suggestions."
],
"metadata": {
"id": "jSlFkICHwHQF"
}
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "PYMZ1x-Pv1ht"
},
"outputs": [],
"source": [
"# Imports math library\n",
"import numpy as np\n",
"# Imports plotting library\n",
"import matplotlib.pyplot as plt\n",
"# Import math Library\n",
"import math"
]
},
{
"cell_type": "code",
"source": [
"# Define the Rectified Linear Unit (ReLU) function\n",
"def ReLU(preactivation):\n",
" activation = preactivation.clip(0.0)\n",
" return activation\n",
"\n",
"# Define a shallow neural network\n",
"def shallow_nn(x, beta_0, omega_0, beta_1, omaga_1):\n",
" # Make sure that input data is (1 x n_data) array\n",
" n_data = x.size\n",
" x = np.reshape(x,(1,n_data))\n",
"\n",
" # This runs the network for ALL of the inputs, x at once so we can draw graph\n",
" h1 = ReLU(np.matmul(beta_0,np.ones((1,n_data))) + np.matmul(omega_0,x))\n",
" model_out = np.matmul(beta_1,np.ones((1,n_data))) + np.matmul(omega_1,h1)\n",
" return model_out"
],
"metadata": {
"id": "Fv7SZR3tv7mV"
},
"execution_count": 2,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Get parameters for model -- we can call this function to easily reset them\n",
"def get_parameters():\n",
" # And we'll create a network that approximately fits it\n",
" beta_0 = np.zeros((3,1)); # formerly theta_x0\n",
" omega_0 = np.zeros((3,1)); # formerly theta_x1\n",
" beta_1 = np.zeros((1,1)); # formerly phi_0\n",
" omega_1 = np.zeros((1,3)); # formerly phi_x\n",
"\n",
" beta_0[0,0] = 0.3; beta_0[1,0] = -1.0; beta_0[2,0] = -0.5\n",
" omega_0[0,0] = -1.0; omega_0[1,0] = 1.8; omega_0[2,0] = 0.65\n",
" beta_1[0,0] = 2.6;\n",
" omega_1[0,0] = -24.0; omega_1[0,1] = -8.0; omega_1[0,2] = 50.0\n",
"\n",
" return beta_0, omega_0, beta_1, omega_1"
],
"metadata": {
"id": "pUT9Ain_HRim"
},
"execution_count": 3,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Utility function for plotting data\n",
"def plot_binary_classification(x_model, out_model, lambda_model, x_data = None, y_data = None, title= None):\n",
" # Make sure model data are 1D arrays\n",
" x_model = np.squeeze(x_model)\n",
" out_model = np.squeeze(out_model)\n",
" lambda_model = np.squeeze(lambda_model)\n",
"\n",
" fig, ax = plt.subplots(1,2)\n",
" fig.set_size_inches(7.0, 3.5)\n",
" fig.tight_layout(pad=3.0)\n",
" ax[0].plot(x_model,out_model)\n",
" ax[0].set_xlabel('Input, $x$'); ax[0].set_ylabel('Model output')\n",
" ax[0].set_xlim([0,1]);ax[0].set_ylim([-4,4])\n",
" if title is not None:\n",
" ax[0].set_title(title)\n",
" ax[1].plot(x_model,lambda_model)\n",
" ax[1].set_xlabel('Input, $x$'); ax[1].set_ylabel('$\\lambda$ or Pr(y=1|x)')\n",
" ax[1].set_xlim([0,1]);ax[1].set_ylim([-0.05,1.05])\n",
" if title is not None:\n",
" ax[1].set_title(title)\n",
" if x_data is not None:\n",
" ax[1].plot(x_data, y_data, 'ko')\n",
" plt.show()"
],
"metadata": {
"id": "NRR67ri_1TzN"
},
"execution_count": 4,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"# Binary classification\n",
"\n",
"In binary classification tasks, the network predicts the probability of the output belonging to class 1. Since probabilities must lie in [0,1] and the network can output arbitrary values, we map the network through a sigmoid function that ensures the range is valid."
],
"metadata": {
"id": "PsgLZwsPxauP"
}
},
{
"cell_type": "code",
"source": [
"# Sigmoid function that maps [-infty,infty] to [0,1]\n",
"def sigmoid(model_out):\n",
" # TODO -- implement the logistic sigmoid function from equation 5.18\n",
" # Replace this line:\n",
" sig_model_out = np.zeros_like(model_out)\n",
"\n",
" return sig_model_out"
],
"metadata": {
"id": "uFb8h-9IXnIe"
},
"execution_count": 5,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Let's create some 1D training data\n",
"x_train = np.array([0.09291784,0.46809093,0.93089486,0.67612654,0.73441752,0.86847339,\\\n",
" 0.49873225,0.51083168,0.18343972,0.99380898,0.27840809,0.38028817,\\\n",
" 0.12055708,0.56715537,0.92005746,0.77072270,0.85278176,0.05315950,\\\n",
" 0.87168699,0.58858043])\n",
"y_train = np.array([0,1,1,0,0,1,\\\n",
" 1,0,0,1,0,1,\\\n",
" 0,1,1,0,1,0, \\\n",
" 1,1])\n",
"\n",
"# Get parameters for the model\n",
"beta_0, omega_0, beta_1, omega_1 = get_parameters()\n",
"\n",
"# Define a range of input values\n",
"x_model = np.arange(0,1,0.01)\n",
"# Run the model to get values to plot and plot it.\n",
"model_out= shallow_nn(x_model, beta_0, omega_0, beta_1, omega_1)\n",
"lambda_model = sigmoid(model_out)\n",
"plot_binary_classification(x_model, model_out, lambda_model, x_train, y_train)\n"
],
"metadata": {
"id": "VWzNOt1swFVd",
"outputId": "a2637ffc-c9b0-4161-84e0-e15ce1c5d852",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 326
}
},
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 700x350 with 2 Axes>"
],
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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"The left is model output and the right is the model output after the sigmoid has been applied, so it now lies in the range [0,1] and represents the probability, that y=1. The black dots show the training data. We'll compute the the likelihood and the negative log likelihood."
],
"metadata": {
"id": "MvVX6tl9AEXF"
}
},
{
"cell_type": "code",
"source": [
"# Return probability under Bernoulli distribution for input x\n",
"def bernoulli_distribution(y, lambda_param):\n",
" # TODO-- write in the equation for the Bernoulli distribution\n",
" # Equation 5.17 from the notes (you will need np.power)\n",
" # Replace the line below\n",
" prob = np.zeros_like(y)\n",
"\n",
" return prob"
],
"metadata": {
"id": "YaLdRlEX0FkU"
},
"execution_count": 7,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Let's double check we get the right answer before proceeding\n",
"print(\"Correct answer = %3.3f, Your answer = %3.3f\"%(0.8,bernoulli_distribution(0,0.2)))\n",
"print(\"Correct answer = %3.3f, Your answer = %3.3f\"%(0.2,bernoulli_distribution(1,0.2)))"
],
"metadata": {
"id": "4TSL14dqHHbV",
"outputId": "b1d634b4-3dfd-4d70-9911-4692557f500e",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Correct answer = 0.800, Your answer = 0.000\n",
"Correct answer = 0.200, Your answer = 0.000\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"Now let's compute the likelihood using this function"
],
"metadata": {
"id": "R5z_0dzQMF35"
}
},
{
"cell_type": "code",
"source": [
"# Return the likelihood of all of the data under the model\n",
"def compute_likelihood(y_train, lambda_param):\n",
" # TODO -- compute the likelihood of the data -- the product of the Bernoulli probabilities for each data point\n",
" # Top line of equation 5.3 in the notes\n",
" # You will need np.prod() and the bernoulli_distribution function you used above\n",
" # Replace the line below\n",
" likelihood = 0\n",
"\n",
" return likelihood"
],
"metadata": {
"id": "zpS7o6liCx7f"
},
"execution_count": 9,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Let's test this\n",
"beta_0, omega_0, beta_1, omega_1 = get_parameters()\n",
"# Use our neural network to predict the mean of the Gaussian\n",
"model_out = shallow_nn(x_train, beta_0, omega_0, beta_1, omega_1)\n",
"lambda_train = sigmoid(model_out)\n",
"# Compute the likelihood\n",
"likelihood = compute_likelihood(y_train, lambda_train)\n",
"# Let's double check we get the right answer before proceeding\n",
"print(\"Correct answer = %9.9f, Your answer = %9.9f\"%(0.000070237,likelihood))"
],
"metadata": {
"id": "1hQxBLoVNlr2",
"outputId": "77086bf9-443f-497e-fa76-85eb53fec814",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Correct answer = 0.000070237, Your answer = 0.000000000\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"You can see that this gives a very small answer, even for this small 1D dataset, and with the model fitting quite well. This is because it is the product of several probabilities, which are all quite small themselves.\n",
"This will get out of hand pretty quickly with real datasets -- the likelihood will get so small that we can't represent it with normal finite-precision math\n",
"\n",
"This is why we use negative log likelihood"
],
"metadata": {
"id": "HzphKgPfOvlk"
}
},
{
"cell_type": "code",
"source": [
"# Return the negative log likelihood of the data under the model\n",
"def compute_negative_log_likelihood(y_train, lambda_param):\n",
" # TODO -- compute the likelihood of the data -- don't use the likelihood function above -- compute the negative sum of the log probabilities\n",
" # You will need np.sum(), np.log()\n",
" # Replace the line below\n",
" nll = 0\n",
"\n",
" return nll"
],
"metadata": {
"id": "dsT0CWiKBmTV"
},
"execution_count": 11,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# Let's test this\n",
"beta_0, omega_0, beta_1, omega_1 = get_parameters()\n",
"# Use our neural network to predict the mean of the Gaussian\n",
"model_out = shallow_nn(x_train, beta_0, omega_0, beta_1, omega_1)\n",
"# Pass through the sigmoid function\n",
"lambda_train = sigmoid(model_out)\n",
"# Compute the log likelihood\n",
"nll = compute_negative_log_likelihood(y_train, lambda_train)\n",
"# Let's double check we get the right answer before proceeding\n",
"print(\"Correct answer = %9.9f, Your answer = %9.9f\"%(9.563639387,nll))"
],
"metadata": {
"id": "nVxUXg9rQmwI",
"outputId": "1f709c1d-825d-425a-93d9-0548520302fd",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 12,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Correct answer = 9.563639387, Your answer = 0.000000000\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"Now let's investigate finding the maximum likelihood / minimum negative log likelihood solution. For simplicity, we'll assume that all the parameters are fixed except one and look at how the likelihood and log likelihood change as we manipulate the last parameter. We'll start with overall y_offset, beta_1 (formerly phi_0)"
],
"metadata": {
"id": "OgcRojvPWh4V"
}
},
{
"cell_type": "code",
"source": [
"# Define a range of values for the parameter\n",
"beta_1_vals = np.arange(-2,6.0,0.1)\n",
"# Create some arrays to store the likelihoods, negative log likelihoods\n",
"likelihoods = np.zeros_like(beta_1_vals)\n",
"nlls = np.zeros_like(beta_1_vals)\n",
"\n",
"# Initialise the parameters\n",
"beta_0, omega_0, beta_1, omega_1 = get_parameters()\n",
"for count in range(len(beta_1_vals)):\n",
" # Set the value for the parameter\n",
" beta_1[0,0] = beta_1_vals[count]\n",
" # Run the network with new parameters\n",
" model_out = shallow_nn(x_train, beta_0, omega_0, beta_1, omega_1)\n",
" lambda_train = sigmoid(model_out)\n",
" # Compute and store the three values\n",
" likelihoods[count] = compute_likelihood(y_train,lambda_train)\n",
" nlls[count] = compute_negative_log_likelihood(y_train, lambda_train)\n",
" # Draw the model for every 20th parameter setting\n",
" if count % 20 == 0:\n",
" # Run the model to get values to plot and plot it.\n",
" model_out = shallow_nn(x_model, beta_0, omega_0, beta_1, omega_1)\n",
" lambda_model = sigmoid(model_out)\n",
" plot_binary_classification(x_model, model_out, lambda_model, x_train, y_train, title=\"beta_1[0]=%3.3f\"%(beta_1[0,0]))\n"
],
"metadata": {
"id": "pFKtDaAeVU4U",
"outputId": "88ac78bc-0f2e-4640-f7d4-3bc2386d4b72",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"execution_count": 13,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 700x350 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 700x350 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 700x350 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 700x350 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# Now let's plot the likelihood, negative log likelihood, and least squares as a function the value of the offset beta1\n",
"fig, ax = plt.subplots()\n",
"fig.tight_layout(pad=5.0)\n",
"likelihood_color = 'tab:red'\n",
"nll_color = 'tab:blue'\n",
"\n",
"\n",
"ax.set_xlabel('beta_1[0, 0]')\n",
"ax.set_ylabel('likelihood', color = likelihood_color)\n",
"ax.plot(beta_1_vals, likelihoods, color = likelihood_color)\n",
"ax.tick_params(axis='y', labelcolor=likelihood_color)\n",
"\n",
"ax1 = ax.twinx()\n",
"ax1.plot(beta_1_vals, nlls, color = nll_color)\n",
"ax1.set_ylabel('negative log likelihood', color = nll_color)\n",
"ax1.tick_params(axis='y', labelcolor = nll_color)\n",
"\n",
"plt.axvline(x = beta_1_vals[np.argmax(likelihoods)], linestyle='dotted')\n",
"\n",
"plt.show()"
],
"metadata": {
"id": "UHXeTa9MagO6",
"outputId": "4a3b5dc5-0dc9-41a8-b101-455474ce0cc3",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 392
}
},
"execution_count": 14,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
],
"image/png": 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hwVb6toxh4jltiYsIrte6E6JCmDuuLwu35rFtfxEALRuH07dVTJ36DahEUDBvHvunPUrM2LE0++B9gtu0IfOGMTgPHKi2/ZEVK8m6406iLruUZh9+QNiggey+5VZKN28GwF1aSmlGBjH/vJlm779P0jMzKNuxkz3//OdfeVmVmE0mzkqL46y0OC1jJSIiJ61PV+/loc82MH5QK+be2pe0JuEMf3UpeUVl1bZfviufcXNWMqxHMvPG9WVw+zhufGMZm/ZVzJNWUu5ifVYBtw5syWfj+vLCdd3ZllfMDbOWnZD6TSYT/VrFMrJPM0b2aVbnwAZgMoy6PBL319pxxTBCOnQg/v77ADDcbraecSYNr72WmBvHVGm/5/bbMY6UkPziC7/3MWwYwW3b0eSBKdWeo2TtWnZefgUtv1lAUELNZjLes2cPycnJ7N69m6SkpNpfmIiIyN+YN9+TFz23iM5JkTx4UQcA3G6DXtMWMKJ3Kv88o+r6nWPfXkGJw8VrI0/x7Bv63CLSEiJ45OKO1Z5j9e5DXPTcIhbdNYDEqBAvruzYlmw/wMs/bGdrbsVIW6vGYdx4egt6NmvkdZ8BM9JmOByUrl9Pg969PPtMZjMNevWiZNWqao8pWbW6UnuAsD59j9kewF1YCCYT5oiIY7YpKyujoKDA81NYWFiraxERETkZFRYWVvr+LCurftTM4XSzLuswfVr+PjplNpvo0zKGFbsOVXvMyl0HK7UHOL11LCt2HTx2PaVOTCaICK7fp8U+XLmHa19ZSrDNwsjeqYzsnYrdauGaV5bw8aosr/sNmNDmPHgIXC4s0ZXfurDEROPMy6v+mLw8LNExNW7vLitj/3+eIOK887CEhR2zlvT0dCIjIz0/aWlptbsYERGRk1BaWlql78/09PRq2x084sDlNog5auWA2DA7uce4PZpbVEZMmO2o9rZj3k4tLXcx7YsNXNg5gfBfVy2oL89+s5W7zmnLc1d3Y1SfZozq04znrunGxLPbMmPBFq/7DZjQdqIZ5eVk3XY7BgbxUyYft+2kSZM4fPiw5ycjI6Pe6ihxuOgz7Rv6TPuGEoer3voVERHxtYyMjErfn5MmTfJJHeUuN7e8vQLDgIeGdqj3/nfnlzCoXVyV/YPaxbH7YInX/QbM26PWhlFgseA66qUDV94BrDHVP9xnjYnBdSDvT9sb5eXsuf12yvfupenrM487ygZgt9ux239P/wUFBbW4kuMzMMg6VOLZFhER+bsIDw8n4jiPH/2mYagNi9lUZZQst6iM2GOs2xkbZievyHFUe0eV0bpyl5uxb61gz8ES3hlzWr2PsgE0iQpm0bY8UmMaVNq/cGseCZHev6kaMCNtJpuN4PbtKV68xLPPcLspXrKEkC5dqj0mpEvnSu0Bin/6qVJ7T2DbtYumM1/D2rDhiSi/xuxWCx+P7cPHY/tg1zJWIiJyErJZzXRIjOSnrb8PvLjdBj9tPUC3lKhqj+ma0rBSe4CFW3LplvL79/pvgW3ngWLeuuFUGjawHd1NvbihX3Me+CSDez5cywcr9vDBij3c/eFaHvwsgzGnN/e634AZaQOIHjmCvXdNIrhDB0I6dSR/1mzcJSVEXXIxAHsnTsTaOI7Gd0wAoNF1w9k1fDgHXptJ2Bn9KZg7j5L164l/8AHg18A2/jZKMzJIfuF5cLlw5uYCYImMxGQ7MX/M47GYTXQ+zhw0IiIiJ4Mb+jbjjvdW0zEpii7Jkby6cCdHHE4u754MwIR3VxEXGczEs9sCMLpPKsNeXMLLP2znzLaN+XT1XtZmHSb9koq5XMtdbm5+cwXr9x7m1RGn4DIM9hdWrFgQFWLDZq2/cazrTkshNszOKz9uZ+7abABaxobx7FVdGdw+3ut+Ayq0RZx7Ls78g+Q+MwNXbh72du1o+vJLntud5XuzwfT7P/TQbl1J/M/j5D49ndynnsKWmkLys88Q3Lp1Rfuc/RR98w0AO4ZeXOlcTWfNosGpPf+iKxMREZE/uqBzAvnFDp6av5ncwjLaJUQwa3RPYsMrbndmHSrB9If5TLunNGL6lV154qtNPP7lJlJjQnnpuh60ia9Yz3vf4VK+3pADwLkzfqx0rnfGnEavOiwvVZ2zO8RzdgfvA1p1AmqeNn9Vn/O0OV1uPltTkcrP79QEq1ZEEBGRAHeyzmfqcLo5UFyG+6ik5e2ccAE10nYycLjc3PbuKgAGt49TaBMREQkwO/KK+ff/VrP8qDniDMAEbE8/z6t+Fdr8jNlkou+vkwNqGSsREZHAc+d7q7GYTbw68hQah9sxUT/f5wptfiY4yMKbN5zq6zJERETESxl7C/j01r60bHz8KcRqS/feREREROpRq7gwDh5x/HnDWlJoExEREamjwtJyz89dZ7clfd4GFm87wMFiR6XPCkvLvT6Hbo/6mRKHiwufXQjAJ7f0JcSmCXZFRET8XacHvqr05JoBXPNK5Qn+9SLC34yBwZb9RZ5tERER8X/vjDnthJ9Doc3P2K0Wzx9ey1iJiIgEhtOa1+/kvNVRaPMzFrOp3mdlFhERkRNrQ3YBbeLCMZtNbMguOG7bdk0ivDqHQpuIiIhIHZ0740d+uWcQMWF2zp3xIyao9iEnPdP2N+J0uVmwcT8AA9s21ooIIiIiAeDHf59JdAObZ/tEUGjzMw6Xm3+8sRyAjAeHKLSJiIgEgKSGodVu1yeFNj9jNpnontLQsy0iIiL+b35GTo3bnpUW59U5FNr8THCQhfdv7u3rMkRERKQWbnxjWY3a6Zk2ERERER/a4WUQqw09MCUiIiJygpSWu+qtL4U2P1NaXrGM1YXPLqzXP7SIiIj8NVxugxkLtnDqI1/TfvKXZB44AsATX23i3V8yve5Xoc3PuA2DNXsOs2bPYdyGlrESEREJNM9+s5X/Ld/DpHPaEWT5/aXC1nHhzPllt9f96pk2P2OzmHltZA/PtoiIiASWD1buIf2SjvRpGcM9H6717G/XJIJtv64v7g2FNj9jtZgZ0Na7V4FFRETE9/YdLiUluupcbYZh4HR7fxdNQzkiIiIi9ahVXBi/7Myvsn/e2n20T/Bu3VGoxUjbpp6nQg0ne22zdInXBZ3sXG6Dn7blAdC7RQwWsybYFRERCSTjBrTijvdWs+9wGW4DvlifzfbcYj5YkcWrvz4C5Y0ah7a4SZM8265Dh8h74QXC+vQhpEsXAEpWraJo0SJibr7J62IEypwurnv1Z6BiGatQm+5gi4iIBJLB7eN5NdTGjAVbCLVZeHL+ZjokRPLKiB70axXrdb81TgRRFw/1bO+5dRyxt95Ko2uv+b3B8OvIf/MtihcvJnrkSK8LOtmZTSbaNYnwbIuIiEhgyT5cQs9mjXjzhlOrfLYi8yDdmjb0ql+vnmkrWrSIsH59q+wP69eX4sWLvSpEKgQHWfh8fD8+H9+P4CCLr8sRERGRWrru1Z85dMRRZf+ynfmMeO1nr/v1KrRZoiIpXPBNlf2FC77BEhXpdTEiIiIiga5rchTXvfozRWVOz76l2w8wauYvjB/Yyut+vXpgKvaWW8m+7z6O/PwzIZ07AVCyeg1FCxfS5MEHvS5GREREJNA9emknbn5rOde//guzr+/J8l0HGTNrGXcMbsPovs287tdkGN5Nu1+yejX5b7xJ2fZtANibt6DRddcS0rmz18UEqj179pCcnMzu3btJSkqqU1+l5S7P0Oms0T11i1RERAJefX5PBgqH083o13+hpNzFxuwC/n12W0b0Tq1Tn16/mhjSuTOJJ2FAO9HchsHSHfmebREREfF/G7ILquy7bVArxr2zkqFdE+nZrJGnzW8vHNaW16HNcLko/HoBjl9H2mwtWxI+YAAmi0aG6sJmMfPc1d082yIiIuL/zp3xIybgj8Mtv/3+9s+ZvPNzJsav+7ann+fVObwKbY5du9j9j5soz8nB1iy1Yt9LLxMUH0/yiy9ga9rUq2KkYhmr8zo18XUZIiIiUgs//vvME34Or0LbvocfJig5mdQ572CJigLAefAge/89kX0PP0zTF1+szxpFRERE/FpSw6prjdY3r0LbkV+WkTpnjiewAVgbNqTxHRPYefU1xz5Q/pTLbbAy8yAAXZs21DJWIiIiAWB+Rg5ntIklyGJmfkbOcduelRbn1Tm8Cm0mmw13cXGV/e4jRzAFBXlViFQoc7q47IWKCYq1jJWIiEhguPGNZfxyzyBiwuzc+MayY7b7y59pCz+jP/sm30+Thx4iuFPFPG2lq1ezb/IUws888fd0/85MmEiNDvVsi4iIiP/b8YcgtsPLUPZnvAptcffcw967JrHzyqswWSu6MFwuwgacSdw9d9drgSebEJuF7/6l4CsiIiKVeRXaLBERJP/fczh27qRs+3bAhL1Fc2wpKfVcnoiIiIj/m7loR43bjurj3aoIdXpgypaaStCvQc1k0q08EREROTm9urBmoc1k8kFoO/TRR+S/+hqOXbuAigAXff1oIi+6yNsuhYplrG5+czkAz1/bXctYiYiIBICFEwec8HN4FdoOzHyd3BkzaHTN1YR0q5i9/8jy5WRPeQDnwYNEjxxZnzWeVNyGwbebcj3bIiIiIuBlaDv45pvET76fqKFDPfvCBwzA3rIVec8+q9BWB0EWM49f1smzLSIiIgJehjZnbi6hXbtW2R/atQvO3Nw6F3UyC7KYubxHsq/LEBERET/j1VCOLaUpBZ9/UWV/weef6w1SERERkRPAq5G2mFtuJWvCBI4sW0ZIt4oRt5IVKylesoTEp56s1wJPNi63wcZ9BQC0jY/QMlYiIiICeBnaIoYMJujdd8mfNYuirxcAYGvRgmb/fZfgtLR6LfBkU+Z0cd6MhYCWsRIREQlEG7ILqt1vMoHdaiEhKhi7tfazQ3idCEI6tCfx8ce8Pdxr+W+9Rf6rr+HMy8Peti3x995DyK9LaVWn4IsvyJ0+g/KsLGwpKTS+8w7C+vf3fG4YBnnPPMPB997DXVBISLeuNJk8GVtq6l9wNVWZMBEXYfdsi4iInKxmL97Ji99vJ7eojHZNInjgwvZ0SY46Zvu5a7J5Yv4m9hwsoVl0A+46py1ntm3s+dwwDJ6av5l3ftlNQUk5PVIb8tDQjjSLaVCvdZ8748fjfoNbLWbO79SERy7uWKupvbx+PdFwuynbsYMjy5dz5JdfKv2cKAXz5rF/2qPEjB1Lsw/eJ7hNGzJvGIPzwIFq2x9ZsZKsO+4k6rJLafbhB4QNGsjuW26ldPNmT5sDr7xC/htv0mTKFFL/+y7mkFAybxiDu6zshF3H8YTYLCy9exBL7x5EiE1ztImIyMnp09V7eeizDYwf1Iq5t/YlrUk4w19dSl5R9d/Py3flM27OSob1SGbeuL4Mbh/HjW8sY9O+Qk+bF77fzsyfdvLw0A58NLYPIUFWhr+2lNJyV73W/uK13UmNaUD6JR2ZN74f88b3I/2SjjSPDWP6lV157NJOLN52gCe+2lSrfr0KbSWrVrFt8BC2n3c+u669jl3DR/z+M2KkN13WyIHXZxF1+eVEXXoJ9pYtiX9gCubgYA69/0G17fPfmE1Y375EX3899hYtaDx+PMFp7Tj41ttAReLOnz2bmJtuInzgQILbtCHh0Wk49++n8OuvT9h1iIiIyPG9snAHV/ZM5ooeybSKC+fhoR0JsVn477Ld1bZ/bdFO+reO5R/9W9CycTh3DG5D+4RIZi3eCVR857+2aAe3DmjJ4PbxtGsSwZPDOpNTUMZXGTn1Wvtz325l8gXtGXZKU9rGR9A2PoJhpzTlvvPTeOXH7QztmsiUC9vz5frander26PZUx4guEMHkl98AWtsbMVN2hPMcDgoXb+emBvHePaZzGYa9OpFyapV1R5Tsmo10SNHVNoX1qcvhQsqnsMr37MHV24eDXr38nxuCQ8npFMnSlatJvK88+r/Qv6E2+3mSEHxX35eERGRPwqNaIDZ7Jv5Qh1ON+uyDvPPM1p49pnNJvq0jGHFrkPVHrNy10Gu79e80r7TW8fy1fp9AOzOLyG3sIw+LWM8n0cEB9ElOYoVuw5yYeeEeqt/475CEqNCquxPjAph468jf2lNIthfWFqrfr0KbY5du0ia/vRfOr2H8+AhcLmwREdX2m+JiaZsR/XrfTnz8rBEx1Rp78zLq/g8t+J/q/YZgzPv2PPNlZWVUfaH26eFhYXHbFtbB/ML6f6fhfXWn4iIiDfW3XU6YVHh9dpnYWEhBQW/P6Rvt9ux2+1V2h084sDlNogJq/xZbJidbbnVD2zkFpURE2Y7qr3Nczs1t6jU08fRfeYe45art1rEhvH8d9tIv6QjNmtF8C13uXn+u220iA0DIKegtMr1/RmvQltIp044MjNP2jnZ0tPTeeCBB05I3y63lq4SEZG/p7SjZpiYPHkyU6ZM8U0xJ9DUoe25YdYyeqXvp22TiuC7aV8hLrfBqyNPASAz/wjXnVa7HFXj0Fa66feH5Rpeew05jz6KMzcPe+vWmIIqdxPcpk2tiqgJa8MosFhwHfXSgSvvANaYmOqPiYnBdSDvmO2tsRX/6zpwgKDGjf/QJg97u3bHrGXSpElMmDDB83tWVlaVfxG9FdkwjHvOagnAZV3itZSViIj4RGhE/b5RCZCRkUFiYqLn9+pG2QAahtqwmE1VXjrILSqrMlL2m9gwO3lFjqPaOzyjWbFhwZ4+GkcEV+ozrUlE7S/mOLqnNOLHiQP4aGUWO/IqRgbP7diEi7okEmavyEyXdEuqdb81Dm07hl5c8ezaHxYxz77nnt8b/PaZyUS7jPW1LuTPmGw2gtu3p3jxEsIHDQIq3mAtXrKEhtdcU+0xIV06U7x4CY1G/P5cW/FPPxHSpQsAQUlJWGJjKF68hOBfQ5qrqIiSNWuIuurKY9Zy9HDuH4d668oeZGXMwPoPvSIiIr4WHh5ORMSfBySb1UyHxEh+2prHkPbxALjdBj9tPcDw3tWPTnVNachPW/O4vm8zz76FW3LpltIQgORGIcSG2/lp6wHaJ0QCUFhazqrdh7i2liNeNRFmt9Z7vzUObS2/nl+vJ/ZG9MgR7L1rEsEdOhDSqSP5s2bjLikh6pKLAdg7cSLWxnE0vqNiFKzRdcPZNXw4B16bSdgZ/SmYO4+S9euJf7Di1qbJZKLR8OHkvfACttQUghKTyJ0xA2vjxp5gKCIiIn+9G/o24473VtMxKYouyZG8unAnRxxOLu9esT73hHdXERcZzMSz2wIwuk8qw15cwss/bOfMto35dPVe1mYdJv2SirlcTSYTo/s045lvtpAa04DkRiE88dVm4iLsDE6Lq/f6dx0o5rWFO9iaWwRAq8bhjOqTSkq09yOYNQ5tQX8YzvSViHPPxZl/kNxnZuDKrbiF2fTllzy3O8v3ZoPp99uJod26kvifx8l9ejq5Tz2FLTWF5GefIbh1a0+b6BtuwCgpIfv+ybgLCgjp3o3kl1/CfIwh2xPN7TbYlX8EgJRGoZi1jJWIiJyELuicQH6xg6fmbya3sIx2CRHMGt2T2PCK7+esQyWY/jB7RfeURky/sitPfLWJx7/cRGpMKC9d14M28b+/THFT/+aUOJxM+mAtBaXlnJLakFmjetZqgtua+H5zLmNmLaNdQgQ9fh3pW7brIG8/9QOvjuhBv1axXvVrMgyjRk++F37zDWH9+mEKCqLwm2+O2zZ8wACviglUe/bsITk5md27d5OUVPt71H90xOEk7f4vAS1jJSIifw/1+T0ZCM6d/iOnt47lrnPaVto/7fON/Lgll7nj+nnVb40TwZ6xt9Bq4Y9Yo6PZM/aWYzc8Qc+0nUzCgxXUREREAtXW3CKeu6Zblf1X9EjitUXVT1NWEzVOB+02ZFS7LfUr1GZl7ZQhvi5DREREvBTdwEbG3oIqa5pmZBcQ08B2jKP+nIZ0REREROrRlac0ZdIHa8jMP0J3zzNt+bzw3TZuOGrVhtqocWjLn/1GjTttNPw6r4oRERERCXTjBrakgd3CKz/u4LEvNwIQFx7MbYNaM6pPqtf91jy0zZpVs4Ymk0JbHZQ5Xdz9wToAHrmkA3Zr/b7RIiIiIieWyWTihn7NuaFfc4rKnACeSXXroubztC34us4nkz/nchu8v2IPULEMhoiIiASu+ghrv6lTT4bDgWNPFramyZisejyuPljNZib9+oqw1awlrERERALBudN/xFTDqVVP+JQff+QuKWHfQw9x+KOPAWjxxefYkpPZN/UhrHFxxNw4xqtipGLpjn/0b+HrMkRERKQWBrev/1UVjuZVaNv/5FOUbdxEyuxZZI650bO/Qe9e5D77nEKbiIiInFRuG9T6zxvVkVehrXDB1yQ9+SQhXbrwx5FAe8uWlGdm1lNpJye322B/YRkAjcPtWsZKREREAPDqoSlX/kEs0dFV9rtLSqjxDV2pVqnTxWnpCzgtfQGlTpevyxERERE/4VVoC+7QnqLvvv99x69B7dB7/yOkS5f6qOukZjWbsGqETURERP7Aq9ujjW+/nd1jbqRs21YMl4v82bNxbN3GkVWrSJk9u75rPKmE2qxsfeRcX5chIiIifsarkbbQ7t1p9tGH4HJhb92a4kU/YYmOJvWddwjpoLnFRERERBxON9tyi3C63PXSn1cjbaWbNxPcujVNpk6t8lnh118TPmhQnQsTERERCUQlDheTP1nH+yuyAPj2jjNoGh3K5I/XERcZzD/PaOlVv16NtO2+YQyOPXuq7C/48iuy/vVvrwqRCmVOF/d9tI77PlpHmV5EEBERCTiPfrGRDdmFzLnxNOzW36NWn5YxfLY62+t+vQptUZddRuao0Thzcz37CubNY+9dd5GQ/ojXxUjFMlZvLNnFG0t24XIbvi5HREREaml+Rg4PXNSeU1IbVZoarXVcOJn5R7zu16vbo7HjbsV1+DCZo0eT8sYbFP24kOz77iPh0UeJGDLY62KkYumq8QNbebZFREQksBwoLiOmgb3K/iMOF3WZG8LrBUPj77uXrDv/xc5hV1K+fz+JT/yH8IED61CKQMUyVrefdeJnVRYREZETo1NiFN9szGFkn2bA71PYvvtLJl1TGnrdb41DW+E331TZF37WWRxZvpyI884Fk8nTJnzAAK8LEhEREQlk/zq7DSNf+5kt+4twug1eW7SDrfuLWL7rIO/e2Mvrfk2GYdTowakN7dJq2KOJdhnrvS4oEO3Zs4fk5GR2795NUlJSnfoyDIOCUicAEcFWTFphQkREAlx9fk8Gil0Hinn+u21syC6g2OGiQ0IEN53RgrbxEV73WeORtnYbMrw+idRcSbmLzg98BUDGg0MItXl9B1tERER8JCW6AdMu7VSvfepJdxEREZF6dM0rS3hv2W4KS8vrtd8aD+Pkz36DqGFXYLbbyZ/9xnHbNhp+XZ0LO1mFBFnY8vA5AFp/VEREJAC1ahzOY19u4r6P1zGgbWOGdknkzLaNCbLUbays5qFt1iwiLji/IrTNmnXshiaTQlsdmEwmgiwKayIiIoFqyoXtuf/8NBZuzePjVXu547+rMZtNnNsxnou6JHJa82iv+q3xiwhybCfjA5YiIiI1dbJ/T5aWu1iwYT/PfruVTfsK2J5+nlf91HikLSd9Ws0amkzE3TXRq2KkYnHZ/3y1CYA7B7fBZtVjhyIiIoFqf2Epn67O5qOVWWzcV0DnpCiv+6pxaCvdsKFmDTVFRZ043W5e+mE7ALcNaoVN74qIiIgElMLScj5ft49PVu1lyfYDNG0UykVdEnn26q6kRDfwut8ah7aU2cd5jk3qjdVs5sbTm3u2RUREJLD0eOhrIkOCOL9TAv8+uw2d6jC69keaBMzP2Kxm7j63na/LEBERES+9MqIHfVrEYK7nWSAU2kRERETqUb9WsSekX4U2P2MYBk53xQu9VrNJy1iJiIgEgPNm/MjbN5xGZGgQ507/8biP+M8d18+rcyi0+ZmSchdp938JaBkrERGRQHFWWpxnxoez0uJOyHuZSgQiIiIidXTboNae7dvPan2clt7T64l+JiTIwurJg1k9eTAhQRZflyMiIiK11O+xbzhY7Kiy/3BJOf0e+8brfjXS5mdMJhORIUG+LkNERES8tOdgCa5qFpxyON3sO1zqdb8KbSIiIiL1YH5Gjmf7h825hAf/Pgjjchv8tC2P5IahXvev0OZnHE43z327FYCxZ7bUMlYiIiIB4sY3lgFgAu54b3Wlz4LMZpIahnDPed7PxarQ5mecbjfTF2wB4B/9m2sZKxERkQCx49eF4Ps++g2f3NKXRg1s9dq/QpufsZhNXHdaimdbREREAsvCiQNOSL8KbX7GbrUwdWgHX5chIiIidXDE4WTp9nyyDpVQ7nJX+mxUn2Ze9anQJiIiIlKP1mUdZtTrv1DqcHGk3EVUSBD5RxyEBFmIDrN5Hdr0wJSIiIhIPZr6WQaD2jVm9eTBBFvNfPjPPiyaOIAOiZHcc673LyIotPmZIw4nLe+eR8u753HE4fR1OSIiIlJLGdkF3NCvOWazCbPZhMPlIiEqhEnntOWxLzd53a9Cmx9yun9fNF5EREQCS5DFjPnXxUdjwuxkHaqYUDc8OIjsQ5pc928j2GphyaSBnm0REREJLO0TIliz5xDNYhpwarNGPDl/MweLHXywMovW8eFe9xswoc116BD7HnqYom+/BbOZ8MFnEX/33ZgbNDjmMe6yMvY/+igFc+fhLi8nrE8f4iffjzUmBoDSjRs58NLLHFmxAtfBgwQlJtLwymE0Gj78r7qsKsxmE/GRwT47v4iISCA5dMTB5E/Ws2DDfkwmOKdDPJMvaE8D+7EjTmm5i4fnbuDTNXtxON2c3iqWqUM7EBtuByBjbwHPf7+NZTvzyS92kNQwhGtOTWF035q9QPCvIW0oKqt4xOnOIW2Y8N/V3PvROlJjQnns0s5eX2vAhLasf/0bZ24uTV97FcPpZO/dd5N9/2QSn/jPMY/JSU+n6PsfSJz+NOawcHKmTmXPreNIfedtAErXr8cSHU3CY48S1KQJJStXkn3/ZDBbaHTtNX/VpYmIiIiXxs9Zxf7CMt64vidOt8G/3lvNpA/WMuOqrsc8ZupnGXy7cT//d3U3woODuP+Tddz05nLev7k3UPH2Z3QDG08N60JCZAjLM/OZ9MFaLGYTI3qn/mlNnZKiPNsxYXZmj+5Z18sEAiS0lW3bRvGPP5L63nuEdKyYwyz+3nvZfeM/aPzvfxMU17jKMa7CQg69/wGJjz9Og9NOA6BJ+iNsP/c8SlatIqRLF6IuvbTSMbbkZEpWraJw/nyfhTaH083MRTuAinlctIyViIhI9bbuL+T7zbl8cksfT1CacmF7Rr3+C/ec1464iKp3rgpKy/nvst1Mv7IrvVtW3Hl7/LLODHrye1ZkHqRb04ZccUpypWOaRoeyYtchvli3r0ah7UQJiNBWsmoV5ogIT2ADaNCrF5jNlKxZTdBZZ1U5pnT9eigvp0HvXp599ubNsSY04civoa06rsIiLJGRx62nrKyMsrIyz++FhYW1vKJjc7rdpH++EYDreqVoGSsREfnbKCwspKCgwPO73W7Hbrd73d+KXYeICLZWGtnq2zIGs8nEysxDnN0hvsox6/Ycptxl0OfXwAbQsnEYiVEhrNhVEdqqrb20nKjQoGo/O9q503/EVM2iRiZTxST6KdGhXNY9id4tYqo2Oo6ASATO3DysjRpV2meyWrFERuLKyzvmMaagICwREZX2W6NjjnnMkRUrKfj8c6KuuOK49aSnpxMZGen5SUtLq8XVHJ/FbOLSbklc2i1Jy1iJiMjfSlpaWqXvz/T09Dr1l1tURkxY5dBntZiJCgkit6jsmMfYLGYiQyoHsJgw2zGPWb4rn8/WZHNVz6Y1qqt/m1gy848QarPQq3k0vZpH08BmZdeBI3RKiiS3sIxrX1nKV+v31ag/z7XVqnU92//EExx4+ZXjtmk+b+5fUkvp5s3sGTuW2LH/JKxvn+O2nTRpEhMmTPD8npWVVW/BzW618MQV3j+kKCIi4q8yMjJITEz0/H6sUbZpn2/khe+3Hbevryf0r9fajmXTvkLGzF7O+IGtOL11bI2OOVjsYEy/5owb2KrS/mcWbCHrUAlvXH8qT87fzDPfbGVw+6qjgcfi09DWaNQoIi+++LhtbElJWGNjcObnV9pvOJ24Dh/GElP90KI1NgajvBxXQUGl0Tbngbwqx5Rt3UrmqNFEXXEFMTff/Kd1Hz2c+8ehXhEREaleeHg4EUfdAavOmH7NuKx70nHbNG0USmyYnbyjRsecLjeHSsqJDas+EMaG2XG43BwuKa802pZX5KhyzJacQq55ZQlX9Uzm1qMC2PHMXZPNp7f2rbL/gs4JXPDMQqZd2okLOyfw6o/ba9wn+Di0WRs1qnLbszohXbrgLiigZN16Qjq0B6B4yVJwuwnpVP2oVHD79hAURPHiJUQMGQxA2fYdOPdmE/qH59nKtmxh18hRRA69iMa331bnaxIREZG6iQ6zE32M0PVH3VKiKCh1snbPYTomVTyP/tO2A7gNg65No6o9pkNSJEEWEz9tzeOcjk0A2JZbRNahErql/P482+acQq5+eQmXdkviX0Pa1qp+e5CZ5bsOkhpTeVqy5bsOYg+qeDLNMAzsQbWbjzUgXkSwt2hBg379yL7/PppMmYLhdJIzdSoR557reXO0PCeHzJGjSHh0GiGdOmEJDyfq0kvIeXQalshIzGFh5Dz0ECFdunheQijdvJnMkaNo0LcP0SNH4szNrTihxVKjMHkiHHE4OfWRBQAsvXsgobaA+BOJiIj85Vo2Dqd/61ju+mAND1/cEafLzeRP1nNBpwTPm6P7Dpdy9StLePKKLnRJjiIiOIgreiTz0NwNRIYGEW4PYvIn6+jWNMrzEsKmfRWB7fTWsVzfrxn7CytWMbCYTDUKkyN6pXLPR2tZm3WYzskVYXL17sO8+8tuxp7ZAoDvN+eS1uTPRx3/KGASQeLjj7Fv6kNkjhz16+S6g4m/527P50a5E8eOHbhLfl8eIm7SJExmM3vGj8dwOAjr24f4++/3fF745Ve48vMp+ORTCj751LM/KCGBlt8s+GsurBqFpVpzVEREpCamX9mF+z9ezzUvL8FsMnF2h3imXNje83m5y8323GJKHC7PvvvOT8Ns2sDNb66omFy3dQxTh/4+Q8W8tdkcKHbw4cosPlyZ5dmfGBXCorsG/GlNtw5sRXKjUGYt3uk5vnlsA6Zd2pGLulQ803ftaSlce1pKra7VZBiGFrmsoz179pCcnMzu3btJSjr+Pfg/43Yb7Mo/AkBKo1DMeoNUREQCXH1+T57MAmak7WRhNptoFnPspblERETE/x0uKefztdlk5h/hxtObExVqY13WYWLC7F4vV6nQJiIiIlKPNmQXcO0rSwkPtrLnYAlXntKUqFAbX6zbx95DJTw5rItX/QbE5Lonk3KXm9mLdzJ78U7KXW5flyMiIiK19NDcDC7rnsR3/zoT+x+WozyzbSxLd+Qf58jj00ibnyl3ubn/4/UAXNY9iSCLcrWIiEggWbP7MI9c3LHK/riI4GOuulATCm1+xmwycW7HeM+2iIiIBBab1VztTBA78oqJbmDzul+FNj8THGTh/67p7usyRERExEuD2sUxY8EWnrumG1CxUHzWoRKmfb6x2kXsa0r33kRERETq0T3nt+OIw0X3qfMpdboZ9uJiznj8WxrYrfxrSBuv+9VIm4iIiEg9iggO4s0bTuWXnflszC6g2OGiQ0IkfVtVv156TSm0+ZkSh4sz/vMtAN/deSYhttqtSyYiIiL+4ZTURpySWn/LYiq0+RkDg5yCMs+2iIiIBJ5FW/NYtDWPA0UO3EctPvX45Z296lOhzc/YrRbmjuvr2RYREZHA8vTXm5mxYAsdk6JoHG6nvuaCUGjzMxazifYJkb4uQ0RERLz01tJM/nN5Zy7pVr/rrOrtUREREZF6VO5y0z2lYb33q9DmZ8pdbt5btpv3lu3WMlYiIiIBaNgpyXy8am+996vbo36m3OXmX/9bA8B5nZpoGSsREZEAU1bu5p2l21m4NY928eFYj/ouv+/8NK/6VWjzM2aTiTPbxHq2RUREJLBs3FdAWkIEAJtyCit9ZqrDawkKbX4mOMjCzFE9fV2GiIiIeGnOjb1OSL+69yYiIiISABTaRERERAKAQpufKXG4OOPxbznj8W8pcbh8XY6IiIj4CT3T5mcMDHYeOOLZFhEREQGFNr9jt1r43029PNsiIiIioNDmdyxmEz1SG/m6DBEREfEzeqZNREREJABopM3POF1uvlyfA8CQ9nFVZlEWERGRk5NCm59xuNyMfXsFABkPDlFoExEREUChze+YTSZObdbIsy0iIiICCm1+JzjIwrv/ODHLX4iIiEjg0r03ERERkQCg0CYiIiISABTa/ExpuYtzpv/IOdN/pLRcy1iJiIhIBT3T5mfchsGG7ALPtoiIiAgotPkdu9XCG9f39GyLiIiIgEKb37GYTfRrFevrMkRERMTP6Jk2ERERkQCgkTY/43S5+WFLLgCnt4rViggiIiICKLT5HYfLzejXlwFaxkpERER+p9DmZ8wmE52SIj3bIiIiIqDQ5neCgyx8cktfX5chIiIifkb33kREREQCgEKbiIiISABQaPMzpeUuLn3+Jy59/ictYyUiIiIeeqbNz7gNg+W7Dnq2RUREREChze/YLGZevK67Z1tEREQEFNr8jtViZkj7eF+XISIiIn5GQzkiIiIiASBgRtpchw6x76GHKfr2WzCbCR98FvF33425QYNjHuMuK2P/o49SMHce7vJywvr0IX7y/VhjYqq0dR48yI6hF+PMyaH1z0uxREScyMs5Jpfb4Ocd+QD0bNYIi1kT7IqIiBzLoSMOJn+yngUb9mMywTkd4pl8QXsa2I8dcUrLXTw8dwOfrtmLw+nm9FaxTB3agdhwe5W2B4sdnDP9R/YVlLJ68mAiQ4JO5OUcV8CMtGX969+Ubd1K09deJfmF5zmybBnZ908+7jE56ekUfvsdidOfJmX2bJz797Pn1nHVts2+9z7sbVqfiNJrpczp4qqXl3DVy0soc+rtURERkeMZP2cVm3OKeOP6nrw28hR+3pHPpA/WHveYqZ9lsGBDDv93dTfevbEXOYWl3PTm8mrb/vv9NbRtEn4iSq+1gAhtZdu2UfzjjzSZOpWQzp0J7d6d+HvvpWDePMpz9ld7jKuwkEPvf0DcxIk0OO00Qjq0p0n6I5SsXEnJqlWV2h585x3cBQVEjx79F1zN8Zkw0apxGK0ah2FCo2wiIiLHsnV/Id9vzuXRSzvStWlDTkltxJQL2/Ppmr3kFJRWe0xBaTn/Xbabe89Po3fLGDomRfL4ZZ1ZvusgKzIPVmr7xpJdFJSUc2O/5n/F5fypgAhtJatWYY6IIKRjB8++Br16gdlMyZrV1R5Tun49lJfToHcvzz578+ZYE5pw5A+hrWzrVnL/7/9IeHQamGr2j6OsrIyCggLPT2FhoXcXVo0Qm4X5E/ozf0J/QmyWeutXRETE1woLCyt9f5aVldWpvxW7DhERbKVTUpRnX9+WMZhNJlZmHqr2mHV7DlPuMujT8vdHpVo2DiMxKoQVu34PbVtyCpmxYAtPDuuCyU/WAg+I0ObMzcPaqFGlfSarFUtkJK68vGMeYwoKqvJsmjU6xnOM2+Eg6447ifvXvwhKSKhxPenp6URGRnp+0tLSanlFIiIiJ5+0tLRK35/p6el16i+3qIyYsMrPoVktZqJCgsgtqj4Q5haVYbOYqzybFhNm8xxT5nRx6zsrufvctiRGhdSpxvrk0xcR9j/xBAdefuW4bZrPm3vCzp/7xJPYWzQn8sILa3XcpEmTmDBhguf3rKwsBTcREZE/kZGRQWJioud3u73qg/8A0z7fyAvfbztuX19P6F+vtf3RY19somXjMC7umnTCzuENn4a2RqNGEXnxxcdtY0tKwhobgzM/v9J+w+nEdfgwlmreBAWwxsZglJfjKiioNNrmPJDnOaZ46VLKNm+m4Mtfb7v+ugLB5l69ifnHP4gdd2u1fdvt9kr/ohUUFBz/QmuhtNzFDbOWAfDKiB4EB+kWqYiI/D2Eh4cTUYPZGcb0a8Zl3Y8fmJo2CiU2zE7eUSNqTpebQyXlxIZVHwhjw+w4XG4Ol5RXGm3LK3J4jvlp2wE27Sugxd3zADB+zQfdps5n7JktmXCWb15c9GloszZqVOW2Z3VCunTBXVBAybr1hHRoD0DxkqXgdhPSqXO1xwS3bw9BQRQvXkLEkMEAlG3fgXNvNqFdugCQNGM67tLfH1QsXbuO7HvuIeXNN7A1bVrHq/OO2zBYuDXPsy0iInKyiQ6zE32M0PVH3VKiKCh1snbPYTomRQIVgcttGHRtGlXtMR2SIgmymPhpax7ndGwCwLbcIrIOldAtpSEAL1zbjdJyt+eY1XsO8e//reG//+hFSnRoHa/OewExT5u9RQsa9OtH9v330WTKFAynk5ypU4k491yC4hoDUJ6TQ+bIUSQ8Oo2QTp2whIcTdekl5Dw6DUtkJOawMHIeeoiQLl0I+TW0HR3MXAcPec7nq3nabBYzTw/r4tkWERGR6rVsHE7/1rHc9cEaHr64I06Xm8mfrOeCTgnERQQDsO9wKVe/soQnr+hCl+QoIoKDuKJHMg/N3UBkaBDh9iAmf7KObk2j6Na0IrSlRFeeAza/2PHr+cJ8Ok9bQIQ2gMTHH2Pf1IfIHDnq18l1BxN/z92ez41yJ44dO3CX/D5yFjdpEiazmT3jx2M4HIT17UP8/ff7ovwas1rMDO2a+OcNRUREhOlXduH+j9dzzctLMJtMnN0hnikXtvd8Xu5ysz23mBLH73Of3nd+GmbTBm5+c0XF5LqtY5g6tEN13fsVk2HoHlxd7dmzh+TkZHbv3k1Skn89tCgiIuJr+p6sHwEz0naycLkN1mUdBqBDYqSWsRIREREgQOZpO5mUOV1c9NwiLnpukZaxEhEREQ+NtPkZEybPRH5axkpERER+o9DmZ0JsFhbdNcDXZYiIiIif0e1RERERkQCg0CYiIiISABTa/ExpuYsxs5cxZvYySsv1IoKIiIhU0DNtfsZtGMzPyPFsi4iIiIBCm98JsphJv6SjZ1tEREQEFNr8TpDFzFU9fbNYvYiIiPgvDeWIiIiIBACNtPkZt9tga24RAC1jwzBrGSsRERFBoc3vlDpdDH7qBwAyHhxCqE1/IhEREVFo80uNGth8XYKIiIj4GYU2PxNqs7LivrN8XYaIiIj4Gb2IICIiIhIAFNpEREREAoBCm58pLXcxfs5Kxs9ZqWWsRERExEOhzc+4DYOPV+3l41V7tYyViIiIeOhFBD8TZDFz3/lpnm0RERERUGjzO0EWM9f3bebrMkRERMTPaChHREREJABopM3PuN0GWYdKAEiMCtEyViIiIgJopM3vlDpd9HvsW/o99i2lTr09KiIiIhU00uaHQoIsvi5BRERE/IxCm58JtVnZMPVsX5chIiIifka3R0VEREQCgEKbiIiISABQaPMzZU4Xd72/hrveX0OZXkQQERGRXym0+RmX22DOL7uZ88tuXG4tYyUiIiIV9CKCn7Gazdw5uLVnW0RERAQU2vyOzWrmlgGtfF2GiIiI+BkN5YiIiIgEAI20+RnDMMgvdgDQqIENk0nLWImIiIhCm98pKXfR/aGvAch4cAihNv2JRERERKGtXrjdbgCys7Pr3FdJuQt32REAsrKytKSViIgEvN++H3/7vhTvKLTVg5ycHAB69uxZr/22frpeuxMREfGpnJwcmjZt6usyApbJMAxNBlZHTqeTlStXEhcXh7kepukoLCwkLS2NjIwMwsPD66FC39M1BYa/2zX93a4HdE2B4u92TXW9HrfbTU5ODl27dsVq1XiRtxTa/FBBQQGRkZEcPnyYiIgIX5dTL3RNgeHvdk1/t+sBXVOg+Ltd09/tegKVpvwQERERCQAKbSIiIiIBQKHND9ntdiZPnozdbvd1KfVG1xQY/m7X9He7HtA1BYq/2zX93a4nUOmZNhEREZEAoJE2ERERkQCg0CYiIiISABTaRERERAKAQpuIiIhIAFBo83M7d+7k+uuvp1mzZoSEhNCiRQsmT56Mw+HwdWlee/jhh+nduzehoaFERUX5uhyvPPfcc6SmphIcHMypp57Kzz//7OuS6uSHH37gggsuICEhAZPJxEcffeTrkuokPT2dU045hfDwcBo3bszQoUPZtGmTr8uqk+eff55OnToRERFBREQEvXr14vPPP/d1WfVm2rRpmEwmbrvtNl+X4rUpU6ZgMpkq/bRt29bXZdVZVlYW1157LdHR0YSEhNCxY0eWLVvm67JOSgptfm7jxo243W5efPFF1q9fz1NPPcULL7zA3Xff7evSvOZwOLj88su5+eabfV2KV959910mTJjA5MmTWbFiBZ07d2bIkCHs37/f16V5rbi4mM6dO/Pcc8/5upR68f333zN27FiWLFnC/PnzKS8vZ/DgwRQXF/u6NK8lJSUxbdo0li9fzrJlyxgwYAAXXXQR69ev93VpdfbLL7/w4osv0qlTJ1+XUmft27cnOzvb87Nw4UJfl1QnBw8epE+fPgQFBfH555+TkZHBE088QcOGDX1d2snJkIDz2GOPGc2aNfN1GXU2c+ZMIzIy0tdl1FrPnj2NsWPHen53uVxGQkKCkZ6e7sOq6g9gfPjhh74uo17t37/fAIzvv//e16XUq4YNGxqvvPKKr8uok8LCQqNVq1bG/Pnzjf79+xvjx4/3dUlemzx5stG5c2dfl1GvJk6caPTt29fXZcivNNIWgA4fPkyjRo18XcZJyeFwsHz5cgYNGuTZZzabGTRoEIsXL/ZhZXI8hw8fBvjb/HfjcrmYM2cOxcXF9OrVy9fl1MnYsWM577zzKv03Fci2bNlCQkICzZs355prriEzM9PXJdXJJ598Qo8ePbj88stp3LgxXbt25eWXX/Z1WScthbYAs3XrVp555hn+8Y9/+LqUk1JeXh4ul4u4uLhK++Pi4ti3b5+PqpLjcbvd3HbbbfTp04cOHTr4upw6Wbt2LWFhYdjtdm666SY+/PBD0tLSfF2W1+bMmcOKFStIT0/3dSn14tRTT+X111/niy++4Pnnn2fHjh3069ePwsJCX5fmte3bt/P888/TqlUrvvzyS26++WbGjRvHrFmzfF3aSUmhzUfuuuuuKg+sHv2zcePGSsdkZWVx9tlnc/nllzNmzBgfVV49b65H5K8wduxY1q1bx5w5c3xdSp21adOGVatWsXTpUm6++WZGjBhBRkaGr8vyyu7duxk/fjxvvfUWwcHBvi6nXpxzzjlcfvnldOrUiSFDhjBv3jwOHTrEf//7X1+X5jW32023bt145JFH6Nq1KzfeeCNjxozhhRde8HVpJyWrrws4Wd1xxx2MHDnyuG2aN2/u2d67dy9nnnkmvXv35qWXXjrB1dVeba8nUMXExGCxWMjJyam0Pycnh/j4eB9VJcdyyy238Nlnn/HDDz+QlJTk63LqzGaz0bJlSwC6d+/OL7/8wvTp03nxxRd9XFntLV++nP3799OtWzfPPpfLxQ8//MCzzz5LWVkZFovFhxXWXVRUFK1bt2br1q2+LsVrTZo0qTKa265dO95//30fVXRyU2jzkdjYWGJjY2vUNisrizPPPJPu3bszc+ZMzGb/GyCtzfUEMpvNRvfu3VmwYAFDhw4FKv6f6IIFC7jlllt8W5x4GIbBrbfeyocffsh3331Hs2bNfF3SCeF2uykrK/N1GV4ZOHAga9eurbRv1KhRtG3blokTJwZ8YAMoKipi27ZtXHfddb4uxWt9+vSpMl3O5s2bSUlJ8VFFJzeFNj+XlZXFGWecQUpKCv/5z3/Izc31fBaoIzuZmZnk5+eTmZmJy+Vi1apVALRs2ZKwsDDfFlcDEyZMYMSIEfTo0YOePXvy9NNPU1xczKhRo3xdmteKiooqjQbs2LGDVatW0ahRI5o2berDyrwzduxY3n77bT7++GPCw8M9zxtGRkYSEhLi4+q8M2nSJM455xyaNm1KYWEhb7/9Nt999x1ffvmlr0vzSnh4eJVnDBs0aEB0dHTAPnt45513csEFF5CSksLevXuZPHkyFouFq666ytelee3222+nd+/ePPLII1xxxRX8/PPPvPTSS355x+ek4OvXV+X4Zs6caQDV/gSqESNGVHs93377ra9Lq7FnnnnGaNq0qWGz2YyePXsaS5Ys8XVJdfLtt99W+zcZMWKEr0vzyrH+m5k5c6avS/Pa6NGjjZSUFMNmsxmxsbHGwIEDja+++srXZdWrQJ/yY9iwYUaTJk0Mm81mJCYmGsOGDTO2bt3q67Lq7NNPPzU6dOhg2O12o23btsZLL73k65JOWibDMIy/MiSKiIiISO3538NRIiIiIlKFQpuIiIhIAFBoExEREQkACm0iIiIiAUChTURERCQAKLSJiIiIBACFNhEREZEAoNAmIrVyxhlncNttt/m6DK+8/vrrmEwmTCaTT65hypQpnvM//fTTf/n5RSSwKbSJyF/u9ddfJyoqqt77HTduHN27d8dut9OlS5dq20RERJCdnc3UqVM9+wzD4P7776dJkyaEhIQwaNAgtmzZUuvzr1mzhn79+hEcHExycjKPPfZYpc/vvPNOsrOz/xaL14vIX0+hTUT+VkaPHs2wYcOO+bnJZCI+Pp7w8HDPvscee4wZM2bwwgsvsHTpUho0aMCQIUMoLS2t8XkLCgoYPHgwKSkpLF++nMcff5wpU6ZUWqMxLCyM+Pj4v8Vi6CLy11NoE5Faczqd3HLLLURGRhITE8N9993HH1fEKysr48477yQxMZEGDRpw6qmn8t133wHw3XffMWrUKA4fPuy5VThlyhQA3njjDXr06EF4eDjx8fFcffXV7N+/v8Z1zZgxg7Fjx9K8efMaH2MYBk8//TT33nsvF110EZ06dWL27Nns3buXjz76qMb9vPXWWzgcDl577TXat2/PlVdeybhx43jyySdr3IeIyPEotIlIrc2aNQur1crPP//M9OnTefLJJ3nllVc8n99yyy0sXryYOXPmsGbNGi6//HLOPvtstmzZQu/evXn66ac9tymzs7O58847ASgvL2fq1KmsXr2ajz76iJ07dzJy5MgTei07duxg3759DBo0yLMvMjKSU089lcWLF9e4n8WLF3P66adjs9k8+4YMGcKmTZs4ePBgvdYsIicnq68LEJHAk5yczFNPPYXJZKJNmzasXbuWp556ijFjxpCZmcnMmTPJzMwkISEBqHiW64svvmDmzJk88sgjREZGem5T/tHo0aM9282bN2fGjBmccsopFBUVERYWdkKuZd++fQDExcVV2h8XF+f5rKb9NGvWrEofv33WsGHDOlYqIic7jbSJSK2ddtppmEwmz++9evViy5YtuFwu1q5di8vlonXr1oSFhXl+vv/+e7Zt23bcfpcvX84FF1xA06ZNCQ8Pp3///gBkZmae0OsREQkEGmkTkXpVVFSExWJh+fLlVR64P95oWXFxMUOGDGHIkCG89dZbxMbGkpmZyZAhQ3A4HCes3t9G+3JycmjSpIlnf05OzjHfQD1WPzk5OZX2/fb70SOKIiLe0EibiNTa0qVLK/2+ZMkSWrVqhcVioWvXrrhcLvbv30/Lli0r/fwWXmw2Gy6Xq1IfGzdu5MCBA0ybNo1+/frRtm3bWr2E4K1mzZoRHx/PggULPPsKCgpYunQpvXr1qnE/vXr14ocffqC8vNyzb/78+bRp00a3RkWkXii0iUitZWZmMmHCBDZt2sQ777zDM888w/jx4wFo3bo111xzDcOHD+eDDz5gx44d/Pzzz6SnpzN37lwAUlNTKSoqYsGCBeTl5XHkyBGaNm2KzWbjmWeeYfv27XzyySeV5lKria1bt7Jq1Sr27dtHSUkJq1atYtWqVccdqfttot2HHnqITz75hLVr1zJ8+HASEhIYOnRojc999dVXY7PZuP7661m/fj3vvvsu06dPZ8KECbW6BhGRYzJERGqhf//+xj//+U/jpptuMiIiIoyGDRsad999t+F2uz1tHA6Hcf/99xupqalGUFCQ0aRJE+Piiy821qxZ42lz0003GdHR0QZgTJ482TAMw3j77beN1NRUw263G7169TI++eQTAzBWrlxZ49qAKj87duwwDMMwZs6caURGRlY5zu12G/fdd58RFxdn2O12Y+DAgcamTZuq9D1ixIjjnn/16tVG3759DbvdbiQmJhrTpk2rtl1KSorx1FNP1eiaRER+YzKMP0yuJCLyN/b6669z2223cejQoVofm5KSwgMPPFAvU5CkpqZy2223BexyYCLiG7o9KiInlcOHDxMWFsbEiRNrfMz69euJjIxk+PDhdTr3I488QlhYmN6GFRGvaKRNRALCTTfdxJtvvlntZ9deey0vvPDCn/ZRWFjoeaMzKiqKmJiYeq3xz+Tn55Ofnw9AbGwskZGRf+n5RSSwKbSJSEDYv38/BQUF1X4WERFB48aN/+KKRET+WgptIiIiIgFAz7SJiIiIBACFNhEREZEAoNAmIiIiEgAU2kREREQCgEKbiIiISABQaBMREREJAAptIiIiIgFAoU1EREQkAPw/wn/shR1tNfcAAAAASUVORK5CYII=\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"source": [
"# Hopefully, you can see that the maximum of the likelihood fn is at the same position as the minimum negative log likelihood\n",
"# Let's check that:\n",
"print(\"Maximum likelihood = %f, at beta_1=%3.3f\"%( (likelihoods[np.argmax(likelihoods)],beta_1_vals[np.argmax(likelihoods)])))\n",
"print(\"Minimum negative log likelihood = %f, at beta_1=%3.3f\"%( (nlls[np.argmin(nlls)],beta_1_vals[np.argmin(nlls)])))\n",
"\n",
"# Plot the best model\n",
"beta_1[0,0] = beta_1_vals[np.argmin(nlls)]\n",
"model_out = shallow_nn(x_model, beta_0, omega_0, beta_1, omega_1)\n",
"lambda_model = sigmoid(model_out)\n",
"plot_binary_classification(x_model, model_out, lambda_model, x_train, y_train, title=\"beta_1[0]=%3.3f\"%(beta_1[0,0]))\n"
],
"metadata": {
"id": "aDEPhddNdN4u",
"outputId": "2e98382f-f667-44d6-dc98-81fee3c7cc94",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 378
}
},
"execution_count": 15,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Maximum likelihood = 0.000000, at beta_1=-2.000\n",
"Minimum negative log likelihood = 0.000000, at beta_1=-2.000\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 700x350 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"source": [
"They both give the same answer. But you can see from the likelihood above that the likelihood is very small unless the parameters are almost correct. So in practice, we would work with the negative log likelihood.<br><br>\n",
"\n",
"Again, to fit the full neural model we would vary all of the 10 parameters of the network in the $\\boldsymbol\\beta_{0},\\boldsymbol\\omega_{0},\\boldsymbol\\beta_{1},\\boldsymbol\\omega_{1}$ until we find the combination that have the maximum likelihood / minimum negative log likelihood.<br><br>\n",
"\n"
],
"metadata": {
"id": "771G8N1Vk5A2"
}
}
]
}