From a5413d6a15c1448a5fbde18b1973703a019dab40 Mon Sep 17 00:00:00 2001 From: Youcef Rahal Date: Fri, 5 Apr 2024 08:42:10 -0400 Subject: [PATCH 01/23] Fix inor typos in chap 8 notebooks --- Notebooks/Chap08/8_1_MNIST_1D_Performance.ipynb | 5 +++-- Notebooks/Chap08/8_2_Bias_Variance_Trade_Off.ipynb | 8 ++++---- Notebooks/Chap08/8_3_Double_Descent.ipynb | 5 ++--- Notebooks/Chap08/8_4_High_Dimensional_Spaces.ipynb | 4 ++-- 4 files changed, 11 insertions(+), 11 deletions(-) diff --git a/Notebooks/Chap08/8_1_MNIST_1D_Performance.ipynb b/Notebooks/Chap08/8_1_MNIST_1D_Performance.ipynb index 0f8c1b3..162b6ee 100644 --- a/Notebooks/Chap08/8_1_MNIST_1D_Performance.ipynb +++ b/Notebooks/Chap08/8_1_MNIST_1D_Performance.ipynb @@ -83,6 +83,8 @@ { "cell_type": "code", "source": [ + "!mkdir ./sample_data\n", + "\n", "args = mnist1d.data.get_dataset_args()\n", "data = mnist1d.data.get_dataset(args, path='./sample_data/mnist1d_data.pkl', download=False, regenerate=False)\n", "\n", @@ -136,7 +138,6 @@ "optimizer = torch.optim.SGD(model.parameters(), lr = 0.05, momentum=0.9)\n", "# object that decreases learning rate by half every 10 epochs\n", "scheduler = StepLR(optimizer, step_size=10, gamma=0.5)\n", - "# create 100 dummy data points and store in data loader class\n", "x_train = torch.tensor(data['x'].astype('float32'))\n", "y_train = torch.tensor(data['y'].transpose().astype('long'))\n", "x_test= torch.tensor(data['x_test'].astype('float32'))\n", @@ -235,4 +236,4 @@ } } ] -} \ No newline at end of file +} diff --git a/Notebooks/Chap08/8_2_Bias_Variance_Trade_Off.ipynb b/Notebooks/Chap08/8_2_Bias_Variance_Trade_Off.ipynb index 269f56c..d75c770 100644 --- a/Notebooks/Chap08/8_2_Bias_Variance_Trade_Off.ipynb +++ b/Notebooks/Chap08/8_2_Bias_Variance_Trade_Off.ipynb @@ -92,7 +92,7 @@ { "cell_type": "code", "source": [ - "# Draw the fitted function, together win uncertainty used to generate points\n", + "# Draw the fitted function, together with uncertainty used to generate points\n", "def plot_function(x_func, y_func, x_data=None,y_data=None, x_model = None, y_model =None, sigma_func = None, sigma_model=None):\n", "\n", " fig,ax = plt.subplots()\n", @@ -203,7 +203,7 @@ "# Closed form solution\n", "beta, omega = fit_model_closed_form(x_data,y_data,n_hidden=3)\n", "\n", - "# Get prediction for model across graph grange\n", + "# Get prediction for model across graph range\n", "x_model = np.linspace(0,1,100);\n", "y_model = network(x_model, beta, omega)\n", "\n", @@ -302,7 +302,7 @@ "sigma_func = 0.3\n", "n_hidden = 5\n", "\n", - "# Set random seed so that get same result every time\n", + "# Set random seed so that we get the same result every time\n", "np.random.seed(1)\n", "\n", "for c_hidden in range(len(hidden_variables)):\n", @@ -344,4 +344,4 @@ "outputs": [] } ] -} \ No newline at end of file +} diff --git a/Notebooks/Chap08/8_3_Double_Descent.ipynb b/Notebooks/Chap08/8_3_Double_Descent.ipynb index ee745d6..cb380cc 100644 --- a/Notebooks/Chap08/8_3_Double_Descent.ipynb +++ b/Notebooks/Chap08/8_3_Double_Descent.ipynb @@ -124,7 +124,7 @@ " D_k = n_hidden # Hidden dimensions\n", " D_o = 10 # Output dimensions\n", "\n", - " # Define a model with two hidden layers of size 100\n", + " # Define a model with two hidden layers\n", " # And ReLU activations between them\n", " model = nn.Sequential(\n", " nn.Linear(D_i, D_k),\n", @@ -157,7 +157,6 @@ " optimizer = torch.optim.SGD(model.parameters(), lr = 0.01, momentum=0.9)\n", "\n", "\n", - " # create 100 dummy data points and store in data loader class\n", " x_train = torch.tensor(data['x'].astype('float32'))\n", " y_train = torch.tensor(data['y'].transpose().astype('long'))\n", " x_test= torch.tensor(data['x_test'].astype('float32'))\n", @@ -267,4 +266,4 @@ "outputs": [] } ] -} \ No newline at end of file +} diff --git a/Notebooks/Chap08/8_4_High_Dimensional_Spaces.ipynb b/Notebooks/Chap08/8_4_High_Dimensional_Spaces.ipynb index e162f17..80b27f0 100644 --- a/Notebooks/Chap08/8_4_High_Dimensional_Spaces.ipynb +++ b/Notebooks/Chap08/8_4_High_Dimensional_Spaces.ipynb @@ -224,7 +224,7 @@ { "cell_type": "markdown", "source": [ - "You should see see that by the time we get to 300 dimensions most of the volume is in the outer 1 percent.

\n", + "You should see that by the time we get to 300 dimensions most of the volume is in the outer 1 percent.

\n", "\n", "The conclusion of all of this is that in high dimensions you should be sceptical of your intuitions about how things work. I have tried to visualize many things in one or two dimensions in the book, but you should also be sceptical about these visualizations!" ], @@ -233,4 +233,4 @@ } } ] -} \ No newline at end of file +} From 5492ed0ee53d2e705bb19dadbd9eaadd05352f1c Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Wed, 10 Apr 2024 15:27:28 -0400 Subject: [PATCH 02/23] Updated comments to make clearer. --- Notebooks/Chap03/3_1_Shallow_Networks_I.ipynb | 21 +++++++------------ 1 file changed, 7 insertions(+), 14 deletions(-) diff --git a/Notebooks/Chap03/3_1_Shallow_Networks_I.ipynb b/Notebooks/Chap03/3_1_Shallow_Networks_I.ipynb index a225f50..80047d3 100644 --- a/Notebooks/Chap03/3_1_Shallow_Networks_I.ipynb +++ b/Notebooks/Chap03/3_1_Shallow_Networks_I.ipynb @@ -1,18 +1,16 @@ { "cells": [ { - "attachments": {}, "cell_type": "markdown", "metadata": { - "colab_type": "text", - "id": "view-in-github" + "id": "view-in-github", + "colab_type": "text" }, "source": [ "\"Open" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "1Z6LB4Ybn1oN" @@ -42,7 +40,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "wQDy9UzXpnf5" @@ -102,8 +99,8 @@ "source": [ "# Define a shallow neural network with, one input, one output, and three hidden units\n", "def shallow_1_1_3(x, activation_fn, phi_0,phi_1,phi_2,phi_3, theta_10, theta_11, theta_20, theta_21, theta_30, theta_31):\n", - " # TODO Replace the lines below to compute the three initial lines\n", - " # (figure 3.3a-c) from the theta parameters. These are the preactivations\n", + " # TODO Replace the code below to compute the three initial lines\n", + " # from the theta parameters (i.e. implement equations at bottom of figure 3.3a-c). These are the preactivations\n", " pre_1 = np.zeros_like(x)\n", " pre_2 = np.zeros_like(x)\n", " pre_3 = np.zeros_like(x)\n", @@ -199,7 +196,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "T34bszToImKQ" @@ -210,7 +206,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "jhaBSS8oIWSX" @@ -269,7 +264,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "osonHsEqVp2I" @@ -354,9 +348,8 @@ ], "metadata": { "colab": { - "authorship_tag": "ABX9TyPBNztJrxnUt1ELWfm1Awa3", - "include_colab_link": true, - "provenance": [] + "provenance": [], + "include_colab_link": true }, "kernelspec": { "display_name": "Python 3", @@ -368,4 +361,4 @@ }, "nbformat": 4, "nbformat_minor": 0 -} +} \ No newline at end of file From ea248af22f236881d41bbc2fd1cdea04209febd9 Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Wed, 10 Apr 2024 15:38:29 -0400 Subject: [PATCH 03/23] Added brackets to plt.show() --- .../Chap01/1_1_BackgroundMathematics.ipynb | 31 ++++++------------- 1 file changed, 10 insertions(+), 21 deletions(-) diff --git a/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb b/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb index c2fe012..3ca132d 100644 --- a/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb +++ b/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb @@ -1,18 +1,16 @@ { "cells": [ { - "attachments": {}, "cell_type": "markdown", "metadata": { - "colab_type": "text", - "id": "view-in-github" + "id": "view-in-github", + "colab_type": "text" }, "source": [ "\"Open" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "s5zzKSOusPOB" @@ -41,7 +39,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "WV2Dl6owme2d" @@ -49,11 +46,11 @@ "source": [ "**Linear functions**
We will be using the term *linear equation* to mean a weighted sum of inputs plus an offset. If there is just one input $x$, then this is a straight line:\n", "\n", - "\\begin{equation}y=\\beta+\\omega x,\\end{equation} \n", + "\\begin{equation}y=\\beta+\\omega x,\\end{equation}\n", "\n", "where $\\beta$ is the y-intercept of the linear and $\\omega$ is the slope of the line. When there are two inputs $x_{1}$ and $x_{2}$, then this becomes:\n", "\n", - "\\begin{equation}y=\\beta+\\omega_1 x_1 + \\omega_2 x_2.\\end{equation} \n", + "\\begin{equation}y=\\beta+\\omega_1 x_1 + \\omega_2 x_2.\\end{equation}\n", "\n", "Any other functions are by definition **non-linear**.\n", "\n", @@ -99,7 +96,7 @@ "ax.plot(x,y,'r-')\n", "ax.set_ylim([0,10]);ax.set_xlim([0,10])\n", "ax.set_xlabel('x'); ax.set_ylabel('y')\n", - "plt.show\n", + "plt.show()\n", "\n", "# TODO -- experiment with changing the values of beta and omega\n", "# to understand what they do. Try to make a line\n", @@ -107,7 +104,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "AedfvD9dxShZ" @@ -192,7 +188,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "i8tLwpls476R" @@ -236,7 +231,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "fGzVJQ6N-mHJ" @@ -279,7 +273,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "3LGRoTMLU8ZU" @@ -293,7 +286,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "7Y5zdKtKZAB2" @@ -325,11 +317,10 @@ "ax.plot(x,y,'r-')\n", "ax.set_ylim([0,100]);ax.set_xlim([-5,5])\n", "ax.set_xlabel('x'); ax.set_ylabel('exp[x]')\n", - "plt.show" + "plt.show()" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "XyrT8257IWCu" @@ -345,7 +336,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "R6A4e5IxIWCu" @@ -373,11 +363,10 @@ "ax.plot(x,y,'r-')\n", "ax.set_ylim([-5,5]);ax.set_xlim([0,5])\n", "ax.set_xlabel('x'); ax.set_ylabel('$\\log[x]$')\n", - "plt.show" + "plt.show()" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "yYWrL5AXIWCv" @@ -397,8 +386,8 @@ ], "metadata": { "colab": { - "include_colab_link": true, - "provenance": [] + "provenance": [], + "include_colab_link": true }, "kernelspec": { "display_name": "Python 3 (ipykernel)", @@ -420,4 +409,4 @@ }, "nbformat": 4, "nbformat_minor": 0 -} +} \ No newline at end of file From 418ea93e83a11f5a79ea9a97f446e681423c894e Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Sat, 13 Apr 2024 12:50:13 -0400 Subject: [PATCH 04/23] Created using Colab --- Blogs/BorealisBayesianParameter.ipynb | 519 ++++++++++++++++++++++++++ 1 file changed, 519 insertions(+) create mode 100644 Blogs/BorealisBayesianParameter.ipynb diff --git a/Blogs/BorealisBayesianParameter.ipynb b/Blogs/BorealisBayesianParameter.ipynb new file mode 100644 index 0000000..cfe39d5 --- /dev/null +++ b/Blogs/BorealisBayesianParameter.ipynb @@ -0,0 +1,519 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyNLPBx/gU0O2uIzg+FDhzdm", + "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": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Bayesian machine learning: parameter view\n", + "\n", + "This blog contains code that accompanies the Borealis AI blog on Bayesian methods for machine learning (parameter view). Contact udlbookmail@gmail.com if you find any problems." + ], + "metadata": { + "id": "XP-HQhwUYPB7" + } + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "m4htzbZZYLLy" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import cm\n", + "from matplotlib.colors import ListedColormap\n", + "from scipy.stats import multivariate_normal" + ] + }, + { + "cell_type": "markdown", + "source": [ + "Create data for linear model. One dimensional inputs and one dimensional outputs. Ones appended to inputs to account for intercepts." + ], + "metadata": { + "id": "7MCklcI7Zlqk" + } + }, + { + "cell_type": "code", + "source": [ + "X = np.array([[-0.21,-0.14,-0.01,0.12, 0.25, 0.21],[1.0, 1.0, 1.0, 1.0, 1.0, 1.0]])\n", + "y = np.array([-0.20, -0.26, -0.06, 0.07, 0.06, -0.05])\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "NXHLf13kZP8w", + "outputId": "c488b903-3581-42ad-9180-c434e08ac309" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Maximum likelihood solution" + ], + "metadata": { + "id": "Vg3idk97clBD" + } + }, + { + "cell_type": "code", + "source": [ + "# Find parameters for maximum likelihood solution\n", + "phi_ml = np.linalg.inv(X @ X.transpose())@X@y" + ], + "metadata": { + "id": "6dh3ycTfa7Mv" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Create x data for plotting line\n", + "x_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "x_plot = np.concatenate([x_plot, np.ones_like(x_plot)],axis=0)\n", + "# Run model\n", + "y_plot = x_plot.transpose()@phi_ml\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.plot(x_plot[0,:], y_plot, 'r-')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "gv1m9Oi-dPl2", + "outputId": "426ec664-e68d-443d-a4ab-679bce81e527" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# MAP Solution" + ], + "metadata": { + "id": "H_gN0Gbogc-Y" + } + }, + { + "cell_type": "code", + "source": [ + "# Helper function to draw 2D Gaussian\n", + "def draw_gaussian_prior(mean, covariance, title, n_contour, filename=None):\n", + " # Define pretty colormap\n", + " my_colormap_vals_hex =('2a0902', '2b0a03', '2c0b04', '2d0c05', '2e0c06', '2f0d07', '300d08', '310e09', '320f0a', '330f0b', '34100b', '35110c', '36110d', '37120e', '38120f', '39130f', '3a1410', '3b1411', '3c1511', '3d1612', '3e1613', '3f1713', '401714', '411814', '421915', '431915', '451a16', '461b16', '471b17', '481c17', '491d18', '4a1d18', '4b1e19', '4c1f19', '4d1f1a', '4e201b', '50211b', '51211c', '52221c', '53231d', '54231d', '55241e', '56251e', '57261f', '58261f', '592720', '5b2821', '5c2821', '5d2922', '5e2a22', '5f2b23', '602b23', '612c24', '622d25', '632e25', '652e26', '662f26', '673027', '683027', '693128', '6a3229', '6b3329', '6c342a', '6d342a', '6f352b', '70362c', '71372c', '72372d', '73382e', '74392e', '753a2f', '763a2f', '773b30', '783c31', '7a3d31', '7b3e32', '7c3e33', '7d3f33', '7e4034', '7f4134', '804235', '814236', '824336', '834437', '854538', '864638', '874739', '88473a', '89483a', '8a493b', '8b4a3c', '8c4b3c', '8d4c3d', '8e4c3e', '8f4d3f', '904e3f', '924f40', '935041', '945141', '955242', '965343', '975343', '985444', '995545', '9a5646', '9b5746', '9c5847', '9d5948', '9e5a49', '9f5a49', 'a05b4a', 'a15c4b', 'a35d4b', 'a45e4c', 'a55f4d', 'a6604e', 'a7614e', 'a8624f', 'a96350', 'aa6451', 'ab6552', 'ac6552', 'ad6653', 'ae6754', 'af6855', 'b06955', 'b16a56', 'b26b57', 'b36c58', 'b46d59', 'b56e59', 'b66f5a', 'b7705b', 'b8715c', 'b9725d', 'ba735d', 'bb745e', 'bc755f', 'bd7660', 'be7761', 'bf7862', 'c07962', 'c17a63', 'c27b64', 'c27c65', 'c37d66', 'c47e67', 'c57f68', 'c68068', 'c78169', 'c8826a', 'c9836b', 'ca846c', 'cb856d', 'cc866e', 'cd876f', 'ce886f', 'ce8970', 'cf8a71', 'd08b72', 'd18c73', 'd28d74', 'd38e75', 'd48f76', 'd59077', 'd59178', 'd69279', 'd7937a', 'd8957b', 'd9967b', 'da977c', 'da987d', 'db997e', 'dc9a7f', 'dd9b80', 'de9c81', 'de9d82', 'df9e83', 'e09f84', 'e1a185', 'e2a286', 'e2a387', 'e3a488', 'e4a589', 'e5a68a', 'e5a78b', 'e6a88c', 'e7aa8d', 'e7ab8e', 'e8ac8f', 'e9ad90', 'eaae91', 'eaaf92', 'ebb093', 'ecb295', 'ecb396', 'edb497', 'eeb598', 'eeb699', 'efb79a', 'efb99b', 'f0ba9c', 'f1bb9d', 'f1bc9e', 'f2bd9f', 'f2bfa1', 'f3c0a2', 'f3c1a3', 'f4c2a4', 'f5c3a5', 'f5c5a6', 'f6c6a7', 'f6c7a8', 'f7c8aa', 'f7c9ab', 'f8cbac', 'f8ccad', 'f8cdae', 'f9ceb0', 'f9d0b1', 'fad1b2', 'fad2b3', 'fbd3b4', 'fbd5b6', 'fbd6b7', 'fcd7b8', 'fcd8b9', 'fcdaba', 'fddbbc', 'fddcbd', 'fddebe', 'fddfbf', 'fee0c1', 'fee1c2', 'fee3c3', 'fee4c5', 'ffe5c6', 'ffe7c7', 'ffe8c9', 'ffe9ca', 'ffebcb', 'ffeccd', 'ffedce', 'ffefcf', 'fff0d1', 'fff2d2', 'fff3d3', 'fff4d5', 'fff6d6', 'fff7d8', 'fff8d9', 'fffada', 'fffbdc', 'fffcdd', 'fffedf', 'ffffe0')\n", + " my_colormap_vals_dec = np.array([int(element,base=16) for element in my_colormap_vals_hex])\n", + " r = np.floor(my_colormap_vals_dec/(256*256))\n", + " g = np.floor((my_colormap_vals_dec - r *256 *256)/256)\n", + " b = np.floor(my_colormap_vals_dec - r * 256 *256 - g * 256)\n", + " my_colormap = ListedColormap(np.vstack((r,g,b)).transpose()/255.0)\n", + "\n", + " # Make grid of intercept/slope values to plot\n", + " intercepts_mesh, slopes_mesh = np.meshgrid(np.arange(-1.0,1.0,0.005), np.arange(-1.0,1.0,0.005))\n", + " slopes_intercepts = np.dstack((slopes_mesh, intercepts_mesh))\n", + " # Evaluate pdf for every set of parameters\n", + " distribution = multivariate_normal(np.squeeze(mean), covariance)\n", + " prob_mesh = distribution.pdf(slopes_intercepts)\n", + "\n", + " fig,ax = plt.subplots()\n", + " fig.set_size_inches(8,8)\n", + " ax.contourf(slopes_mesh,intercepts_mesh,prob_mesh,256,cmap=my_colormap)\n", + " ax.contour(slopes_mesh,intercepts_mesh,prob_mesh,n_contour,colors=['#80808080'])\n", + " ax.set_xlim([-1,1])\n", + " ax.set_ylim([-1,1])\n", + " ax.set_xlabel('Slope, $\\phi_0$')\n", + " ax.set_ylabel('Intercept, $\\phi_1$')\n", + " ax.set_title(title)\n", + "\n", + " if filename is not None:\n", + " plt.savefile(filename,format='svg')\n", + " plt.show()" + ], + "metadata": { + "id": "mPAqJ0YFjyG3" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Define a prior over the parameters and draw the prior\n", + "sigma_sq_p = 0.4\n", + "sigma_sq_n = 0.005\n", + "prior_mean = np.zeros((2,1))\n", + "prior_cov = sigma_sq_p * np.identity(2)\n", + "draw_gaussian_prior(prior_mean, prior_cov, title='Prior $Pr(\\phi)$',n_contour = 10)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 724 + }, + "id": "obwwLhN3eRun", + "outputId": "593ab44e-b9fd-4107-f81a-f79b71940f7e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Draw some samples from the prior\n", + "np.random.seed(9)\n", + "slopes, intercepts = np.random.multivariate_normal(np.squeeze(prior_mean), prior_cov, 5).T\n", + "\n", + "# Create x data for plotting line\n", + "x_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "x_plot = np.concatenate([x_plot, np.ones_like(x_plot)],axis=0)\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(slopes.shape[0]):\n", + " y_plot = x_plot.transpose() @ np.array([[slopes[i]], [intercepts[i]]])\n", + " ax.plot(x_plot[0,:], y_plot, 'r-')\n", + "\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "Qm4uaAH9-yqE", + "outputId": "2b003378-2604-4014-f77c-d560d6aad5ed" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Find parameters for maximum likelihood solution\n", + "phi_map = np.linalg.inv(X @ X.transpose()+(sigma_sq_n / sigma_sq_p)*np.identity(2))@X@y" + ], + "metadata": { + "id": "r_0b8SZhoh0O" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Create x data for plotting line\n", + "x_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "x_plot = np.concatenate([x_plot, np.ones_like(x_plot)],axis=0)\n", + "# Run models\n", + "y_plot_ml = x_plot.transpose()@phi_ml\n", + "y_plot_map = x_plot.transpose()@phi_map\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.plot(x_plot[0,:], y_plot_ml, 'r-', label='ML')\n", + "ax.plot(x_plot[0,:], y_plot_map, 'g-', label='MAP')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "ax.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "d0UvkrKkxAJ0", + "outputId": "e4a9ef3c-b4c4-4af9-86a6-c259ec732738" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Bayesian approach" + ], + "metadata": { + "id": "kwoM3SCeygPG" + } + }, + { + "cell_type": "code", + "source": [ + "# Compute posterior distribution over parameters\n", + "post_mean = np.linalg.inv(X @ X.transpose()+(sigma_sq_n / sigma_sq_p)*np.identity(2))@X@y\n", + "post_cov = sigma_sq_n * np.linalg.inv(X @ X.transpose()+(sigma_sq_n / sigma_sq_p)*np.identity(2))\n", + "draw_gaussian_prior(post_mean, post_cov, title='Posterior $Pr(\\phi|\\mathbf{X},\\mathbf{y})$', n_contour=5)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 724 + }, + "id": "6LZ5kJjkxsmi", + "outputId": "5c8909f3-6f6e-4f23-abf4-f4e7214d3350" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Draw some samples from the posterior\n", + "np.random.seed(9)\n", + "slopes, intercepts = np.random.multivariate_normal(np.squeeze(post_mean), post_cov, 5).T\n", + "\n", + "# Create x data for plotting line\n", + "x_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "x_plot = np.concatenate([x_plot, np.ones_like(x_plot)],axis=0)\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(slopes.shape[0]):\n", + " y_plot = x_plot.transpose() @ np.array([[slopes[i]], [intercepts[i]]])\n", + " ax.plot(x_plot[0,:], y_plot, 'r-')\n", + "\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "SW3ocOwnDGHg", + "outputId": "56270a37-9390-424e-c51e-2fff9809b947" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Create x data for plotting line\n", + "x_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "x_plot = np.concatenate([x_plot, np.ones_like(x_plot)],axis=0)\n", + "# Run models\n", + "# Make predictions for mean and variance\n", + "inv_term = np.linalg.inv(X @ X.transpose()+(sigma_sq_n / sigma_sq_p)*np.identity(2))\n", + "y_plot_bayes = x_plot.transpose() @ inv_term @ X @ y\n", + "y_plot_var = np.zeros_like(y_plot_bayes)\n", + "for i in range(x_plot.shape[1]):\n", + " y_plot_var[i] = sigma_sq_n * x_plot[:,i] @ inv_term @ x_plot[:,i]\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.plot(x_plot[0,:], y_plot_bayes, 'm-')\n", + "ax.fill_between(x_plot[0,:], y_plot_bayes-2*np.sqrt(y_plot_var), y_plot_bayes+2*np.sqrt(y_plot_var), color='lightgray')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "LftzsFaevj6L", + "outputId": "15a11946-c4a2-4d26-878d-efb8b6d7eb26" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Create x data for plotting line\n", + "x_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "x_plot = np.concatenate([x_plot, np.ones_like(x_plot)],axis=0)\n", + "# Run models\n", + "# Make predictions for mean and variance\n", + "inv_term = np.linalg.inv(X @ X.transpose()+(sigma_sq_n / sigma_sq_p)*np.identity(2))\n", + "y_plot_bayes = x_plot.transpose() @ inv_term @ X @ y\n", + "y_plot_var = np.zeros_like(y_plot_bayes)\n", + "for i in range(x_plot.shape[1]):\n", + " y_plot_var[i] = sigma_sq_n * x_plot[:,i] @ inv_term @ x_plot[:,i] + sigma_sq_n\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.plot(x_plot[0,:], y_plot_bayes, 'm-')\n", + "ax.fill_between(x_plot[0,:], y_plot_bayes-2*np.sqrt(y_plot_var), y_plot_bayes+2*np.sqrt(y_plot_var), color='lightgray')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "ZHrZl3uD0Dtj", + "outputId": "e277a087-a031-4c11-c0c3-99d4ce1a8e7e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From 19c0c7ab3efaf513c04da0785bf914e39f4cfe7b Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Sun, 14 Apr 2024 09:25:48 -0400 Subject: [PATCH 05/23] Created using Colab --- Blogs/BorealisBayesianFunction.ipynb | 1097 ++++++++++++++++++++++++++ 1 file changed, 1097 insertions(+) create mode 100644 Blogs/BorealisBayesianFunction.ipynb diff --git a/Blogs/BorealisBayesianFunction.ipynb b/Blogs/BorealisBayesianFunction.ipynb new file mode 100644 index 0000000..474610a --- /dev/null +++ b/Blogs/BorealisBayesianFunction.ipynb @@ -0,0 +1,1097 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [], + "authorship_tag": "ABX9TyOAGunK61kwWVlnodqlpTsm", + "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": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Bayesian machine learning: function view\n", + "\n", + "This blog contains code that accompanies the Borealis AI blog on Bayesian methods for machine learning (function view). Contact udlbookmail@gmail.com if you find any problems." + ], + "metadata": { + "id": "XP-HQhwUYPB7" + } + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "m4htzbZZYLLy" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import cm\n", + "from matplotlib.colors import ListedColormap\n", + "from scipy.stats import multivariate_normal" + ] + }, + { + "cell_type": "markdown", + "source": [ + "Create data for linear model. One dimensional inputs and one dimensional outputs. Ones appended to inputs to account for intercepts." + ], + "metadata": { + "id": "7MCklcI7Zlqk" + } + }, + { + "cell_type": "code", + "source": [ + "X = np.array([[-0.21,-0.14,-0.01,0.12, 0.25, 0.21],[1.0, 1.0, 1.0, 1.0, 1.0, 1.0]])\n", + "y = np.array([-0.20, -0.26, -0.06, 0.07, 0.06, -0.05])\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "NXHLf13kZP8w", + "outputId": "9f800a70-f720-4409-9cf5-cf7bf58f2880" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Function prior" + ], + "metadata": { + "id": "Vg3idk97clBD" + } + }, + { + "cell_type": "code", + "source": [ + "# Define a prior over the parameters (2 dimensional as intercept + slope)\n", + "sigma_sq_p = 0.4\n", + "sigma_sq_n = 0.005\n", + "prior_param_mean = np.zeros((2,1))\n", + "prior_param_cov = sigma_sq_p * np.identity(2)\n", + "\n", + "# This then defines a prior over the function\n", + "# Define some points to plot function\n", + "X_plot = np.atleast_2d(np.arange(-0.5,0.5, 0.01))\n", + "X_plot = np.concatenate([X_plot, np.ones_like(X_plot)],axis=0)\n", + "n_data = X_plot.shape[1]\n", + "\n", + "# Prior mean and covariance for function, f\n", + "prior_func_mean = np.zeros((n_data, 1))\n", + "prior_func_cov = sigma_sq_p * X_plot.transpose() @ X_plot\n", + "\n", + "# Prior mean and covariance for output, y\n", + "prior_output_mean = np.zeros((n_data, 1))\n", + "prior_output_cov = sigma_sq_p * X_plot.transpose() @ X_plot + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "0HZFJr5Tg-4X" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function prior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(prior_func_mean), prior_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(X_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "tgsXmo6ljQuW", + "outputId": "6e42555a-5f17-4a95-ef19-8caa1e0361cd" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function prior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(prior_output_mean), prior_output_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(X_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "n_JQBqOznJ2U", + "outputId": "851401e0-21cf-447c-df34-c298fafbafaf" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Inference" + ], + "metadata": { + "id": "gaTVZ9oVmT-E" + } + }, + { + "cell_type": "code", + "source": [ + "# Posterior mean and covariance for function, f\n", + "inv_term = np.linalg.inv(X.transpose()@X + (sigma_sq_n/sigma_sq_p) * np.identity(X.shape[1]))\n", + "post_func_mean = X_plot.transpose() @ X @ inv_term @ y\n", + "post_func_cov = sigma_sq_p * X_plot.transpose() @ X_plot - sigma_sq_p * X_plot.transpose() @ X @ inv_term @ X.transpose() @ X_plot\n", + "\n", + "# Posterior mean and covariance for output, y\n", + "post_output_mean = X_plot.transpose() @ X @ inv_term @ y\n", + "post_output_cov = sigma_sq_p * X_plot.transpose() @ X_plot - sigma_sq_p * X_plot.transpose() @ X @ inv_term @ X.transpose() @ X_plot + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "gtmWCs6Gl_-e" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function posterior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(post_func_mean), post_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(X_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "HEfVfdwqsUrt", + "outputId": "acc3fe78-b577-4014-d3b9-9d515028d480" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "post_func_cov_diag = np.diag(post_func_cov)\n", + "ax.plot(X_plot[0,:], post_func_mean,'r-')\n", + "ax.fill_between(X_plot[0,:], post_func_mean-2*np.sqrt(post_func_cov_diag), post_func_mean+2*np.sqrt(post_func_cov_diag), color='lightgray')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "MIU4JCqiu6YN", + "outputId": "5617b064-fdda-4c6b-d5c6-28387a02ecc0" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the output posterior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(post_output_mean), post_output_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(X_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "YH6g39sEsfk-", + "outputId": "f70c151d-2ae2-47b9-bc94-972981f84fda" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "post_output_cov_diag = np.diag(post_output_cov)\n", + "ax.plot(X_plot[0,:], post_output_mean,'r-')\n", + "ax.fill_between(X_plot[0,:], post_output_mean-2*np.sqrt(post_output_cov_diag), post_output_mean+2*np.sqrt(post_output_cov_diag), color='lightgray')\n", + "ax.set_xlim(-0.5,0.5)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "ZHrZl3uD0Dtj", + "outputId": "5ca4f73e-346d-4c9e-b858-9ad46fcc8eb6" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Create data for non-linear model" + ], + "metadata": { + "id": "U1RaVDjQ4Zmy" + } + }, + { + "cell_type": "code", + "source": [ + "np.random.seed(7)\n", + "I = 15\n", + "X = np.atleast_2d(np.random.uniform(-1.4, 1.4, I))\n", + "X = np.concatenate([X, np.ones_like(X)],axis=0)\n", + "y = np.cos(X[0,:]*4.5) * np.exp((-X[0,:]/2-0.5)*2) * 0.5 + np.random.normal(size=(I)) * 0.1\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "ax.set_xlim(-2.,2.)\n", + "ax.set_ylim(-.5,.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "_qE-r1xouncS", + "outputId": "3fa4d187-6941-4898-f258-aba296fc8300" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Fit polynomial model" + ], + "metadata": { + "id": "ab2puftWC30A" + } + }, + { + "cell_type": "code", + "source": [ + "# Transform input data to polynomials\n", + "def nonlin_polynomial(x):\n", + " X_out = np.zeros((5, x.shape[1]))\n", + " X_out[0,:] = np.ones((1, x.shape[1]))\n", + " X_out[1,:] = x\n", + " X_out[2,:] = x * x\n", + " X_out[3,:] = x * x * x\n", + " X_out[4,:] = x * x * x * x\n", + "\n", + " return X_out" + ], + "metadata": { + "id": "Ec5p5VZ65bEr" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Define some points to plot function and transform\n", + "x_plot = np.atleast_2d(np.arange(-2,2,0.04))\n", + "Z_plot = nonlin_polynomial(x_plot)\n", + "n_data = x_plot.shape[1]\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[0:1,:]),'r-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[1:2,:]),'b-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[2:3,:]),'g-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[3:4,:]),'c-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[4:5,:]),'y-')\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "ZzYfB7_y-f5j", + "outputId": "01b9e5e3-f29b-4aa0-bdfd-b1ca93394693" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Define a prior over the parameters (2 dimensional as intercept + slope)\n", + "sigma_sq_p = 0.4\n", + "sigma_sq_n = 0.005\n", + "prior_param_mean = np.zeros((2,1))\n", + "prior_param_cov = sigma_sq_p * np.identity(2)\n", + "\n", + "# Prior mean and covariance for function, f\n", + "prior_func_mean = np.zeros((n_data, 1))\n", + "prior_func_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot\n", + "\n", + "# Prior mean and covariance for output, y\n", + "prior_output_mean = np.zeros((n_data, 1))\n", + "prior_output_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "X2f3BLkaCvcX" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function prior and plot them\n", + "np.random.seed(1)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(prior_func_mean), prior_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(x_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "21ur1PakEGhV", + "outputId": "2c849940-e742-4488-ecdb-6bf1996aad7e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Transform training data\n", + "Z = nonlin_polynomial(X[0:1,:])\n", + "\n", + "# Posterior mean and covariance for function, f\n", + "inv_term = np.linalg.inv(Z.transpose()@Z + (sigma_sq_n/sigma_sq_p) * np.identity(Z.shape[1]))\n", + "post_func_mean = Z_plot.transpose() @ Z @ inv_term @ y\n", + "post_func_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot - sigma_sq_p * Z_plot.transpose() @ Z @ inv_term @ Z.transpose() @ Z_plot\n", + "\n", + "# Posterior mean and covariance for output, y\n", + "post_output_mean = Z_plot.transpose() @ Z @ inv_term @ y\n", + "post_output_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot - sigma_sq_p * Z_plot.transpose() @ Z @ inv_term @ Z.transpose() @ Z_plot + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "-yUpv11OF5rf" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function posterior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(post_func_mean), post_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(x_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-2.,2.)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "buOlX1h_GtAh", + "outputId": "d0c14b47-c614-4820-8a42-ea02d2d14c1e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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yX6GCDqYCA2VrPXynlA6gAKlWXrSo69tZiDCAIu/EHigiKkzMSxJERuoAKj1dttYB1KVLegFhIPsSL5RvDKDIOzGAIqLCxHz4zmTSQ3hXrsjWXg0oo9eJw3dOxwCKvJOtMgYcwiMiX2VewsD8sr0aUEYCubH2HXugnI4BFHkn9kARUWFiXkTzyhUZogN0oGSvhEFAgGzZA+V0DKDIO9kKoC5f1vVOiIh8iXkPlLEfHi7r4AUEZK/xZARQRo4UAyinYwBF3ikszPaMkvPn3d8WIiJX++cf2VapogMoY13QSpVkcWFzRgBlrBHKITynYwBF3ovDeOQkGRnA2rXAF1/INiPD0y0isnLkiGyrVNEJ5MaXSOvhO4A1oNyAARR5LwZQ5ARLl8qX8zZtgEcekW2lSnKcqEBISbFc787ogTLym3IKoAAgIkJKH5BTMYAi78VimpRPS5cC3bpZftYAkpfbrRuDKCogjh2TwphFisgMZCOASkuTra0AykguB9j75CIMoMh72SplwB4oyqWMDGDECL1QvTnj2MiRHM6jAsB8+M68BtTly7KtWdPy/MRE+TEw/8klGECR92IPFOXD+vXZe57MKSUzx9evd1+biGwyEsiNniajByo+XrY33WR5vtH7FBwsW/ZAuQQDKPJezIGifIiLc+55RC5j3gOVnq4j/7Q0ICQke4BkXB8SIlsGUC7BAIq8FwMoyoeYGOeeR+Qy5j1QcXEyrmyULahZ034JAwOH8FyCARR5Lw7hUT60bAmULy8pJbaYTFKbsGVL97aLKBujB8p8Bl5EhGyth+8APYRnJJmzB8olGECR92IPFOWDvz8wa5bsWwdRxuWZM7N/uSdyK6Usi2gaCeSBgbK1FUBZ14BiD5RLMIAi72UrgDp/ntOmKNe6dgWWLAHKlbM8Xr68HO/a1TPtIsoSHw9cuwb4+UlPktEDZfyfyymAAmTVhpIlXd/OQijA0w0gyrNixWSWifn6d5mZMozHxBXKpa5dgc6dZbZdXJy8dVq2ZM8TFRDG8F1sLBAUpAMoo0zBjQKoSpXsj1NTvjCAIu9lMkkvlPEPxXDmDAMocoi/P9C6tadbQWSDdQkDYwgvNVV6papXz34b8wCK+U8uwyE88m62hvHOnHF/O4iIXME8gRyw/MJYtaqu9WS4dg24eFFfZgDlMgygyLsxgCIiX2ZeA0op3QMF2B6+M/7/GWPQTCB3GQZQ5N0YQBGRLzMfwktIAJKS9HU55T8FBcmWPVAuwxwo8m4MoAqVjAwme1MhY94DZQzfBQZKjaecAqjMTNmyB8pl2ANF3o0BVKGxdKl8FrRpAzzyiGwrVZLjRD7pyhVdHLhqVT18Z6x2nVMAlZoqW/ZAuQwDKPJuZcpkP8YAyucsXQp065Z9hYrTp+U4gyjyScbwXYkSQGSk7oFKT5dtrVrZb2P8kSglw3i2vmSSUzCAIu/GHiifl5EBjBihv3SbM46NHMn6qeSDzIfvAMsE8nLlgPDw7LexLmHgx495V+FvlrybvfXwjO5r8nrr12fveTKnFHDypJxH5FOsa0CZlzCwNXwHWAZZHL5zKQZQ5N3sdU/Hx7u3HeQycXHOPY/Ia+RUA8peAHX0qN5nArlLMYAi71a8OBBgYzIph/F8Rm6LyrP4PPkc80WEgRvXgLp8WX4M7IFyKZYxIO/m5yeJ5NYBEwMon9GypSzue/q07Twok0mub9nS/W3LldOngbVrgTVrgG3bpO5CsWJA0aKyjYwE2rYFOnaUhV+JDOY9UKmplt2stgKoY8dka5Q5YA+USzGAIu/HAMqn+fsDs2bJbDuTyTKIMtZInTmzgNWD+vtv4K23gFWrgMOHb3z+Bx8ARYoA998PPPww0L599iU6qHBJT9cBUZUq2b9B5BRAGYnj7IFyKQZQ5P04E8/nde0KLFkis/HME8rLl5fgqWtXjzXN0vnzwKRJwPvv66nmfn5Ao0ayWvHtt8vU8itXpKL0lSuS1/L11/Lh98UX8hMZCTz3nEwvDAz03PMhzzl1St5DQUEy4858lkTx4rZLuBj5T6wB5RYMoMj7MYAqFLp2BTp3LqCVyK9dk26yyZOBxEQ5dt99wJAh0siIiJxv/8YbwNatwKJFwFdfyft3zBjg88+BDz8EmjZ1/XOggsUYvqtcWd7k5gnktWrp7ldzRg+UUpIbWrasy5tZmDGAIu/HAKrQ8PeXjpwCZeNGoGdP/QHXqBEwfbqUSrclLg7YtEl+Nm4E9uyRXobwcPmpWlXe0wcPAn/+Cdx6KzBsGPDaa7br/pBvcjSBHLCcgVe+vO0JNuQ0Xj0Lb86cOahUqRJCQkLQrFkzbN261e65H330EVq2bInixYujePHiaNeuXY7nkxdhAEWe8sUXwJ13SvAUGwssWCCJ4tbBU3Ky5ERVrSq9Ag8+KEHWxo0ylHfxonz4/fmndLHt3Cm3AaQ34Z13gJo1gd9/d/9zJM+wLmGQmwDK6IECmEDuBl4bnn755ZcYPXo03n//fTRr1gwzZ85E+/btcfDgQZSxMTa8du1a9OzZEy1atEBISAimTp2Ku+++G/v27UO5cuU88AzIaRhAkbspJT1CL74olzt3luG2IkUsz7t2TYbgpkzRtcn8/IC6dYHmzYEWLYAmTeR4QoIM/yUmygfhsmXSS2WIj5fut7lzgb59Xf0MydOsAyijRwqwHUApZdkDxfwn11NeqmnTpmrYsGFZlzMyMlTZsmXV5MmTc3X79PR0VaxYMfXpp5/m+jETEhIUAJWQkOBwe8mFfv5ZKUApk0m2xk9ysqdbRr7o+nWlevfW77Onn1YqPd3ynLQ0pWbPViomRp9XqZJSH3+slCP/P06eVGrWLKWaN7d8b/foIY9BvqtRI3mtly+Xy7Gx+vU/ciT7+RcuWL5HJk50a3MLOld8fnvlEF5qaiq2b9+Odu3aZR3z8/NDu3btsMn8G1sOkpOTkZaWhhIlStg9JyUlBYmJiRY/VADZmo0CsDQ1OV9CAnD33TJU5+8PvPeeDMWZZ7KfPQu0awc8+aS8BytUkF6ogweBAQMcy2MqXx546ikZ6lu3DihZUo5/+aVcx/VrfJNSlj1Q167JekWAlLew1btk9D4FBcmWPVAu55UB1IULF5CRkYEoq6GbqKgoxOdyCY+xY8eibNmyFkGYtcmTJyMiIiLrJzY2Nl/tJhcx3gfWVRY5jEfOlJYmxah++00KYP7wAzB0qOU5mzdLEvm6dVIoc84c4NAhYNAg/cGWV3fcIcN4994rl8+elWPPPQdkZubvvqlg+fdfCdYBmYVnPjRXs6btqadG/pMxO696dZc2kbw0gMqvKVOmYNGiRVi2bBlCQkLsnjd+/HgkJCRk/Zw0vgFQwVKqlO0pvQygyFmUkpIEv/4qeU5r1kixS/Pr33tPApozZ2Sa+bZtwBNP5D9wMhcQIIHbG2/oY5MnS/HNa9ec9zjkWUbvU0yMVKc3L8Zau7bt2xhBVkqKbBlAuZxXBlClSpWCv78/zp49a3H87NmziI6OzvG206dPx5QpU/Dzzz+jXr16OZ4bHByM8PBwix8qgAICJIiyxgCKnOXVV4F58yQB/MsvgcaN9XUpKcBjj0mwlJYmM+y2bpUgylWeeUbqRRlfHBYvlpl/Vv8TyUtZJ5AfOqSvy80MvGLF7Kc2kNN4ZQAVFBSExo0bY9WqVVnHMjMzsWrVKjRv3tzu7aZNm4ZXXnkFK1euRBNj5gv5Bs7EI1f53/+ACRNk/513ZM06Q1oa0KMHMH++BFfTpkkwU6yY5X0oBVy/LkMzthb0M5eUJB+gSUk5n9e9OzBjhr68ZQvQrBmwd2+unxoVUNY1oMx7oOrXt30b82G+6tVt98qTU3ltGYPRo0ejb9++aNKkCZo2bYqZM2fi6tWr6N+/PwCgT58+KFeuHCZPngwAmDp1KiZMmICFCxeiUqVKWblSRYsWRdGiRT32PMhJoqKyf3AwgKL8WrNGepcA4Nlngccf19dlZsp1y5dLYu/y5ZJgvnu3LM3y00+ytItRmiAtTW5XurRUFm/aFAgJkZ6DM2ekzs/x4xJkGSIjJRm4QgXJhbnnHklQNwokjhghwdbs2fKBefy4lEb48UdZNoa8k9HjZPRA/f23vq5hQ9u3Me+B4vCdezhtPp8HzJ49W1WoUEEFBQWppk2bqs2bN2dd16pVK9W3b9+syxUrVlQAsv1MdGCqJ8sYFGCPPGI5hRdQqk0bT7eKvNmhQ0pFRsp7qXt3pTIy9HWZmUo98YRcFxCg1FtvKTVmjFJVq2Z/H+blJyTE/nWlS8tjr18vbUpPV6pTJ7kuMFC2ERFK/fmnx351lE/Nmsnr+OWXcrlsWblcrJi896xlZioVGqrfIy+84N72egFXfH6blLpRfzIZEhMTERERgYSEBOZDFTSjRsmqsuZq1gQOHPBIc8jLpafLGnabN0vBy1WrgNBQff1zz0nytskkPQI7dujrQkIkwbxrV+kJMJZo2bwZeP11YNcufa6fn+UMumbNgOefl3X0kpJk6vqJE/Kzc6f0bF24oM+vUAF44QUZRrzzTmD7dnn869eB6GhgwwY9DETeQSnpeUxMlN7MGjXkvaeU9CraKl1x9qy83oZPPwX69HFbk72BSz6/nRaKFQLsgSrAJk/O/k29WDFPt4q81SuvyHsoPFyp48ctr5syRb/HAgL09qGHpMcgKcny/OPHlXrgAcvb3H+/UosXK3XtmlJ//aVUv376vgDpgdiyJXu7UlOVWrFCqT595P1tnF+vnjx2hQq63YD0iMXFue73RM53+rS8dn5+UrT1wAHLoq22bNok1/v7y3bjRve22QuwkCaRPUYSuXl9lKSkGyfiEln74w/g5Zdlf84c6eUxLFwIjBunL6enS07S7t0yO++hh6T+EwCkpgJTp8qsqWXL5L359NNSXHP5cqkpFRIis/XmzZNE4eHD5diWLcBtt0m5AvMeqsBAoEMH6WE4e1Z6XYsXl8fv0UPWPwsMlN6LkiUlP6pDB11TiAo+o9e8ShXJrTNPIG/UyPZtjPynjAzZ1qjhsuaRxgCKfIMRQPlZvaVZjZwckZwM9O4tgVH37kCvXvq6ffuAfv305QoVgCVLgJ9/zj61fM8eGdobN07u8/bbZQhu+nTbJTcASRafPVs+DLt3lzaMGSOFM22VJwgNlSTyQ4ek6rm/vxT5ND5Er16VIOrPP4H772edKG/x11+yNd5TuUkgN5+BV7y4rlhPLsUAinyDrTIGAGfikWPGjpUegJgY4P339VTws2clF8qYSTd2rHzQPfhg9uniP/4oM+H275cZd/PnS2Bz8825a0NUlPRmffCB9Eb99JNMXf/lF9vnlywJvP22zEK9917dY3X9unyYFismj//kkw7/OsgDrAOoP/6QbUCA/Z4lzsDzCAZQ5BuMACo93fI4AyjKrZ9+kjpPgAypGetknjghH2bGcPDHHwNTpkiFaGvvvAN06gRcuQK0bi0fhn37Ol6Tx2QCBg+WD886dSSAa9/esu6TtVq1gO+/B959V5c5OHxYEtNNJmDuXBn6o4LNOoAyyrNUqGB7CRcgew0ocgsGUOQboqLkQ4Lr4VFe/Psv8F8NOQwfrpdp+eMPoF49XZvpnXdkQWBrGRmy6O+TT+r6UD/9lP+hlDp1ZEmYwYPlvT16tORV2WMySa2qDRv0UOGvv0rvGSDX7dmTvzaRa1kHUCdOyDanHkz2QHkEAyjyDYGBtpcuYABFuTFxouTL1aypA5T166WUgZGAPWIEMGxY9ttevQp07iz5S4D0Tn38sfPWwAsNleHEiRPl8rhxwCuv5Hybpk3lg9hYAH3jRsmxunZNktc5uaJgSkjQeZu1asmQsfH+a9HC9m0yM6WAqoEBlNswgCLfUa5c9mMMoOhG9uyRYS9AZt2FhcmwSadOkkcESCD15pvZb5uaKnlQP/wg+UpLlkh+lLOX0TCZgJdekjX5AFla5sUXc14WplQpnYcFyIdssWKSlDxw4I2XlCH3M3qfypYFIiLkNTNepzZtbN8mLk7ehwYGUG7DAIp8R9my2Y8xgKKcKCU9SxkZUviybVsZMjGf+l+mjCzca51/kpkps/J++kmCrlWrJJhypeefl9IGgART48fnHAgVLQqsWKEDuqQkman61VcSLFLBYj18t2mTvq5ePdu3Mc9/AhhAuREDKPId7IEiRy1dKuvdhYRID9PFi5L/dPq0PufDDy2rPAM68PriC0nYXrrU/hCLsz3zDDBrluxPnQq89lrO5zdubDkDz5ilN3q0ZQV18jzrAOr332UbHi41oWwxz38qXVqqmJNbMIAi32GrB+r0aQ5VkG3XrklhS0DqLZUpI0uoHDig85e6dpX8JmuvvCIJ5SYT8NlnOuncXZ56SudcvfiiBHA5eeWV7F8w0tJkhqD58A95lnUA9eefsjVy2WzhDDyPYQBFvsP4gDAfarl+nVWYybY33pAck9hYCaR69JD16kJDJagoVkzqK1l77z2d0P3220DPnu5tt2H4cOkFA6T4p/kae9bCw/Vz8ffXBWf37r1xDxa5j3UAZfQu1a5t/zacgecxAZ5uAJHTGD1Qfn66GjMgw3js1iZzx4/LYsCAVAefPl1qKAUH63yhyZOz99r8+KOeiTdhggQxthw9KsMviYkSxKekyE96usyuatpUPuysK+c7avp0+dD9+WepNr5tm/2isg88IInx330nH8j798vxV1+V6xo0yF9bKH+uX9e9SUYAdfGibI0yFLawB8pjGECR7zACKOshu9Onc/4GR4XPs8/KB1arVlIw05jddvPNUvvp1luBoUMtb3PihPT0KAUMGiSz4gyJiZJL9fPP8mO+fpk9kZHALbdIoctevSSwclRAgFQtb9ZMZtc98IC0w1a+jMkkw46rV0vw9OijwP/+JzlR998v6+YFBjreBnKOv/+W1yIyUoLgc+d0YeC77rJ/O/ZAeQyH8Mh3GL0FrEZOOdm4EVi8WHp/JkzQQdFdd0nwFBAgiePmQ8GpqTLEd+kS0KSJ5B+ZTDKF/MknJXm3Sxcph3D4sNy2RQupufToo1J884knpJBlixaStH75sizP8uqr0uNw330S3DiasxcZKb1KkZEya8soumlLhQp6oeQffpByBgBw8qTtAqHkPubDdyaTBOIG67UWDenputAmwADKzdgDRb6jZElJ/rVOimUAReYmTJBtv34yiy0+Xnp/jCGtZ57JXvV5/HjJj4qMlBIAV65I8vY77+hFeqtVk2Tyu++WZVzCw+23IS1N6k9t3SplBr77TgKaH36Qde9GjwYeeUQvyXIjNWpIu+65R5Lamza1XfQTkLyp//1PcqYCAoDbbpPK5QsWyFp6Dz+cu8ck57LOf/rtN9kWK2Z/CZfTpy3TFapVc137KDtFuZaQkKAAqISEBE83heypVEkp+f6tf4YP93SrqKBYu1beE4GBSo0dK/uhoUoNHSr7VaoolZxseZtly/R76auvlHrpJaWKFdPHbr1VqVWr8teuQ4fkfRoWpu+3SROl9u517H7eektuGxKi1P799s9bt07O8/dXatcupUqVkssBAUodPpy/50J589BD8hq88YZcbtJELtesaf82a9bo90t0tFua6a1c8fnNITzyLSymSfYopXuf7rtPErABYNIk6bUBZGZeaKi+zT//SE8VIOvbTZkiuU9JSZJ0/f33MiR45535a1u1ajIsePKkJK8XLy7DiY0ayWXrYWl7RoyQXrDr1yWvyl6JgjvukCHHjAwpzrlhg/RypKdL75lRgZ3cx7oH6p9/LC/bYp7/VKOGS5pF9jGAIt/CYppkz5o1MiwSFARs2SLBQ8+ekrybnCwznR54QJ+fkiJ5TwkJskbe119L4cmSJYFFi4Dt24GOHZ27bEuJErLW3d69EuSlpgLPPSd5U8YQY078/IBPPpE27typyy3YMnWqDOH98IPk0Rjr6506xXwod8vIkPchIAHT1auSbwfIcKw9nIHnUQygyLfY6oE6dcr97aCCxbz3qUYNCaqrVgVGjQLmzpXjb7xhGQy99pr0AoWEAAcPSiDVvLkEJj165L8EQU7KlgW+/RaYP1/WRNu2TXqj5s/P3W0//FD2p07VuTTWatSQxHZA6mA9/bT+EF64EPjoo/w+C8qtY8ckYA8JkUWfd+/W1zVqZP92DKA8igEU+RZbPVBxcZaJllT4/PKLDFMFBUnvDiCB06uvytTxLl0kmdqwezfw+uuybwxnjR4NrFuXVRU6IwNYu1ZWc1m71gVvMZNJKoXv2yfJ4SkpQP/+MuR4o5l6XbvKkKNSMsvQXjHZCRMkMX73bkksN4YyAQmutm512tOhHBjDdzVrylDq9u36upwSww8d0vsMoNyOART5FqMHyrwnISNDZlpR4WTe+1S0qGwfe0x6kL79Vj6wjKKagOQB9emjI6KICFkq5c03s+okLV0KVKoEtGkjk+XatJHLN1pRJU/KlZNcq/Hj5fLEiVKHKi0t59vNnAlUqSLDc/YKfpYsCbzwguy/8AJQt64EbYD8Hh58EDh/3ilPg3Jgnf+0fr1s/fykR8qegwf1PgMot2MARb7F1nIugGWtFCpcVqyQnKfAQMkrKV0amDZNimkCUgvJvIjla6/pNcjKlJHyBWa5UUuXSnkn65Hh06fluEuCKD8/6RF77z3ZnztXil9euWL/NsWKSa+Sn59sv/7a9nnDh0ugFRcnifVTp+oSDKdOSZ5YbpPYKW+sA6iNG2UbHW2/lMWFC8C//+rLVau6rn1kEwMo8i1GD5Sx4rzh+HH3t4U8z7z3yehRmjVLEsq3bAGKFLGsKL51qy40GREh+UNmwVVGhkx0szWCZhwbOdKFI8ZDhwLffCMzBVeulErq587ZP795c91z9dRTUjHdWnCwzC4EJA8sI0P/DgBg1SrLHjpyPiOAqlVLXk8jOs9pBQUj6RwAypcHwsJc1z6yiQEU+RZ7ARR7oAqnn36SfBI/P3lPdOggw1JGUPHMM/ItHwDOnpVyBEpJrtTmzZKTYmb9+pznJCgllQiMERiX6NRJkq5Kl5ZZge3bS1Vze55/XnonzpzRwaS1bt0k2EpOlh64YcOAOnX09S+/rHtFyLmUsuyB2rBBX5dTCQMO33kcAyjyLUWL2q4AzQCqcDJqPWVmyjf0d9+V4azDh2V47umn5fpLl4DGjWX6OCCLBttYmy4uLncPm9vz8qxpU/mgjYqSiuKdOknwY0toqDxvQGpN7diR/RyTSfcyffSRjEfOnq2vy8iQulL2ktEp7+Lj5ffq5yczI3//XV+XU20n8x4o1oDyCAZQ5HtslTJgAFX47Nwpw0+GSZNkBp0xu27sWMkTSk+XWXinT8vxceOAtm1t3mVMTO4eOrfn5Uv16tLDFhEhH7rdutkvnHn33bJES2YmMGSI7THGVq3keaelSU2oNm3kPpWSIOzYMfvLw1DeGb1PVarIcKp5D1TduvZvxx4oj2MARb7HVikD5kAVPm++qffr15fkpS+/BI4ckdlnQ4bIdc8+q8fcateW0gZ2tGwp6Sb2ameaTBKjtWzppOdwI/XrSyHM0FBJlu/b134C1owZEmz98Qfw/vu2zzGKaX76qUyRnzxZkpivXZMeks8/lx48ch7z4bvkZHl9DObDqNbMe6ByypUil2EARb7HVg8UA6jC5eRJqRZumDFDAoDXXpPLo0dLAvm8eTLd3zB3rv2FWyFXzZol+9ZBlHF55swc78L5brtNpv4FBspzHj7cdpZ7dLTufXvuOdsV+ps3l+rqRiJ5tWqSuG7cHpD6UEeOuOa5FEZGXbLatWUSgxEAR0VJnpstGRmWNaCsF78mt2AARb7HVg9UQoLtGUjkm2bN0h9EnTrJcNSyZfJtPyJChqI2bdLBASAFnW699YZ33bUrsGRJ9rdZ+fJyvGtXJz6P3OrQAViwQKK499+XUgS2DBkC3HKL/C2MHm37nEmTZLtwoRTxfPFFyS08c0bywpKSJB/qRnWoKHd27pRtgwaW+U859T6dOKGHayMibP/PI5djAEW+x1YPFCC9EuT7EhKkXhIgvU7TpkmPjDE099RTEgQ88ID+EAoJ0VP5c6FrV0kJWrNG4ow1a2RVDY8ET4YePXTi93PPSZkDa/7+wAcfyO/lyy+BX3/Nfk6jRjJTUSkp2lmmDDBmjFyXnCyTNLZssR+kUe5lZOhlWxo2tAygcpv/dPPNzl2PkXKNART5HnvfxjiMVzh89JGekTZkiPSa/PijzFYrWlSOdekiZQuCguS8MWOylmjJLX9/oHVrqTPZurWbh+3sGTZMqpQrJQ07fDj7OQ0b6srko0fbzpl6+WX5UP76a+khGT1ahvBOnJACnoD0VBkFRylvDh6U/LKiRSWJfNMmfV1OAZR5/lNO55FLMYAi32P0QFkv9sqZeL4vLU1Pxw8OlkBAKZ0c/cQTwFtvSW2osDDpgSpbVvew+ILZsyWX6fJl6WWzVa184kRZA2/PHskDs1anjgxpAlI7qkgRXVxz5UrJk0pLA/r1sz/zj27MGL6rXx/Yv1+GVo3epJyG8Kx7oMgjGECR72ExzcJrwQKp6QRIAcnSpaWUwZYtMkzXtKkEUIBOtJ48WQIEXxEcLMlY0dGSoNy/f/ak8hIldFHNF1+0H2T5+8s6fFu2yPqBtWrJEiLVq8tMxl27dGI+Oc6oyWU+fGe8VrmdgcceKI9hAEW+x14RHgZQvk0pvTBuRIRe687IferbFxg1SvZr1ZKhkyZNgEcfdX9bXa1sWRl+CwyUYMpWvtKwYVKhPD5e8sSsVa8O9O4t+6+9JuUMjN69Dz7Qv9fXXrNdnJNuzOiBatTIMv8pNlbew/YYpQ8A9kB5UJ4CqJNMxqWCLDBQEl+tHTvm9qaQG337rS4BPnWq9Dht2gSsWyfvifPnZSJBhQrAgQNy3syZgJ8fMjJkdZQvvpCty9ayc6cWLSyTyq0TxoOCdGA1fbrtNWrGj5eh8O++k96mzp3lfq9dkxl63bvLL6tvXyAlxaVPx+copQMo6wTynHqfkpN10deYGKB4cde1kXKUpwCqVq1amDBhApLtLR1A5Gm2EsmPHnV/O8h9xo2TbalSkkgNSP0nQNdK8vMDKleWYw8+CNx2G5YuBSpVkkoHjzwi20qV5HSvN2QIMGCAfFj36QNcvGh5fdeuwO23S0D0/PPZb1+jhszuA6SnyWTSPU8ffiiBWenSMlRovgAx3dixY5KnFhgoSeSnTun8p5yG5czrP9Wr58oW0g3kKYD65Zdf8NNPP6F69eqYP3++k5tE5AS2ShnEx8uyHeR79u7VvUoTJkigdPy4DGMBeojpscekR8pkAiZNwtKlslqJdefL6dNy3CeCqLffliHLuDg9Q89gMumcsM8+k+R6a889J9uvv5ZE5zZtZNphaqrUnPrgA7l+6lTLKtqUM6P36eabpYAmIIEUkPsZeBy+86g8BVAtWrTAli1bMHnyZLz44oto3Lgx1rt0+XEiB9nqgcrMdMMqr+QRRkHMokX1FP3Zs+U1L1FCZjc1bqwjpUceQUbN2hgxwnbRbuPYyJE+MJwXFibFqgIDpZjoxx9bXn/LLXrG3dNPZ/+F1K0rPVVK6RwoY1bj3LlSALJnT/ldP/YYZ+Xllq3hO+MLXm5n4DGB3KPylUTep08fHDx4EB07dsQ999yDbt264SiHSaggsFdMk7WgfM/p08DGjbI/dKj0qiQlST0oQGblhYRIcLBypcwsmzgR69fbTvsxKCUpUz7x3bBhQ72My8iRlh/CgARGISHSO/fDD9lvbwzvLVwotaVuv10WKE5Pl2Bq1iyZlbdnj+2EdMrO1gy8a9fk/XvTTfZvxxIGBYZTZuHdfffdGDhwIJYtW4batWtjzJgxuGJrWiyRu9grpsmZeL7niSck2gkI0MuQzJsnvU5GdcuXXgI++UT2+/YFqlfPdWekz3Rajh4NtG0rSci9eln2FFWoIBXaAZnJaF0CpFEj4N575bhRsd34XX/2meTyvP22XH7lFctZYmSb0QNVrZpeDw+Qgpo5ldUwzvXzyznQIpfLUwD1/vvvY8CAAahXrx4iIiLQtm1brF+/HkOHDsWsWbPwxx9/oHbt2viD4+HkKfZ6oBhA+Zb4eKlTBEh18dBQGXMzVvzNyJBFWhs3lllogYFS9wj2q11Yy+15BZ6fH/DppzKkuX27rgNlGDNGlmn5808pfWDNKBHx6afyd9SsmV54eNIkGcbr2FECswEDnD726VMzJc+elcjcZJKAVimZ/ADkPHynlE4ij42V9zt5jsqD8uXLqwcffFC98cYbav369So5OTnbOa+99pqqU6dOXu6+wEpISFAAVEJCgqebQjeyc6dSgFJ+frI1fh5/3NMtI2fq10+/tocPy7FvvrF8zdesUaply2yvf3q6UuXLK2UyWZ5u/JhMSsXGynk+ZelS/QTXrbO87qWX5LqaNZVKS8t+27Zt5fphw+Ty9u36vvbvV+rECaWKFZNjb7/ttCZ//bW8VuavT/nyctwrrVghT6JWLaXGjZP9GjVk+9xzWaelp8vbd+FC2aafOat/AZ07e6r1XskVn995CqByIz4+Xvn5+bnq7j2CAZQXOXfO9qdi+/aebhk5y5kzSvn7y+t6yy36+B136Ne7d2+lfvpJ9oODlTp1yuIuvv5aPvutgyjjmNd+QN/IwIHyRKtVU+rqVX08IUGpEiXkuvnzs99uzRr9uzxzRo498IAce+ghufzuu3K5SBGljh3Ld1ON18hWgOu1r9Frr8mT6NlTqXr1LAOohQuVUraDxgdKr9cXJk707HPwMl4VQGVmZqq1a9e66u49ggGUF8nIUCowMPt/3erVPd0ycpYnntCv67ffyrEdO/Sx8HCl4uKUatpULo8cafNubH1QxcZ66Qdzbl2+rFS5cvJkn37a8rqpU+V45cpKpaRYXpeZqdRtt8n1Y8bIsd279S9u92752zN6/Nq3l9vkkdFLaOu7kFf3EnbrJk/g+ect36+AUn/+aTdoHICP9YXFiz39LLyKVwVQvogBlJepWDH7f6DQUE+3ipwhLk6pgAB5TaOi9Ceo8cEEKDVnjh4qCQ1VKj7e7t1lGyrxtg/kvPj+ez3MvXmzPn71qvxOAaXeey/77b77Tn/gX74sx7p3l2M9esjlgwellwpQasGCPDfR6PC60c+aNXl+CM+oWlUH9YBSjRrJ1t9fpV+9bjdonIJnsy6k7zvg6WfhVVzx+c218Mh32Uokv3YNSEhwf1vIuWbN0jVznnpKZtvFx+vCmTfdJFW4jbpFQ4cCUVF2787fX2pD9uwpW2Pynk/r2FHWATTqNxlLsYSF6bIFr7wifzPm7r1XEp0TE4H33pNjRoL5V19JQdMaNWQxYkDKJpw/n6cm+uRMyYQE4MgR2TeKvxr1nGrUwPqtwXbLazTETgBAGgLwe1xVFzeUboQBFPkue6UMWAvKuyUmAu+8I/sBAcDAgbI/YYJ8Nwdkav2WLcBvv8nMu9GjPdPWgm7mTFk3cv9+WarFMHiwlDY4c0aqjZvz8wPGjtW3v35dlhTp3Fl+/8b9PPOMHL94Mc+/f5+cKblrl2wrVJD3JyA1tACgTp0cg8GbIAHXMVTCmXMBrmsj5QoDKPJdLGXgmz74ADDqzHXpIgFAerpMrweAVq2AJk10vaLevYHy5T3S1AKvZElgzhzZnzxZShgAQHCwLnMwebL+fRseflgCgLNn9e/9v/IQWcU2AwOlmKnJBPzvf8BPPzncvJYt5aUzloizZjLJbP6WLR2+a88x6j+VLy8lDMqWBf79V47VrWs3GPRDBmJwBgDwJ+p5V9DooxhAke9iMU3fk5Ki124DpN4QIB/eRmHIefOk2OB338kn7Jgx7m+nN+nWTZZqSU8H+vcH0tLkeJ8+UuTx/Hng3XctbxMYKJXdAeCNN6QoU+PGutimMXTatKku0Dl0KHD1qkNN8/fXJb2sgyjj8syZXjbkagRQRiGre+8F9u2T/bp17QaNlXAMAZACp39HNPOuoNFHOT2A8vPzw5133ontthalJHInowfK+j8Rh/C81+efS64TIAHyXXdJ4GRUwb71VqByZVnYFpDAoGZNz7TVm8yZAxQvLh/uxu8yMFDnNr35pvSWmBswQHqwjhzRuWdGL9RnnwHHjsn+q69Kb9WxYzovygFdu0pdT+vvQ+XLy/GuXR2+S88ylnAx/g916KADqDp17AaNNaAXEW71ZD3vChp9lNMDqE8++QR33HEHhg0b5uy7JnKMEUBZ/6cxKvmSd8nMtFxnrV8/eW1ff11/uL/7LnD0qJSrBoBx49zeTK8UHQ1Mny77EyfKIoCALDJcuTJw7hzw4YeWtylSBHjySdmfMkXyn269VYLa9HQ9hFq0qE42nzEDyMMKFV27Svy1Zo2MEK5ZIy+z1wVP167pZW7i4yVIrVFD3r9BQdLjB9tBY23sy9q/bQgXES4QnDafrxBgGQMvc+CAnqZtPhe4Xj1Pt4zyYtkyy9fx0CGZRh8aqqs6KyVVsgGl2rXzaHO9TkaGrvH0wAP6+IcfyrGYGKWuXbO8zYULSoWFyfU//STHfvtNLgcFKXXypD63Z0853qCBUqmprn8+BdHWrfI7KFpUv0e//Vb269fPdrp5eY34Vv+V6AgJyVdtrcKqwJQxOHHiBJQx28UyGMMJ5pdQQREbK1vrhVHtzRGmgkspPSwHSKJ4tWoy48uYZv/yy5LUPHeuXB4/3v3t9GZ+ftJTFBAALFum1xjs21f+luLi9ILMhpIlgUGDZN94fVq2lNcnNdWyx3DmTFmHb9cuyzy2wsQYvgsKku299+rFgW2sgWdeXiMqbrccrFDBflY9uVWeAqjKlSvjvI26HpcuXULlypXz3SgipwgLA0qXzn783391oix5h/Xrgc2b9eXHHpNhppkz5XLx4sADD0j+zvXrkrzcpo1HmurVbr4ZGDVK9p98Ug8tGWULpkzRyfqG0aMl6Fq9Gti2TY4ZuVAffqhz1sqU0YHTSy8VzqH0LVtke/mybDt21EFVvXr2b6eUzilr2NBVrSMH5SmAUkrBZCMCvnLlCkJCQvLdKCKnqVgx+zGlgNOn3d8Wyjvz3qdixYAHH5QPaSMQHjZMeqKMKfnjxvFbel5NmCA9TseOSQI4IAnjMTEStH72meX5FSpIFwkgM/IA4M47gebNs8+a7NNHcqSuX5eeK+veYV+3fr1sMzOlB7VGDWDrVjnWrJn92x0/rgNXTr8rMEzK1licHaP/K4Y2a9YsDBo0CGFhYVnXZWRkYMuWLfD398eGDRuc39ICIDExEREREUhISEB4eLinm0O50a2bniFkbt064I473N8ectz+/ZbDG4MGASNGSG+JUhIoHT8OLF0qVa9r1pTb+LFKS55984306AUGypBb7dqSAD56tCSVHzwo1xn27JEeFD8/4O+/gapVgR9+AO67T5LIjx+X4TtAsr/r1pXerQ8+kKKdhUF8vGXFzxEjJNCPiZH3cEKCfDmwxXg9AOmxYi+Uw1zx+e3Qf5idO3di586dUEphz549WZd37tyJAwcOoH79+pg/f75TGkbkFOY9UOYfqMzV8x7GtHpjNuVjj0m+k/Hdr1MnmXFpzP0eOZLBU3517iy/17Q04Ikn5Hc9ZIgMiR89KlPhzN18s0zHz8zUPU733itB1ZUrunI8IAGY0bP17LNS7bww+P132Qb8V0H83nv1kGft2vaDJ0CmHQLyN1CXM/AKjLxknvfr169QzkTjLDwvNGuW7VU5X3nF0y2j3Lh4Uc+yA5SqXVupP/+0fC1//FHP0CteXBbDpfw7elT/7o0FgadMkcs1amRfcXn1ar1w87lzcmzRIjlWooRSSUn63PR0pW65Ra7r0qVwzCp76in9ni1SRKnr15V64QW53L9/zrc1fleVKrmnrT6owMzCmzdvHoewyDsYPVDW+TBGLRYq2D76SHKbjHQBo/fJULEicPfdMrwESC+JWWoB5SwjA1i7VspmrV2ri2MDACpV0oU0x4wBkpKkN6pECRmmW7LE8s5at5Zq5Oa5aN26AdWrA5cuyXCdwd8f+Phj6Y355hvbw+y+xuiBAoB27WS5HCP/qWnTnG/7939FNBs1ck3bKE8cyoEyTJo0KcfrJxhrKPkY5kB5oV27JF/A39/y06FpUz0jhgqmtDSgShVddsLfX9ZTa9dOn/PSSzLU1LixfBgfO2Z/CR+ysHSppOGYV/UoX15GQrMKVKakyJDR4cMy3DZtmgSwL70ENGgg+TjmX06++gro0UPKG5w4IcHsJ5/oJPR//gHMJxq98IKUooiKkrw1I0/K1yQmykxRI2l+wQKgVy95vpcvA9u32w+Orl6VPDKgcOWMOZlLPr/z0m3VoEEDi586deqosLAwFR4erho2bOi07rGChkN4XujSJdtDeDExnm4Z3ciXX8prZRRqvO8+Ge4xXkOTSaljx5Tq3VsuP/KIp1vsNb7+Wn591n8WJpP8fP212cnffy9XBgQo9ddflsUzV660vOO0NKUqV5br3nlHjqWkKBUbK8fee8/y/GvXpAAqoFSvXi59zh7100/6lxweLsPMf/8tl4ODcy4sahQmBZT65x/3tdnHFJghPPPk8Z07d2Lv3r2Ii4tD27ZtMcqoIUJUEERG2k7OPH9eJyFTwWQkhRuzvW67TYZ7DG3bSo2iRYvk8siR7myd18rIkJ4nW29/49jIkWYdth07yk96utywRAndC2Is12IICNCLDL/1ltwmKEh6rwApR5Gers8PCZHFn/38ZJ3D5cud9TQLFqN8ASA9dGFheviuUSPLGY3WfvxRtoGBMqxKBYbTpqqEh4fj5ZdfxotGATU3mDNnDipVqoSQkBA0a9YMW403pB2LFy9GrVq1EBISgptvvhk/Gm9M8l0mk+1aUOnpUlmZCqZt24CNG2XYzpjebXwImedDvfuuDPXddhtwyy2ea68XWb8+52L8Skm5J/PPfMycKYHQzz9LkPP00/KBvnatZYFTAOjfX4bw/vlHxgkBGcIrXVqGWI2A13DrrTroGjpU8qV8zdq1er9/f9nmNv/JKAsUG8vaZgWMU+f6JiQkICEhwZl3adeXX36J0aNHY+LEidixYwfq16+P9u3b49y5czbP37hxI3r27IkBAwZg586d6NKlC7p06YK9Rhl98l32ShkcPuz+tlDuGL1PVarItnVr+Sbu5yf1gyIjgfbtgfffl+vZ+5Rruf3eYHFetWrAM8/I/qhREiA9+qhctu6FCgsDhg+X/TfekIgsLExXOJ88OXsBzUmTgFq1pFbSiBEOPZ8CLzVV51tWqiQBI5D7AOrAAdk2aOCK1lF+5GXcb9asWRY/M2fOVGPHjlVly5ZVPXv2dNr4Yk6aNm2qhg0blnU5IyNDlS1bVk2ePNnm+Q899JDq2LGjxbFmzZqpIUOG5PoxmQPlpZ54QucQBAfr/U8+8XTLyJbTpyXfBlCqWDHZNmump3ED8pp+9JHsV6wouTeUK2vW2E4LtP5Zs8bqhleuKFW+vFz50kuSD2UkUu3bZ3nuuXO6BMLq1XLs8mWlIiLk2LJl2Ru2ebNe+Hv5cqc/b4/ZuFH/Ul9/XY6lpOj/RYcO2b9tZqb+nbz7rnva66Nc8fmdpwCqUqVKFj9VqlRRzZo1U+PHj1eJiYlOa5w9KSkpyt/fXy2z+iPs06ePuv/++23eJjY2Vs2YMcPi2IQJE1S9evXsPs7169dVQkJC1s/JkycZQHmjqVP1P7DAQL0/erSnW0a2PP+8vD5GcnFUlGz9/fXrt22bUnXqyP6bb3q6xV4lPV3iIFtJ5EYieWxs9jJPSimd2B8SInWiunaVy336ZD/X+OJyzz36mPHa3nKL7dpPY8bI9dHRUgPMFxjPCZAvB0op9ccfum5ZTjWwdu7Ut42Pd0tzfVWBSSI/evRo1s8///yDw4cPY/PmzXj99ddRLKdqqk5y4cIFZGRkICoqyuJ4VFQU4o2FK63Ex8c7dD4ATJ48GREREVk/sbGx+W88uZ/5EJ75IsK7d7u/LZSz69d1vSBjqnFEhGwbNZLXr359mRa+bx9QpIjk11Cu+fvrEVLrlBrj8syZuvC7he7dZTj1+nVJDDcWGV64UJZrMTd6tAy5rlih/9ZGjABCQyXHbdWq7Pf/8su+N5S3bJlsa9WSivmA5fBdTnlNxqSJoCAp9UAFSp5zoObOnYu6desiJCQEISEhqFu3Lj7++GNnts3jxo8fn5XXlZCQgJMnT3q6SZQX9oppMgeq4Fm8GLhwQT5odu6UY0YRwatXZWskjwOyOK0RYFGude0qdTCtS2aVLy/Hs+pAWTOZJPry85MTk5Nl4eD0dMtFgwFZD69bN9mfPl22pUvLWoYA8Prr2e8/JASYP1/u/3//k7pS3iwtDThyRPZ799bHc5v/9NtvsmVtswIpTwHUhAkTMGLECHTq1AmLFy/G4sWL0alTJ4waNcotRTRLlSoFf39/nD171uL42bNnER0dbfM20dHRDp0PAMHBwQgPD7f4IS9kBFDW87bj4ljKoKAxKlg3aSIfPkZhxVatpNBiUBDQpo3+Zv7EEx5ppi/o2lUmxa1ZIx1Ia9bIMnd2gydDvXpS8R2QXiKjRMFHH0nwa8647osv9PqTzzwj5Q7WrAE2bcp+/82aAc89J/tDhnj3upXz5umE+Sef1MdzG0AZKybUq+f8tlH+5WXcr1SpUmrhwoXZji9cuFCVLFky3+OKudG0aVM1fPjwrMsZGRmqXLlyOSaR33fffRbHmjdvziTywiAjQ6mgINsJHxcueLp1ZDDyQgIDlWraVPaNBNqHHpJt9+5KTZgg+3fc4ekWF14XLkj+DqDUnDlKNW6sk8ut3XmnXDdqlD722GNyrFMn2/efmqonDtxxh52ELC/QpIk8h3Ll9LGEBJ2AllNeU2am5P0BsqYn5UuBSSKPiIhQf//9d7bjBw8eVBEREfltU64sWrRIBQcHq/nz56v9+/erwYMHq8jISBX/3xuyd+/eaty4cVnnb9iwQQUEBKjp06erv/76S02cOFEFBgaqPXv25PoxGUB5sWrVLLNkjf3Nmz3dMjIMGKA/VM2D3JYtlSpZUva//VYSjAFJaCbPmT1bXoeSJZX6+GO9b72Y88qVcl3RorIygFJKHTyo/w5377Z9/4cPy23MZ695k3//1V8ABg3Sx41FlytWzPn2e/fqv4GjR13Y0MKhwCSR9+7dG++991624x9++CF69eqVrx6x3OrRowemT5+OCRMmoEGDBti1axdWrlyZlSh+4sQJxJkVMmnRogUWLlyIDz/8EPXr18eSJUvwzTffoG7dum5pL3mYeSK5sa4UoGuskGf9+6+MIwFAmTKyNWp2tW4NXLwoeVFXr0qCcXQ00KWLJ1pKhqFDgTp15LXZuROoXFn2582zPO/uu2UI6soVXberRg1JSAey15EyVK0KvPOO7E+YIInn3uSzz/TwnfFcgdwP3xnJ5wEBtosBk+flJeoaPny4Cg8PV3Xq1FEDBgxQAwYMUHXr1lXh4eFq+PDhatSoUVk/voQ9UF7MGDIAlCpTRu8/+aSnW0ZKKfXWW/J63HyzUjVq6NenYUO9/t2zz8pwDiDDeOR5v/6qS0w895zsV6mSvS7XggW6JMW1a3LMmKLv5ye9TbZkZurh22rVlEpKcunTcZrkZP1/xs/Pst1G6Yc33sj5Ptq2lfPKl3dtWwuJAtMDtXfvXjRq1AilS5fGkSNHcOTIEZQqVQqNGjXC3r17s9bI27Vrl1ODPaI8M/8GZ14Fec8e97eFLGVmAkaP9n336Vl3gCTe/vCD7N96q8xK8vfnivQFRdu2wAMPyMJ5GzdK0r/5Ei6GHj1kKZKzZ4EFC+RYgwbAvffK6z9tmu37N5mk1yo2VmbNPvWUS5+O07z3HmCsitGwoWWvd257oPbtk+3NNzu/feQcTgvFCgH2QHmx+fN1r4ZRIRlQqkIFT7eMjJXqw8OlR9B4bWrUUOqdd2S/QQOlHn9c9h980NMtJnNHjuiq2j16yLZx4+wFImfM0K+rkRS+fr0cCwpS6tQp+4+xdq3OmfroI5c9FadISlKqdGn9Pn76aX3d6dO2e6WspaTo5zt1quvbXAgUmB6oEydOQNmZ/n3Cm6ecku8y74G6dk3v21k7kdzIvKaTec/F2LFSCwgAHnpI91wMG+be9lHOqlTR6+Rt3iy1nLZvlzIF5gYOBIoXlx5GowzF7bcDd9wh68UZtaJsadUKePVV2R82TK8tVxDNng2cP69z+O67T19n5HHVrm3ZK2Xtzz91iZV27VzTTsq3PAVQlStXxvnz57Mdv3jxIipXrpzvRhE5nb0kzOvXgaQk97aFtBMngO++k/2mTYHTp2U/JkbqAW3eLB9ESkkS8k03SVI5FSzjx0uxx+PH9aK3b7xheU7RonqR4cmTdYDwwguy/eCDnL/QjB8vw4WpqcCDD8pkgoImIUE/78xMKfJ62236+o0bZXuj4bufftL7deo4t43kNHkKoJRSMNkoP3/lyhWEhITku1FETle+vP5GCFh++2NFcs/54AP5oGnTxrKo4siRwJdfyn779ron6okncl76gjyjSBEdOPz5p7xGK1dmXy7pqaeAsDDpofr1VznWrp0EFNeuATNm2H8Mkwn49FMJok+fll5J86WZCoIZM2RGacmScvmee4DAQH298Zxv9CXgl19kW7o0EBzs9GaSc5iUvbE4G0aPHg0AmDVrFgYNGoSwsLCs6zIyMrBlyxb4+/tjw4YNzm9pAZCYmIiIiAgkJCSwKrk3io0FTp2S/apV9RILH3/M9dQ8ITVVXpNz5yRYGjxYvsGHhMgHZOPGUir7xReBV16RD+nTp7l0S0GllAzH/f47UKGC9C4++qgeejWMHCnLwbRpA6xeLce+/Rbo3Fm+2Bw/rivQ23LwoARciYkyyeDtt132lBxy8aIMZyYmyvv65EkJ/I3SPhcuSIkOpYAzZ6SX1ZbMTFkH8upVSdI3gi7KF1d8fjvUA2XMrlNKYc+ePVmXd+7ciQMHDqB+/fqYP3++UxpG5HTmw3jmH8LGrBhyr2++keApJkY+OBMS5PjAgTID6dgxoFgxPSuvZ08GTwWZySTBjMmkl19ZtCj7UixPPy29MmvW6Fym++7TtaJmz875cWrW1EHZ7NnSK1UQTJ8uwdNNN0nw5O8vPVCGVaskeKpb137wBEivnbHu4513urbNlD95yTzv169foZyJxll4Xu6RR/TMmFtu0fu33+7plhVOxhIfL7yg1P3369fjn3+kcjMgr5kxw2vbNk+3mHJj8GBdedx6CRdD//5yXefO+tiXX8qx4sWVSky88eMYS/oEBkq1c086e1apsDBpj/H8rZcaMirt36g+4tSp+m9h3TrXtbmQKTCz8ObNm8chLPI+5j1Q5rkTx465vSmF3qFDMnxjMskq9StWyPE2beTb+VdfyeWICCAlRWrpNG7sufZS7r36qrxuV67I5Y8+krwgc2PHymu/fLmud/Tgg9K79O+/ui5YTiZO1HlQDzwgQ4eeoJQMPycny9Di8eNy3Hz2nVI6r+muu3K+v++/l62fnyyqTQVWQF5uNGnSpByvnzBhQp4aQ+RS5gGUMVwEyJRjcq8PP5TtPfcA69frgPb112VWXkKC5JEYOTKDBzN53FuULg1MmgSMGCHDWMYSLuPH63Nq1gS6dgW+/hqYOlWWPfH3B557DujbF3jzTZmxZ5Znm42fnwzlJSVJAN6xowwLNmrk+udobsYMCQSDgmQYzyg70KmTPufQIRnKDAqSPDF7rl+XmacAUKtWzs+fPC8v3VYNGjSw+KlTp44KCwtT4eHhqmHDhk7rHitoOITn5Vas0F3jwcFKBQToy8nJnm5d4XH9ulKlSsnvfflypWrVkv2yZeV6YzHhXr1kW6SIrGBP3iM1Vak6dfTfV3S0vO7m/vhDLwNjLJabmqpUpUpyfNas3D3W1auy4DQg76u//nLqU8nRhg36/8h77ym1dKnsV61qWUh0zhw53rp1zvdnLI0DKDVsmGvbXsgUmCE88+TxnTt3Yu/evYiLi0Pbtm0xatQo50Z4RM5i3gOVkmJ5+eBB97ensFq6VGYklSsnvQXGgs6jR8txYzjP6CXs2VNmJZH3CAzUCwEDUrPJKEVhaNxYhrMyMnQRzcBAYNw42Z82Tf5ObyQsTIa9GjeW90+7du4Zlj9/XoYQ09PlPTpkiK5p1qmTZY9pbofvjPMAy/pRVDA5LRRTSu3evVtVrFjRmXdZoLAHystduaK/3QFKtWql9995x9OtKzyM3/vEiUr16aMTgdPTlXr3Xblcr55OHt+61dMtprwyn7hRo4ZSGRmW169eLdeFhCh15owcu35dqXLlHP+7PH9eqZtuktvFxiq1Y4fznoe1jAyl2reXx6pZU5LeMzL0AsK//qrPTUuTZYpy815u0ED/voxeOXKKAtMDZU9CQgISzHNLiAqSIkV0gTvAslfDWGKBXOvAAWDdOslf6d8fWLJEjrdrJzkwn38ulytVkt6HBg2YSOvN3nhDF639+2+dIG1o3Rpo0UJyf4xCnMHBkgsFSE7c9eu5e6xSpaQHp0YNKSNw2226GKuzTZ4s1cJDQ4HFi6XcxrZtUpYjPBxo2VKfu22blDcoXjzn/KwLF6QIKSB5ZPZWT6ACI09J5G9bFS5TSiEuLg4LFizAPeZ1L4gKmooVpeAdYFmZ/K+/PNOewsZIHu/YUZLHk5Pl8qRJMuyyYYMMfRgzs4YMYfK4NytbFnj5Zan9BACvvQbcf7++3mSS2XTt28vMuzFjgOhoKWw7ZYoEQh99JAUzc6NcOakt1bOnVEJ/+GGpq/TKK5Z/73mlFPDJJ4AxUerdd4Gbb5Z9Izjs0EGSxQ3GsNydd8qXBHtWr9bL29x+O9/33iAv3VaVKlWy+KlSpYpq1qyZGj9+vErMTf0OL8UhPB/wwAO6i9zoggeUionxdMt837VrSpUoIb/v77+XoQ8j8VcppSZPlssNG8o2LIzJ474gNVW/1oBSGzdaXp+ZqVTz5tlrJL33nv7bdHSSR3q6Us8+qx+zU6f8v5euXlWqb199nwMHWl5fv74c/+wzy+O33y7H338/5/sfOFDf97Rp+WsrZeOKz+985UCdO3dOnT9/3lltKfAYQPmAkSP1P6kmTfR+UJCnW+b7FiyQ33WFCnoGFqDU00/L9XXryuVmzWQ7YIBn20vOs3atfr1tzURbuVIpQKUHh6ql78apNWuUSk9OkfcKoNTMmXl73AULdC5d2bKSY5eS4vj9HDig359+fhLsm+dznTihrzP/TExM1LP0jhyxf/+ZmUpVrKh/R+vXO95GylGByIG6fPkyhg0bhlKlSiE6OhpRUVEoVaoUhg8fjsuXLzu5f4zIyczzCo4elVwDQNZlS031TJsKiw8+kO3AgVLnxzBgALBnD7B3rwx97Nwpx4cMcX8byTVatdKFJdeuBfbvt7h66ZW7sT3oVvinXMM/T7yBNm2ASjWCsOOe5+WEKVNksWFHPfqoDBVXrCjrzz3xBFC9uqx/mZuFiDMzgYULJQ9v714ZXly9WmYKmg8JLlsm2+bNJRfLsHatzNKrUkV+7Dl8WBfg9Pdn0Vhv4Ui0dfHiRVWjRg1VpEgRNXjwYDVjxgw1Y8YMNWjQIFWkSBFVq1YtdenSJadFdwUNe6B8gFGnxfgx6scAUtOFXGPfPl3zZ+dO2Rr1cpRSatw4PfvO2JrX0SHvd+aM7o1p3jzr8NdfK2UyKdUeUqftKkJVGcQrk0mpIKSoK6Urym1mzMj7Y1+/rtTs2TIcaPy9V60qywgtWCCz4y5flnNPnlTqk0+U6tFDqZIlLXvO4uKy33dmpn7fvv225XVPPinHhwzJuX3G7FNAlpkip/P4EN6IESNU3bp1VXx8fLbr4uLi1M0336xGjhzptMYVNAygfMCOHfJPymSSbY8e+h/XlCmebp3vGjVKfsf336/Uyy/r3/krr8hQiDFUY2ytP4jINzz9tH7tt25V6elKlS9vHMpUmyDDt2/g6aw/02eLfyQnREVJHlJ+JCcr9eabSpUubflFyvgpXjz7sfBwpV58UcoR2LJ1qy7FYN2BYBSJXbIk53aZ52Y+9VT+niPZ5PEAqmLFimplDos2rlixgnWgqGBLSLD852gs8GkEU+R816/rb/LLlll+eB04IPkegFQcByRn5eJFT7eaXCEjQ6lixbJ6gNaszrT4c+yAHy16oQClApCqkqMryQlvvumcdiQlSa/PoEFSlyw6WjfCz0+pW2+VxYp//12S4HNiLHz96KOWx0+e1F/WchqZSUtTKiJCP/6iRfl9dmSDx3Og4uLiUKdOHbvX161bF/Hx8fkYUCRysfBwoEwZfdl8qjCrkbvGsmVSOqJ8eakubqw9WK+erIm2cKFcLldOtl27AiVKeKat5Fp+fpLPBABHjiBk0XyLq1eiA7agKcJwDc9AqpOnIxC7O70gJ0yZohcpzo+iRYHHH5eyGmvXAnFx8t7ctUvqMW3aJOUXbrtNqqPbc+UK8MUXsj9woOV1RvmCJk2kBpQ9f/xhuTZn8+Z5eUbkAQ4FUKVKlcKxHErkHz16FCX4j48KuurV9b55YuqpU+5vS2Fg1H7q3x8wryHXo4ck8n71lVw2fv/WH0TkW4YOzZq80WTBU4jEv2ZXmvASXgIADMMcxOAMAOD6Q32AatUk+H7rLde0KzwcqF8/52DH2pdfShBVvXr2RYKNIp4dO+Z8Hz/9pPfLlpVFtMkrOBRAtW/fHs8//zxSbcxWSklJwYsvvogOHTo4rXFELmEeQMXH66J3//5r+3zKu8OHgTVrpKevXj1gxw59XffuwM8/S+9UeLgU1axSRapTk+8y64UKuHYFH4SNtugIXokO2IAWCMM1vIyXEBsL3N4mUIpwAlKx/Nw5DzTcho8/lu3AgZa92fHxugfqkUfs314py2rpzZuzgKYXcSiAmjRpEg4ePIjq1atj2rRp+Pbbb7F8+XJMmTIF1atXx19//YWXX37ZVW0lcg7zAOqff/TljAyZ6kzOY3zAdOgALFqkjzdsKL93Y/iuSBHZPvaYcypGU8HWu3fWUPpDyfPRWq0xixtMGINpAIDHMBdzn/lLCnh36ybDYVeuAK++6pFmW9i7F9i8GQgIAPr2tbxu0SIpgdCsmeX/G2u7d8sqCMZ7nsN3XsWh/1Tly5fHpk2bULt2bYwfPx5dunTBAw88gOeffx61a9fGhg0bEMvuRyrozP+hnTghPSOGFSvc3x5flZoKzJsn+1266Fo5gKxif/Uq8M03cjkuTj5E+vVzcyMprzIyJH3oiy9km5HhwI0DA/V6dwC+jR6MajFXsy5vxG34KbQz/JGJu1aPl4N+fsDUqbL//vvy5ceTjC8H998PREVZXve//8n20Udzvg/jC4SRZ8UAyqs4/FWvcuXKWLFiBS5cuIDNmzdj8+bNOH/+PFauXIlq1aq5oo1EzmUeQGVkWP7zW7vW7c3xWd99J0MtUVHAoUPyjdzoZujeXa5PTgYiIuTYPffoRHIq0JYulfWe27SREao2beTy0qUO3MnAgUBkJACgaPxhHLj/WaxZIzHFmjVAu62TJWhavlzWSARkPbn27SV37sUXnfysHHD9OrBggexb5+wdOABs3y4FMXv0sH8fmZk6AT0lRYKonBYbpgInz33lxYsXR9OmTdG0aVMmjpN3sQ70jdXiAb0aOuXfRx/JtndvWYAVkJyPxo2BqlX1kJ5REZrJ415h6VIZTbOec3H6tBzPdRBVpAgwYkTWRb/330Prqz+gZ09Jg/Ove5NUqQeAZ5/VC+1OnizbhQt11Xp3W7YMuHRJEr7vvtvyus8/l22HDnqlA1t+/10WSw4Lk8uNGgEhIa5pL7kEkw2o8ClaFIiJ0ZfNkzaN5RQof44dkwRxQEoSXLqkPxy6dwcuX9bDpcnJ0kt1o9lK5HEZGRLzGLGMOePYyJEODOcNH64DCEBy4MwTxF96CQgNlbICxnBvw4Y6MXvcOMeegLMYw3ePPSY9TQalHB++M9JeWrRwbhvJ5RhAUeFk3gt15YrOQUhMzNuaW2Tpk0/kw+TOO3VPU0qKbLt3l2/wqam6969v35zr7VCBsH59ztU+lJJOlfXrc3mHpUrpNQ/DwiR4GjRIR2NlywKjR8v++PGyrhwAvPKKvF9+/hn49dc8PZc8O3JE1sMzmaQ0h7mNG+XLQ9GikhtlT2oqsHix7Buzf++6yyXNJddhAEWFk3ke1LFjQO3a+rKnhgV8RXq6HrJr2VJmGgUF6eG7KlV0UHX1v8Thxx7zTFvJIXFxzj0PAPDMM/L+SE6WoOjbb3UPDwCMGSOB1sGDwNy5cqxKFSmECQBjxzqYwZ5PRjmF9u0tFycHdO/Tgw9a9qxZ+/ln6ZUtVUqCxuBgWXCZvAoDKCqczAOoI0eApk31ZWPoifJmxQpJiClVSoInQOeCdO8uHxirVsllpYDbb5eK5FTgmY98O+M8ANLLZATQlSvLduRImXgASI0wI2F84kQZ/gWAF16Q63bs0AG7q+3ZA8yfL/svvWR5XWqqrumU2+E744tbq1Y5B1xUIDGAosLJOoBq2FBf3rTJ/e3xJUby+AMPSG8CIIUFAckyXrJEegyCg+WYkShMBV7LlrIij71ajyaTpPS0bOngHY8dK7lEf/8tvZTJyUCvXnrYd+hQoEYN4OxZCZwACcqNuoPjx0uPjquNGydBf7duUuPJ3IoVMhwXEyPTEu25ckVmFgIymw+QGajkdRhAUeFkHkBdvWrZFb9/v/vb4ytOnwZ++EFfzsgAatWSbcOGlrPvUlIkV6RbN8+0lRzm7w/MmiX71kGUcXnmTMu86lypVElmawIy6SAyEti2DRg2TAKWoCDgvffk+nffBbZulf3hw4G6daWa/fPPO/6EHLF6NfDjj1I48/XXs19vDN898kjOv4Bvv5UAsWpVnS7AFTy8EgMoKpysSxmYTx+Oi3NvToUvmTdP6tu0aAF8/TUAICldfrf/NO6OjGNWGcYPP2xZRoIKvK5dpRPRumRX+fJyvGvXPN7xuHEShf3yiwQofn6S8/Tuu3L9nXfK0JhS0iOVni7BzJw5cv0HH0j9JVfIzJRcLEAe27q6eEKC1DUDcj9817SplPCoVIlD2F6KARQVTmFhlp8AcXHyCQBI8HT4sGfa5c0yM3WS7003AZcu4bRfeYQe3gMAaP9xN7ze4L+Fg42lK5g87pW6dpW5F+aFL48ezUfwBEgQ8dBDsr9una46PmKEPAAATJ8uvVM7dwLvvCPH7rhDen2Ukh6pzMx8NMKOL7+U4KxYMdsFPD//XHpUa9eWBYntuXBBLx5sdNl16MD177wUAygqvKzzoMyrAP/xh/vb4+1+/VU+VSMikPCrDLFsyGyOAGRgF+rjMKrjnoT/Ki9nZsrQ3q23eq69lC/+/lLwMqvwpaPDdrYYy7t89RVw332SB5WRIZMPjh6VemFGYPXii7qmwhtvSE/m5s3Ap586oSFmUlJ0u8aOzVrDL8v163pIb+jQnIOhRYuk56xRI2DLFjnG/CevxQCKCi/zYbwjRywL2XFJF8f9lzyeeWdbRBzfg2SEogQksXcxuqMaDqEJtsOowZjZfwC/eZOlevWAzp2lN2nKFHlPNW4sOU5dukgC9sCBsmbclSsyWw+QmXwTJ8r+2LG6tpIzvPuufDEoWxYYNSr79R9+KLl/5ctLDSt70tKAN9+U/Y4d5X9OYGDOCedUoDGAosLLvAfqn38sZ+Jt2+b+9nizc+eyZhZdPpEEAFiMbmiFdf/td0cPyBRvE4B0+GNTtd4eaSoVcEYy+P/+J4HJN99Iz9Pu3UCfPtJ7+f770uX19dd60sKIETJ0fP6889bJ+/df4NVXZX/SpOylBpKTde/TCy/kvBTL//4ngVhUlF7/sWVLGRYkr8QAigov6yG8Bg30ZeZAOebTT+Ubdv36iNy5GgBwCDUQiHTsxs04hOroiS+yTv8e9+FESpS9e6PC7JZbgHvvlaG7l1+Wnp2vv5bemmXLJN/pppt0hfLHH5cSBoGBwOzZcuzdd3XeVF6lp8skh0uXJLepb9/s57z7rpRWqFQpe1Vy6/syAq1nnpEZfQBn33k5BlBUeJkHUHFxkkNhfBu8elXXLqKcKaUrR5crB7/MDKxBazSH1NNajO6oi72og/1Zw3dzMcCxYotUuEyaJNvPP5eyIrfdJlP8AgNlCZQePaT2U9WqsnZMv37yPmzbVi8F07evzI7Lq1GjpKhuWBiwYIHM+DOXlCTDjIAMHwYF2b+vRYvkS1nJktJWI7hjAOXVGEBR4VW1quXlo0clsdmwa5dbm+O1fvtNCiAWKZKVGLus+GO4C78AyD58F4do7C1/j+PFFqnwaNxYpvQppXOb7r9feqCCgmTbt68EWMHBUkLAyC966y1Z6uXkSeDJJ/P2+HPm6Fl+CxZYTjAxvP225GbVqJFz6YKMDL38y+jRUjn92jWZBVy3bt7aRwUCAygqvEJD9UrogAzjmVcX5ky83DEqjzdpIh8oFSqgzyPpCEIa9qIODqImHsairNMXoA/enBXgnFlb5LteflkmGSxZogtOduwohShDQiRomjRJZuABUkdq40bpSV6wQEplLFigF+3NrZ9/lnwqAJg82XZthsuXpaQCIAGede+Uua+/Bg4ckPILw4dLxXKA5Qt8AAMoKtysE8nvuENf3rDB/e3xNhcvygccoIc8n3gCTY4vBQD8FN4djbEd1XAka/iuwduP5a9eEBUOdetKjQQAmDBBH2/fXoKn0FCpDL5kifROZWTI0N6FCzKjdvx4OX/oUODMmdw95v79UjIhI0MS1seOtX3ejBkSRNWuLY9pT2amTkIfMULW7lu5Ui6zfIH3U5RrCQkJCoBKSEjwdFPIWYYMUUoGCpQaPlypw4f15ZgYT7eu4HvrLfldVa8u25AQpf75R6mgIKUAlb57nzrx0NNZv9PMFrd5usXkTQ4eVMrPT94/mzZZXrdmjVJFish1xYopFRUl+/fco1RGhlIpKUo1aiTH2rdXKjMz58fau1epKlXk/NtvV+r6ddvnnT8vjwcotXhxzve5bJlu36VLSh09Kpf9/ZX699/c/Q7IKVzx+c0eKCrcrGtBVa6su+Pj4qTWDNmmlCyfAehp2b16Sc9daipQuzb869RC7MYvs25iGsDK4+SAGjX07Dfr0gStW0s+UfPmktB99qwM261YIUNvQUEyhBcSItW/jSVhrCUnS29VgwbSC125suRYGYtdm0tPlzX7kpKk4nhOXalKAa+8IvvDhwPFi+vhuxYtZEiPvBoDKCrczIfwDh+Wf8DmeVG7d7u/Td5i/Xrg4EEZSjES7p98UuecdOsGbNqkq0WHhemlOohya8IEmX3366+yxIu5GjXkfThtmgRMxjIuL7wgt6tdW1cuHzVKlw8wrFghQ4VTpkhwdP/9MimiVCnbbRkzRobgQkOBTz7RSxLZsny5BHhhYboA5+efy7ZTJ8d+B1QgMYCiws06ByolBbj5Zn2MM/HsM3qfatWSD5877pBv78ZaX927y/RtAxcOpryoVEmqjwMSGClleb2/P/Dss5Jo3rixPv7KK1I9/OJF4O67pU7Z/ffL8YkTpdbUvffK7Nvy5aXXaflyvSamtblzJfcJAD77zPbMPMOpU7oq+ZNPAqVLyxe0DRsk6OrVK0+/CipgnDYYWAgwB8oHXbumc54ApfbsUWraNH15wABPt7BgOn8+K89JFS+u80E+/1z2a9VSKjVVqdKl9e9ywwZPt5q81alTkl8HKLV0qf3zUlOVmj1bqQoVLP+u7f34+ys1erRSSUk5P/66dUoFBsptXn4553PT0iSHClCqYUP5H6OUUi+8oHO0yO2YA0XkbCEhQMWK+vL+/VKMz7B5s/vb5A0++0zynCpWlOUuYmNlrTLz4bvffpNlNQAZamne3GPNJS9Xrhzw9NOy/8wz0lNsS2Cg5BsdP26ZMxUQIDlNRrHLkiXl+p07pX5UTj2j//wjuU5paTLj7kbLxEyYAPz+uxTl/eor+R+TmakXOe7XL1dPmQo+BlBE5sN4+/cDderoy3/9JVXJSVNKFlAFdM7J8OFSHNBIku3eHfhSJ49j4EDWvKH8GTcOiI6WgMZYsiUnkyYBs2bJfnq65N/99htQpowM623dalk415Z//pFhv4sXpc7ZvHk5v4+NBHZAhvyMSSpr1khhz8hIuT/yCQygiMwDqH375Jtq8eJyOTMzq7o2/WfdOp08fvKkbAcOlEVdU1Kkt6lmTfn2DUjOR28uHEz5VLSoXk/ulVd072ZOnnpKFh4GZEbenXdKAndoqOTq9e4tgb+18+elblOtWvI/oWxZyY8KDbX/WKdO6ff5sGHyJcIwf75sH3445wWHyaswgCKy7oECZCkIw++/u7c9BZ2RPB7132LAffoAJUpYDt+tWqXXIevYUXoOiPKrb1+gYUMgMdGyuGZOhgyRmXq33iolC+bOlaE8k0l6SZs2lUrhSknZkldekWWe3n5bhu3at5fZe2XL2n+MtDQJji5elORyo0o5IG39+mvZ5/CdT2EARWReC+rvv+WfoflsHgZQ2vnzwFKpMo4TJ2T71FPywfPjj3K5e3dg4UJ9G2MGFVF++fnpmXAffgjs3Zu7291+uyzz8vXX0kOakKBn8+3dC9x0k+RJlSghgVlSkvwP+PVXKVtQs6b9+z58GGjVSmbYhYfrvCfDkiXSy1WrlgRr5DMYQBHddJPeT0+Xf4jmq6Rv2iTHSRJhU1Ol9ykzE7jrLqm18+OPwPXrEozWqKGDrOLFuWQFOVerVpLUnZkpi/NalzWwx2SS2+3dC7z3npRHMF+QMTNTvjxVqSLlN7ZutZxQYs3IBWzQQP5HhIfL7awXKTeG7/r2ZR6gj2EARVS5smVuw/79lgHUlSssqAnIB4yRPJ6YKFtj0VXz4buVK3VeycCBMjOKyJmMwpm//KJ7PnMrMFDWxzt6VAKmxETgMbMK+aGh0rua0/p58fGSSzVkiEwyad0a2LMn+5eFw4dl+JB5gD6JARSRv7/lzLv9++WfaIkS+hgXFpbhjEOHZHji2jXJHbvnHvkA+eEHOad7d6nQbDD/YCJylqpVdfA+erT0fuaFySTlBubOlZ6isDBJGh8zBqhQQXqg5s6VCuKvvirv59atZTjuhx9kwslbb0nOX4UK2e//s89ke9ddUoqBfAoDKCLAsvr4vn2yrV1bH2MelF5LzMjveOopvfbYtWsy9FGtmq5E3qDBjaeJE+XV88/L5IS//5aSBfnVt6/MKv3gA6BlSxmiW71aelEffVTqP82bJ7NQExJkLbw//pBlWmwt6cLaTz4vwNMNICoQ6tbV+8ZMvLZtdeD0++/yD7Ww5jCcOAF8953sX74s+R7GIq/G8F337jLV28gXM3oIiFwhIkKC+q5dZUivW7ecl1fJjRIlgMGD5efoUZkM8e230jNVubJ8STC2t9yiFx63Ze1a+buJiAA6d85fu6hAMimV2ww8SkxMREREBBISEhAeHu7p5pAz/fKLrJcFSG7F1atSRM989o2xUnth9MILwGuvyQfMpUvyrfutt2RaeOnSst22TQpqbtkiv8NLl4AiRTzdcvJ1PXrIzLf69eU9WFBy7tq1k6G9oUMlaZ08yhWf3xzCIwIsh/BSUyVYqlHD8p9xYR3GS0kBPvpI9i9dkuGK4cPl8g8/SPBkfDPfulWOP/AAgydyj9mzZWmWP/8Epk71dGvEr79K8BQYCIwd6+nWkIswgCICZFp+qVL6sjGMFxurjxXWAGrpUuDcOT1TsWtXXWjUqDb+0ENS6dno0B4zxv3tpMKpTBm9ZMsrr+gcRk9RCnjuOdl//HEpl0A+iQEUESC5TbbyoG65RR8rrAGUkTxuLOBqLOp65YqefffQQ/q8smXzn4tC5IhHHgHuu096jwcMADIyPNeWZctkKLFIEUl0J5/llQHUpUuX0KtXL4SHhyMyMhIDBgzAlStXcjz/ySefRM2aNREaGooKFSrgqaeeQoKx1AQRYDmMZwRQ5gt/7t8vSzUUJrt3S+BoMsmsohYtZEkMQIKna9dk5l2ZMlLiAJCcDyJ3MplkzbvwcMnBmznTM+1IT9dB0+jR8ndBPssrA6hevXph3759+OWXX/D999/jt99+w+DBg+2ef+bMGZw5cwbTp0/H3r17MX/+fKxcuRIDBgxwY6upwLNVysC8oCYgy0EUJkavkjHb6Jln9HXmw3dvvSX7JhPw5JPuax+RoVw54M03ZX/8eKkO7m4LFsi6eiVK6J5a8l3Ky+zfv18BUNu2bcs6tmLFCmUymdTp06dzfT9fffWVCgoKUmlpabm+TUJCggKgEhISHGozeYmNG5WSDAalQkKUSk+X40WL6uNjxni2je50+bJSRYro5161qv6dJCbK7whQatcupcqUkf0mTTzbZircMjOV6tpV3ovR0UqdOuW+x752TanYWHnsN95w3+NSrrji89vreqA2bdqEyMhINGnSJOtYu3bt4Ofnhy1btuT6foypjAE51PFISUlBYmKixQ/5MPMcqOvXgWPHZN+8lEFhqki+YIGUczBmIo4apdcO++47+R3VqCHHzp2T40byLJEnmExSvLJuXVlupWvXvFcpd9T770shznLlgGHD3POY5FFeF0DFx8ejjNW4ckBAAEqUKIH4+Phc3ceFCxfwyiuv5DjsBwCTJ09GRERE1k+s+Yws8j3FilnOmDHyoFq10se2bXPfP2RPyswE3nlH9tPSZEjCvJqy+fDdSy/Jfmgo0KWLGxtJZEPRosA338hC1lu3ykw4V5c7TEqSOmkAMHGi5dqa5LMKTAA1btw4mEymHH8OHDiQ78dJTExEx44dUbt2bbxk/OO3Y/z48UhISMj6OXnyZL4fnwo4WzPx7rtPH0tNleUbfN1PPwEHD+oep8cf13WdEhNl+RZAAihj/557Cm+ldipYqlaVIN/PT9a4mz3bdY+lFPDEE8CFC9Ij27+/6x6LCpQCs5TL008/jX43WC+oSpUqiI6OxjljuOA/6enpuHTpEqKjo3O8fVJSEjp06IBixYph2bJlCLxBxdrg4GAEBwfnqv3kI26+Gfj+e9k3Aiiz4WIAMivt9tvd2y53mzFDthkZUlXcKJwJyNIWqamyzt2hQ1JIE5DFVokKinbtgDfekGTu0aPly9Gddzr/cV5/Hfjf/+TLxnvv5by8C/mUAvNKly5dGqVLl77hec2bN8fly5exfft2NG7cGACwevVqZGZmolmzZnZvl5iYiPbt2yM4OBjffvstQowFUYnM2SplUKyYLFdy/rxc/u03YNw497fNXfbtk6VtDL16yaKtBvPhu9dfl/2YGOCmm9zXRqLcGDUK2LlTApz77weWLMk+szY/liyRZY4AGfJ2RYBGBVaBGcLLrZtuugkdOnTAoEGDsHXrVmzYsAHDhw/Hww8/jLJlywIATp8+jVq1amHrf8tKJCYm4u6778bVq1cxd+5cJCYmIj4+HvHx8cjwZME1KnisA6jMTNk3Lwy5dq3UP/JVRlVng/l07MuXZXgPADp2BHbskH2WBKGCyGQCPvxQeqOuXpXh+PnznXPff/wB9Okj+yNGsP5ZIeR1ARQAfP7556hVqxbatm2Le++9F7fffjs+/PDDrOvT0tJw8OBBJP83tLBjxw5s2bIFe/bsQbVq1RATE5P1w7wmsmDMKgNkaOrECdm/6y59zrVrwOrV7m+bO1y4ILPvDF26AHXq6MvLl8vwXe3aUnFZKfmQ8uUeOfJuoaFS9PXRR2VIun9/WfIlP4nlp05Jj9a1a8C99+r6U1SoFJghPEeUKFECCxcutHt9pUqVoMz+OFq3bm1xmciuoCAZitq7Vy7v3y8z85o3tzzvu++kB8bXfPCB5SzD8eMtrzcfvpszR/YbNeLCwVSwBQUBn30GlC8PTJkCTJggJQfefdfxnKXz5yV4iouTvKovvtBfuqhQ8coeKCKXspUH1aCB5Tnff+/6qdHulpqqgyJAhj2aNtWXL14Efv5Z9mvW1Dlhzz7rvjYS5ZXJBEyeLO9xPz/go4+A226TSRHGUH1OUlIkKb1aNcmrKl1avkiFh7u+7VQgMYAismarlEFYmGWNqNOngV273Nkq1/vqK/lWbbBeCHXJElnrq0EDnUcSHAw8+KC7WkiUf088ASxdKn/TW7cCnTsD9erJ0HVaWvbzlQIWL5ae6TFjpIxHw4byZcL8fwIVOl45hEfkUuY9UMZQHgC0bKmrkwPy7bNhQ7c1y6WU0qULABmyNC8gCshQBQA88AAwaZLsd+zIadvkfTp3Bo4ckUWH331XZp726QO8+KIMSWdkyE9mJnDmDPDnn3K7smVl5mnv3tKLRYUa3wFE1swDqN279bfSW2+1PO+779zXJlf7/Xc9ow6QJVnMi2KePi3lGwD94QJwwVTyXtHRkg914oQERWXKAMePy+SIb7+VxPMVKyR4CguTivt//w307cvgiQAAJsXs6lxLTExERERE1jp65KMyMyWv4epVubxjh/Q07dgB/Fd7LMvp0/Kt1Ns98IAsfwHIcMauXZYB1FtvSbB0223ygXPyJFCypORBsfo4+YJr12SW6eXLkhRu/AQGAq1b+8bfeSHmis9v9r0TWfPzk16ozZvl8rZtEkDVrw9ERAAJCfrcH38EBg70TDudZd8+HTwB2XufAD18d+utekHlfv0YPJHvCA0FHn7Y060gL8J+SCJbzIfxjLXv/P2BNm0sz/OFYbwpU/R+9epAt26W1x86JL8Df3/g8GF9/LHH3NM+IqICiAEUkS3mAdS2bXrfeqmGX37x7qrk//wDmNdUGzs2e00bo/fpjjskLwSQgqO1a7unjUREBRADKCJb6tXT+3v26CDJugfK26uST5uma+BUraqXpjAopQOoEiWkjAHApVuIqNBjAEVkS6NGOr8nI0PXfKpTByhVyvLc7793a9Oc5swZ4JNP9OVJkyRh1tyffwIHDki9p/Xr5ZjJBDzyiPvaSURUADGAIrKlWDHLgppGHpTJlH0Yz1urkr/1li7RULeu7QRao/epQQPg3DnZb9NGlsQgIirEGEAR2WNe98k8D8p6GO/UKe+rSn7xIvDee/ryq69mr22TmQksWiT75jMP+/VzefOIiAo6BlBE9tgLoKx7oADvm4339ttAcrLsN20qi6Na27RJaj4VKSLDeIAUFOza1X3tJCIqoBhAEdnTrJneP3hQ1sACZKq/dVG9r77ynmG8pCRZwsLw+uu26zkZw3cxMfpY9+4SUBERFXIMoIjsuekmvdK6UnqpE+s8KJNJilFu3Oj+NubFe+/pYPDOO4G2bbOfk5oKfPml7B8/ro9bz9IjIiqkGEAR2ePnJ8NbBlt5UCaT7nn64AP3tS2vEhKkx8nw2mu2z1uxArhwQZLpjUTz2FhZ0oKIiBhAEeXIfBgvp0RyQIbxLl50fZvyY+pUnRB+333ZF0g2fPZZ9mNcgZ6IKAv/GxLlxDzAMEoZAEDlykClSrr3KTQUSEmxHXgUFKdPA2++Kft+fpY9UeYuXdJJ8UlJ+jiH74iIsjCAIsqJeQ/U0aMyrGUweqH8/XWl8g8+KLjJ5BMmSG4TAAwbZrlcjblFi2TYzjxZvFkzoGZN17eRiMhLMIAiyknp0kCVKvqyeS+UkUgeGSnbgACZrffbb25rXq4dOADMmyf7kZFSddweoxft6lV9jL1PREQWGEAR3Yi9YTyjB+rSJdkaa8oVxGTyUaN0z9hbb+mgz9rBg8CWLZZlDQIDgR49XN5EIiJvwgCK6EbsJZKXKyc1oZSShXiNAGrJEuD8efe2MScbNwIrV8p+/fpA3772zzV6n8yHIe+7DyhZ0nXtIyLyQgygiG7EXkVyQA/jGcN8QUGSPzR/vluadkNKAUOH6stz59qfSZeZCSxYoC8HB8s2p4CLiKiQYgBFdCMNGkhgBABxcTKbzWAUofznH6B4cZ2k/eGHukfKk5YvB/bskf1HHwUaN7Z/7rp1wMmT+nJKChAVBdx7r2vbSETkhRhAEd1IUBDQqJG+bJ4H1aGD9NQcOSJDXYAkkx8+DKxZ4952WktOBgYOlP2QEMvlW2z59FO9b+RI9esnOVBERGSBARRRbtgbxitWDLjnHtkvWlS26emyNWouecqwYbqw55QpOecxXb0quVsGY6mXAQNc1z4iIi/GAIooN8wTybdutbzuoYdk++uvQPv2su/nJ8uh/Pije9pnbcMGnYfVuDHw5JM5n79smS5bULKkDD+2bi1J8kRElA0DKKLcMO+B2rBB8oMM990nw3iHDuneKCNnauRInRflLmlpQJcush8cDPzww42XYPnkE71vzMAzhv+IiCgbBlBEuVGxIlCmjOwnJwObN+vrzIfxzp4FKlQArl8HIiIkqJo1y71tHTRIV0yfN08SwXNinq8VESF1rYoXBx580LXtJCLyYgygiHLDZLLshfr1V8vrjWG8JUuAIUNk3ygDMGmSzN5zh40bdTL43XcDPXve+DbmhT8rVJDto49K4jkREdnEAIoot3IKoMyH8Vq1AmJigHPnpNjmlSvAuHGub196up4JWLQo8M03N75NaqoOoIoWlSVfAA7fERHdAAMootxq0ULvb90KXL6sL5sP4/34ox62O3tWtp99Bmza5Nr2PfAA8O+/sr90KRAaeuPbLF4MJCXJfqtWkj/VtClQr57r2klE5AMYQBHlVvPmulRBZiawdq3l9cYw3uLFkj90zz3SKxQTI8effNJ1xTVHjgS+/172u3cH7rord7czFhUuWlR6zwD2PhER5QIDKKLcCgrSS7cAOQ/j7dkDvPOO5BHFxUlv0PbtwLvvOr9dU6fqHq/atYEvv8zd7fbsAf7+W/Z79pT9IkWAhx92fhuJiHwMAygiR3TooPetAyjzYbyvvpL18V58US77+8t2xAhg4ULnteeTT3R+VVSUFPk0mXJ3W6M2VGgocO2a7D/8sDwPIiLKEQMoIkcYhTIB4OBBy7XjAMthPKWAZ54BbrpJEslvukmG8Hr3BhYtyn9bli3Tw21FigA7dgBhYbm77fnzwG+/yX6vXhLwAVICgYiIbogBFJEjqlSxrM6d0zDe7t0y7Pf++3LdX38BnTpJEPXoozpocZRSwP/+B3TrJvv+/pKPVbZs7u/j8cfltgEBMlMwNVWSx80rrhMRkV0MoIgcldthPCMX6Y47ZFFeAFi/HujYEcjIAB55xHL9udw4dkzuv3dvnZD+xRdAkya5v4+LF3WJg06dgI8+kv2nnnKsLUREhRgDKCJHmQ/j/fpr9pl1RhL23LlSkRwAZsyQOlKXLwOrVkkyekaGJG+/8IIERjlJT5fFievUAX76SR9/5RVkdO2OtWsljlq7Vu42R2PG6JNatwbOnAGio2X2HhER5YpJKWPhK7qRxMREREREICEhAeHh4Z5uDnnK1auy1Elamlz+80/LuklpaUDVqpIf9f77ujL51atAjx56bbpmzXRtKJNJSg8MHAjcf78cO3xYClseOAB8/TWwc6d+jMBA4L33sLT4AIwYAZw6pa8qX14m5XXtaqPt+/cDdevK8F2TJjLEuHEj8NJLwMSJzvoNEREVKK74/GYA5QAGUJTlrrv08N2bbwKjR1teP3MmMGoUUK2aBEDGLLy0NEnUNpZb6dlTErrNhwKLFpX19uzVjKpYEVi6FEuPNcpKgzJnTMJbssQqiFJKhhN//10uT58uSe6BgcCJE9ILRUTkg1zx+c0hPKK8sB7GszZwoPRSHT5suaRKYKAs8Dt2rFz+4gsgPh4YMECCqZgYmbGXmSkz6qKiLMsK3HsvsGMHMuo3wogR2YMnQB8bOdJqOO/zz3XwVKmS9JwB0ivG4ImIyCEMoIjywjyRfN06ICXF8vqiRYFhw2R/6lTLSMdkAqZMkbyogABg717Jl/riC0nwrlNHZvIlJ8tSMElJMtT2yivAd98BJUpg/XrLYTtrSskI4vr1/x24fNmyl+zxx3WSO5PHiYgcxgCKKC/q1NFlA5KTgc2bs5/z5JNSiXzbNgmyrI0cKVXKFy0CHntMlxPYt08CsvLlZbhv6VIZ5nvhBcmdgtwsN7LOe+EFuQ8AKFVKgrLUVElsv+UWh546ERExgCLKG5Mp53IGAFCmDNC/v+xPm2b7fkqVkiG0uXOly2j/fqnxtGeP5CV9+KEsEmw1Zm8sr3cjMTGQJWTmzNEHhwyRxwN0NXIiInIIAyiivDIPoL791vY5Tz8tvUYrVkhhzZyYTFKtvFcvmSmXw5IsLVtKB5W9U0wmIDYWaNkiQ4brDMHBcsO4OMl76tYt5zYREZFNDKCI8qpdOx3B7N5tO0CqWlUHKW+84bSH9vfX6wdbB1HG5ZkzAf+P3pchxIAAOdi7N/Dxx7I/dKjkVhERkcMYQBHlVfHikkNkWLDA9nnPPivbL74Ajh932sN37SqlCsqVszxevvx/JQwq7ZAeMEBPx2vSRIb0wsKAJ55wWluIiAobBlBE+WE+jPe//0nFcGtNmujK46++6tSH79pVipivWQMsXCjbo0eBrm3+lZ6vlBSpG6WUrNM3f77c8PHHgdKlndoWIqLChAEUUX507qz34+NlmRZbjCrfH38MfP+9U5vg7y8rsvTsKVt/UybQp49EUhUqSCkEAGjTRmYLhoRIAU0iIsozBlBE+VG/PtCggb5sbxjvjjt0HabHHpNgy1WmTJEgLThYFh6+fh1o3BhYvlyuHzSIhTOJiPKJARRRfhmlCgCp2ZSUZPu811+XNfPOn5fbuGIVpVWrgBdflP1p0yTvCpDhu99+k0roY8Y4/3GJiAoZBlBE+dWrlwQmAHDtmiz8a0twsCQqhYQAK1cC77zj3HacOiXjeJmZsjTM8eNAYqL0kG3YIOf07y9Z5kRElC8MoIjyq2RJy1woe8N4gFQwN8oZPPusLOPiDIcPSwLU+fMSMI0ZowO0vn2l0Ke/PzBunHMej4iokGMAReQM5sN4a9ZIFXF7hg2TRYFTUoBHHpEcpfzYuhVo0QI4cgSoXFmGESdPlqVaWrfWVdJ795briYgo3xhAETnD3Xfr9VWUAj7/3P65JhPwySdSRmDPHuDBB4ELF/L2uN9/L7Przp8HGjUCNm6Utfk++0yu798f+OEHqYY+fnzeHoOIiLJhAEXkDAEBMlRmWLAg5yTxqCg5JygI+PFHSS5fvdqxx/zoIxk6TE4G2rcH1q6V2XXPPy95UF27Al99Jef26AHUqOHw0yIiItsYQBE5i/kw3l9/ScXvnLRvL8NvtWrJ2nTt2knwk5Zm/zaZmcDPP0vgNHiwXO7XD/juO6BYMemBWr5cepzat5fep4AAXYeKiIicggEUkbPUqCG5SIZ58258m/r1gT/+AAYOlB6r11+XmlHvvivDc3v2yEy6y5dl8btatSQwMhYvfvFFGQ4MDJTbG0ni/foBb74p+yNGADVrOvOZEhEVeialXFGMxjclJiYiIiICCQkJCA8P93RzqCD6+GMpVAnI8NyBA7lP3P7qK+lVSkjIfp2fn/Q2AdLT1K+frGVXq5Y+54cfpN6TUWn81VeBMmWAv/8GIiLy9bSIiLyZKz6/2QNF5EwPPQSEhsp+aqoMyTly2127ZAHgzp2Bhg2BEiXkusxMoG5d4L33gDNngLfftgyeEhNldh8gNaBmzZL9KVMYPBERuUCApxtA5FPCw4Hu3fUsuC++kCVcmjTJ3e0rVQKmT7c8duUK8O+/UgDTZLJ9u5EjpXBm5coy3JeUBNxyi2ViOxEROQ17oIic7YknLC8/+2z+lm0pWhSIjbUfPC1fLvlWJhMwdqwuofD22zL0R0RETueV/10vXbqEXr16ITw8HJGRkRgwYACuXLmSq9sqpXDPPffAZDLhm2++cW1DqXBq1kx6oQAJYNaulfwkVzh3TudcPf20Tlzv0we49VbXPCYREXlnANWrVy/s27cPv/zyC77//nv89ttvGDx4cK5uO3PmTJjsfZMncpYpUySJ3Ej8HjsWSE937mMoJUnn589LflS1asCWLdJjNWWKcx+LiIgseF0A9ddff2HlypX4+OOP0axZM9x+++2YPXs2Fi1ahDNnzuR42127duHNN9/EJ5984qbWUqFVpQrw1FOy7+8P7N+fu7IGjvj0Uxm+CwwEJk2SHigAmDBBV0UnIiKX8LoAatOmTYiMjEQTs6Tcdu3awc/PD1u2bLF7u+TkZDzyyCOYM2cOoqOjc/VYKSkpSExMtPghyrXnn5eFhjMy5PKECZIQ7gzHj+sA7YUX5OfqVeDOOyVpnYiIXMrrAqj4+HiUKVPG4lhAQABKlCiB+Ph4u7cbNWoUWrRogc6dO+f6sSZPnoyIiIisn9jY2Dy3mwqhyEjg5Zdl388PiI+XoCq/pddOngTuuktm2rVoIbWm9u+XXqeFC6XHi4iIXKrABFDjxo2DyWTK8efAgQN5uu9vv/0Wq1evxsyZMx263fjx45GQkJD1c/LkyTw9PhVigwdLvSYjF+rtt4Hnnst7EPXPP0DLlsChQ0DFikDHjlIqwd8f+PJLWWOPiIhcrsDUgXr66afRr1+/HM+pUqUKoqOjce7cOYvj6enpuHTpkt2hudWrV+PIkSOIjIy0OP7ggw+iZcuWWLt2rc3bBQcHIzg4OLdPgSi7wECp63TffRLkZGRIgndmpmwdmdBw4ADQtq0U0qxWDZg5UxYMBoDJkyWwIiIit/C6pVz++usv1K5dG3/88QcaN24MAPj555/RoUMHnDp1CmXLls12m/j4eFy4cMHi2M0334xZs2ahU6dOqJzLpTa4lAvliVLA3XcDv/4qhS6PHpXjzz4LTJ2auyBq924Ztjt3DqhdG1iyRHqfjh4F7r8f+OYbx4IxIqJChEu5ALjpppvQoUMHDBo0CFu3bsWGDRswfPhwPPzww1nB0+nTp1GrVi1s3boVABAdHY26deta/ABAhQoVch08EeWZySRDd5GREvBUrSrH33jjxkU2r1wB5s4F2rSR4KlhQ8lzeuQRua/KlYH58xk8ERG5mdcFUADw+eefo1atWmjbti3uvfde3H777fjwww+zrk9LS8PBgweRnJzswVYSmbnpJuCXX2RduiNHZAgOAN58U64bPhxYuhS4dEkCqq1bJX8qJgYYOFCO33qrBF0dOsiaeaVLy22KF/foUyMiKoy8bgjPkziER/m2bRvQrp0s/lujhvQipaXp600moGxZ4PRpfax6dVkgODoaGDoUuH5dCmd+952snUdERDniEB6Rt7vlFuDnn2XR4b//lmVfFiyQHqibbpLep9OngZAQ4NFHZRmY/fslaOrXT7YdOwIbNjB4IiLyIPZAOYA9UOQ0mzdLYnlSkiz50rYt8MADMkwXHy+9U9u2Ad9/D/z4oyzXAgCjRskwHms9ERHlmis+vxlAOYABFDnV5s0yNLd/vz5mMgF16gAHD1oO7UVGSuA0cKDbm0lE5O1c8fldYOpAERU6t94K7NsH/PUXsGyZ/PzxB7B3r1xfo4bUj7rvPuD226WmFBERFQjsgXIAe6DI5U6elJ6p+vUlgCIionxjDxSRr4uNlR8iIirQOAuPiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEMoIiIiIgcxACKiIiIyEEBnm6AN1FKAQASExM93BIiIiLKLeNz2/gcdwYGUA64ePEiACA2NtbDLSEiIiJHXbx4EREREU65LwZQDihRogQA4MSJE057AbxBYmIiYmNjcfLkSYSHh3u6OW7D583nXRjwefN5FwYJCQmoUKFC1ue4MzCAcoCfn6SMRUREFKo3niE8PJzPuxDh8y5c+LwLl8L6vI3Pcafcl9PuiYiIiKiQYABFRERE5CAGUA4IDg7GxIkTERwc7OmmuBWfN593YcDnzeddGPB5O+95m5Qz5/QRERERFQLsgSIiIiJyEAMoIiIiIgcxgCIiIiJyEAMoIiIiIgcxgLLj2LFjGDBgACpXrozQ0FBUrVoVEydORGpqao63u379OoYNG4aSJUuiaNGiePDBB3H27Fk3tdo5XnvtNbRo0QJhYWGIjIzM1W369esHk8lk8dOhQwfXNtTJ8vK8lVKYMGECYmJiEBoainbt2uHQoUOubaiTXbp0Cb169UJ4eDgiIyMxYMAAXLlyJcfbtG7dOtvrPXToUDe1OO/mzJmDSpUqISQkBM2aNcPWrVtzPH/x4sWoVasWQkJCcPPNN+PHH390U0udy5HnPX/+/GyvbUhIiBtbm3+//fYbOnXqhLJly8JkMuGbb7654W3Wrl2LRo0aITg4GNWqVcP8+fNd3k5nc/R5r127NttrbTKZEB8f754GO8nkyZNxyy23oFixYihTpgy6dOmCgwcP3vB2+f37ZgBlx4EDB5CZmYkPPvgA+/btw4wZM/D+++/jueeey/F2o0aNwnfffYfFixdj3bp1OHPmDLp27eqmVjtHamoqunfvjscff9yh23Xo0AFxcXFZP1988YWLWugaeXne06ZNw9tvv433338fW7ZsQZEiRdC+fXtcv37dhS11rl69emHfvn345Zdf8P333+O3337D4MGDb3i7QYMGWbze06ZNc0Nr8+7LL7/E6NGjMXHiROzYsQP169dH+/btce7cOZvnb9y4ET179sSAAQOwc+dOdOnSBV26dMHevXvd3PL8cfR5A1Kl2vy1PX78uBtbnH9Xr15F/fr1MWfOnFydf/ToUXTs2BFt2rTBrl27MHLkSAwcOBA//fSTi1vqXI4+b8PBgwctXu8yZcq4qIWusW7dOgwbNgybN2/GL7/8grS0NNx99924evWq3ds45e9bUa5NmzZNVa5c2e71ly9fVoGBgWrx4sVZx/766y8FQG3atMkdTXSqefPmqYiIiFyd27dvX9W5c2eXtsddcvu8MzMzVXR0tHrjjTeyjl2+fFkFBwerL774woUtdJ79+/crAGrbtm1Zx1asWKFMJpM6ffq03du1atVKjRgxwg0tdJ6mTZuqYcOGZV3OyMhQZcuWVZMnT7Z5/kMPPaQ6duxocaxZs2ZqyJAhLm2nszn6vB35u/cGANSyZctyPGfMmDGqTp06Fsd69Oih2rdv78KWuVZunveaNWsUAPXvv/+6pU3ucu7cOQVArVu3zu45zvj7Zg+UAxISEnJciHD79u1IS0tDu3btso7VqlULFSpUwKZNm9zRRI9au3YtypQpg5o1a+Lxxx/HxYsXPd0klzp69Cji4+MtXu+IiAg0a9bMa17vTZs2ITIyEk2aNMk61q5dO/j5+WHLli053vbzzz9HqVKlULduXYwfPx7Jycmubm6epaamYvv27RavlZ+fH9q1a2f3tdq0aZPF+QDQvn17r3ltgbw9bwC4cuUKKlasiNjYWHTu3Bn79u1zR3M9xhde6/xo0KABYmJicNddd2HDhg2ebk6+JSQkAECOn9fOeM25mHAuHT58GLNnz8b06dPtnhMfH4+goKBs+TNRUVFeN6bsqA4dOqBr166oXLkyjhw5gueeew733HMPNm3aBH9/f083zyWM1zQqKsriuDe93vHx8dm66wMCAlCiRIkcn8MjjzyCihUromzZsti9ezfGjh2LgwcPYunSpa5ucp5cuHABGRkZNl+rAwcO2LxNfHy8V7+2QN6ed82aNfHJJ5+gXr16SEhIwPTp09GiRQvs27cP5cuXd0ez3c7ea52YmIhr164hNDTUQy1zrZiYGLz//vto0qQJUlJS8PHHH6N169bYsmULGjVq5Onm5UlmZiZGjhyJ2267DXXr1rV7njP+vgtdD9S4ceNsJs2Z/1j/Yzl9+jQ6dOiA7t27Y9CgQR5qef7k5Xk74uGHH8b999+Pm2++GV26dMH333+Pbdu2Ye3atc57Enng6uddULn6eQ8ePBjt27fHzTffjF69euGzzz7DsmXLcOTIESc+C/KE5s2bo0+fPmjQoAFatWqFpUuXonTp0vjggw883TRyspo1a2LIkCFo3LgxWrRogU8++QQtWrTAjBkzPN20PBs2bBj27t2LRYsWufyxCl0P1NNPP41+/frleE6VKlWy9s+cOYM2bdqgRYsW+PDDD3O8XXR0NFJTU3H58mWLXqizZ88iOjo6P83ON0efd35VqVIFpUqVwuHDh9G2bVun3a+jXPm8jdf07NmziImJyTp+9uxZNGjQIE/36Sy5fd7R0dHZkonT09Nx6dIlh96zzZo1AyA9tVWrVnW4va5WqlQp+Pv7Z5sRm9PfZnR0tEPnF0R5ed7WAgMD0bBhQxw+fNgVTSwQ7L3W4eHhPtv7ZE/Tpk3x+++/e7oZeTJ8+PCsiTA36i11xt93oQugSpcujdKlS+fq3NOnT6NNmzZo3Lgx5s2bBz+/nDvsGjdujMDAQKxatQoPPvggAJndcOLECTRv3jzfbc8PR563M5w6dQoXL160CCw8wZXPu3LlyoiOjsaqVauyAqbExERs2bLF4RmMzpbb5928eXNcvnwZ27dvR+PGjQEAq1evRmZmZlZQlBu7du0CAI+/3vYEBQWhcePGWLVqFbp06QJAuvpXrVqF4cOH27xN8+bNsWrVKowcOTLr2C+//OLxv2VH5OV5W8vIyMCePXtw7733urClntW8efNsU9i97bV2ll27dhXYv2N7lFJ48sknsWzZMqxduxaVK1e+4W2c8ved1yx3X3fq1ClVrVo11bZtW3Xq1CkVFxeX9WN+Ts2aNdWWLVuyjg0dOlRVqFBBrV69Wv3xxx+qefPmqnnz5p54Cnl2/PhxtXPnTvXyyy+rokWLqp07d6qdO3eqpKSkrHNq1qypli5dqpRSKikpST3zzDNq06ZN6ujRo+rXX39VjRo1UtWrV1fXr1/31NNwmKPPWymlpkyZoiIjI9Xy5cvV7t27VefOnVXlypXVtWvXPPEU8qRDhw6qYcOGasuWLer3339X1atXVz179sy63vp9fvjwYTVp0iT1xx9/qKNHj6rly5erKlWqqDvuuMNTTyFXFi1apIKDg9X8+fPV/v371eDBg1VkZKSKj49XSinVu3dvNW7cuKzzN2zYoAICAtT06dPVX3/9pSZOnKgCAwPVnj17PPUU8sTR5/3yyy+rn376SR05ckRt375dPfzwwyokJETt27fPU0/BYUlJSVl/vwDUW2+9pXbu3KmOHz+ulFJq3Lhxqnfv3lnn//PPPyosLEw9++yz6q+//lJz5sxR/v7+auXKlZ56Cnni6POeMWOG+uabb9ShQ4fUnj171IgRI5Sfn5/69ddfPfUU8uTxxx9XERERau3atRaf1cnJyVnnuOLvmwGUHfPmzVMAbP4Yjh49qgCoNWvWZB27du2aeuKJJ1Tx4sVVWFiYeuCBByyCLm/Qt29fm8/b/HkCUPPmzVNKKZWcnKzuvvtuVbp0aRUYGKgqVqyoBg0alPUP2ls4+ryVklIGL774ooqKilLBwcGqbdu26uDBg+5vfD5cvHhR9ezZUxUtWlSFh4er/v37WwSN1u/zEydOqDvuuEOVKFFCBQcHq2rVqqlnn31WJSQkeOgZ5N7s2bNVhQoVVFBQkGratKnavHlz1nWtWrVSffv2tTj/q6++UjVq1FBBQUGqTp066ocffnBzi53Dkec9cuTIrHOjoqLUvffeq3bs2OGBVuedMT3f+sd4nn379lWtWrXKdpsGDRqooKAgVaVKFYu/c2/h6POeOnWqqlq1qgoJCVElSpRQrVu3VqtXr/ZM4/PB3me1+Wvoir9v038PTkRERES5VOhm4RERERHlFwMoIiIiIgcxgCIiIiJyEAMoIiIiIgcxgCIiIiJyEAMoIiIiIgcxgCIiIiJyEAMoIiIiIgcxgCIiIiJyEAMoIiIiIgcxgCKiAq9fv37o0qWL2x+3devWFqu1ExEZGEAREREROYgBFBF5ndatW+Opp57CmDFjUKJECURHR+Oll16yuH748OEYPnw4IiIiUKpUKbz44oswXzu9UqVKmDlzpsX9NmjQIOt++vXrh3Xr1mHWrFkwmUwwmUw4duxYrtr3xRdfIDQ0FHFxcVnH+vfvj3r16iEhISGvT5uIChAGUETklT799FMUKVIEW7ZswbRp0zBp0iT88ssvFtcHBARg69atmDVrFt566y18/PHHub7/WbNmoXnz5hg0aBDi4uIQFxeH2NjYXN324YcfRo0aNfD6668DACZOnIhff/0VK1asQEREhGNPlIgKpABPN4CIKC/q1auHiRMnAgCqV6+Od955B6tWrcJdd90FAIiNjcWMGTNgMplQs2ZN7NmzBzNmzMCgQYNydf8REREICgpCWFgYoqOjHWqbyWTCa6+9hm7duiE6OhqzZ8/G+vXrUa5cOceeJBEVWOyBIiKvVK9ePYvLMTExOHfuXNblW2+9FSaTKety8+bNcejQIWRkZLilfffddx9q166NSZMmYdmyZahTp45bHpeI3IMBFBF5pcDAQIvLJpMJmZmZub69n5+fRU4UAKSlpTmlbQCwcuVKHDhwABkZGYiKinLa/RJRwcAAioh80pYtWywub968GdWrV4e/vz8AoHTp0hZJ3omJiTh69KjFbYKCgvLUY7Vjxw489NBDmDt3Ltq2bYsXX3wxD8+AiAoy5kARkU86ceIERo8ejSFDhmDHjh2YPXs23nzzzazr77zzTsyfPx+dOnVCZGQkJkyYkBVcGSpVqoQtW7bg2LFjKFq0KEqUKAE/v5y/dx47dgwdO3bEc889h549e6JKlSpo3rw5duzYgUaNGrnkuRKR+7EHioh8Up8+fXDt2jU0bdoUw4YNw4gRIzB48OCs68ePH49WrVrhvvvuQ8eOHdGlSxdUrVrV4j6eeeYZ+Pv7o3bt2ihdujROnDiB+fPnW+RWmbt06RI6dOiAzp07Y9y4cQCAZs2a4Z577sFzzz3nuidLRG5nUtZJAEREXq5169Zo0KBBtjpPzjBx4kSsW7cOa9eudfp9E5H34BAeEZEDVqxYgXfeecfTzSAiD2MARUTkgK1bt3q6CURUAHAIj4iIiMhBTCInIiIichADKCIiIiIHMYAiIiIichADKCIiIiIHMYAiIiIichADKCIiIiIHMYAiIiIichADKCIiIiIHMYAiIiIichADKCIiIiIH/R8ZaN1wQLQtHQAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "post_output_cov_diag = np.diag(post_output_cov)\n", + "ax.plot(x_plot[0,:], post_output_mean,'r-')\n", + "ax.fill_between(x_plot[0,:], post_output_mean-2*np.sqrt(post_output_cov_diag), post_output_mean+2*np.sqrt(post_output_cov_diag), color='lightgray')\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "7EKeLD7nNa0j", + "outputId": "186dc930-7964-4a1e-b666-9caaa02490c7" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Fit the ReLU model" + ], + "metadata": { + "id": "fm7nIGqxDCC3" + } + }, + { + "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", + "# Transform intput data to ReLU basis functions\n", + "def nonlin_relu(x):\n", + " X_out = np.zeros((6, x.shape[1]))\n", + " X_out[0,:] = np.ones((1, x.shape[1]))\n", + " X_out[1,:] = ReLU(x-1.2)\n", + " X_out[2,:] = ReLU(x-0.6)\n", + " X_out[3,:] = ReLU(x-0.0)\n", + " X_out[4,:] = ReLU(x+0.6)\n", + " X_out[5,:] = ReLU(x+1.2)\n", + " return X_out\n" + ], + "metadata": { + "id": "qBE-YZ-jDBRb" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "x_plot = np.atleast_2d(np.arange(-2.,2.,0.04))\n", + "Z_plot = nonlin_relu(x_plot)\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[0:1,:]),'r-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[1:2,:]),'b-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[2:3,:]),'g-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[3:4,:]),'c-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[4:5,:]),'y-')\n", + "ax.plot(np.squeeze(x_plot), np.squeeze(Z_plot[5:6,:]),'m-')\n", + "ax.set_xlim(-2.,2.)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "rfNZEYAg_fW6", + "outputId": "5e06d02d-b7c0-491b-ccca-3d52571f13d7" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Define a prior over the parameters (2 dimensional as intercept + slope)\n", + "sigma_sq_p = 0.4\n", + "sigma_sq_n = 0.005\n", + "prior_param_mean = np.zeros((2,1))\n", + "prior_param_cov = sigma_sq_p * np.identity(2)\n", + "\n", + "# Prior mean and covariance for function, f\n", + "prior_func_mean = np.zeros((n_data, 1))\n", + "prior_func_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot\n", + "\n", + "# Prior mean and covariance for output, y\n", + "prior_output_mean = np.zeros((n_data, 1))\n", + "prior_output_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "zcDOa1L-B5lR" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function prior and plot them\n", + "np.random.seed(30)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(prior_func_mean), prior_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(x_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "GqjzMzsYLpCx", + "outputId": "bdb35cb9-2c9d-464f-e1a0-5af13ba533b2" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Transform training data\n", + "Z = nonlin_relu(X[0:1,:])\n", + "\n", + "# Posterior mean and covariance for function, f\n", + "inv_term = np.linalg.inv(Z.transpose()@Z + (sigma_sq_n/sigma_sq_p) * np.identity(Z.shape[1]))\n", + "post_func_mean = Z_plot.transpose() @ Z @ inv_term @ y\n", + "post_func_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot - sigma_sq_p * Z_plot.transpose() @ Z @ inv_term @ Z.transpose() @ Z_plot\n", + "\n", + "# Posterior mean and covariance for output, y\n", + "post_output_mean = Z_plot.transpose() @ Z @ inv_term @ y\n", + "post_output_cov = sigma_sq_p * Z_plot.transpose() @ Z_plot - sigma_sq_p * Z_plot.transpose() @ Z @ inv_term @ Z.transpose() @ Z_plot + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "VUFQhgofLrei" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function posterior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(post_func_mean), post_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(x_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-2.,2.)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "X58kHDFtMmJK", + "outputId": "143f8ef9-65ff-4d49-ca8c-8e5957e09dd7" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "post_output_cov_diag = np.diag(post_output_cov)\n", + "ax.plot(x_plot[0,:], post_output_mean,'r-')\n", + "ax.fill_between(x_plot[0,:], post_output_mean-2*np.sqrt(post_output_cov_diag), post_output_mean+2*np.sqrt(post_output_cov_diag), color='lightgray')\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "YIFtN_kKM6-x", + "outputId": "288e2712-f757-4b3d-a0f3-833c7c764f81" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "# Gaussian kernel regression" + ], + "metadata": { + "id": "-fo4ggLyOob5" + } + }, + { + "cell_type": "code", + "source": [ + "def gaussian_kernel_one(x_i, x_j):\n", + " return np.exp(-0.5 * (x_i-x_j) * (x_i-x_j)/0.25)\n", + "\n", + "def gaussian_kernel(X1, X2):\n", + " K = np.zeros((X1.shape[1], X2.shape[1]))\n", + " for i in range(X1.shape[1]):\n", + " for j in range(X2.shape[1]):\n", + " K[i,j] = gaussian_kernel_one(X1[0,i],X2[0,j])\n", + " return K" + ], + "metadata": { + "id": "uahupUlxN8vy" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Define a prior over the parameters (2 dimensional as intercept + slope)\n", + "sigma_sq_p = 0.4\n", + "sigma_sq_n = 0.005\n", + "prior_param_mean = np.zeros((2,1))\n", + "prior_param_cov = sigma_sq_p * np.identity(2)\n", + "\n", + "# Prior mean and covariance for function, f\n", + "prior_func_mean = np.zeros((n_data, 1))\n", + "prior_func_cov = sigma_sq_p * gaussian_kernel(x_plot, x_plot)\n", + "\n", + "# Prior mean and covariance for output, y\n", + "prior_output_mean = np.zeros((n_data, 1))\n", + "prior_output_cov = sigma_sq_p * gaussian_kernel(x_plot, x_plot) + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "5q5OKtSTPnGD" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function prior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(prior_func_mean), prior_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(x_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "eQBEap4qRFNL", + "outputId": "a2d71f52-cb2a-4a47-ae4b-e2cd264be7c7" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "# Posterior mean and covariance for function, f\n", + "inv_term = np.linalg.inv(gaussian_kernel(X[0:1,:], X[0:1,:]) + (sigma_sq_n/sigma_sq_p) * np.identity(X.shape[1]))\n", + "post_func_mean = gaussian_kernel(x_plot, X[0:1,:]) @ inv_term @ y\n", + "post_func_cov = sigma_sq_p * gaussian_kernel(x_plot, x_plot) - sigma_sq_p * gaussian_kernel(x_plot, X[0:1,:]) @ inv_term @ gaussian_kernel(X[0:1,:], x_plot)\n", + "\n", + "# Posterior mean and covariance for output, y\n", + "post_output_mean = gaussian_kernel(x_plot, X[0:1,:]) @ inv_term @ y\n", + "post_output_cov = sigma_sq_p * gaussian_kernel(x_plot, x_plot) - sigma_sq_p * gaussian_kernel(x_plot, X[0:1,:]) @ inv_term @ gaussian_kernel(X[0:1,:], x_plot) + sigma_sq_n * np.identity(n_data)" + ], + "metadata": { + "id": "0IWgyKyyRH4q" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "# Draw samples from the function posterior and plot them\n", + "np.random.seed(5)\n", + "function_draws = np.random.multivariate_normal(np.squeeze(post_func_mean), post_func_cov, 5).T\n", + "\n", + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "for i in range(function_draws.shape[1]):\n", + " ax.plot(x_plot[0,:], function_draws[:,i].transpose(), 'r-')\n", + "\n", + "ax.set_xlim(-2.,2.)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "M68DxpzpS-yp", + "outputId": "d44f8271-f3e7-4ea8-c4ee-e19e1d4752e7" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "code", + "source": [ + "fig,ax = plt.subplots()\n", + "ax.plot(X[0,:],y,'bo')\n", + "post_output_cov_diag = np.diag(post_output_cov)\n", + "ax.plot(x_plot[0,:], post_output_mean,'r-')\n", + "ax.fill_between(x_plot[0,:], post_output_mean-2*np.sqrt(post_output_cov_diag), post_output_mean+2*np.sqrt(post_output_cov_diag), color='lightgray')\n", + "ax.set_xlim(-2,2)\n", + "ax.set_ylim(-0.5, 0.5)\n", + "ax.set_xlabel('Input, $x$')\n", + "ax.set_ylabel('Output, $y$')\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 452 + }, + "id": "4ne57tXsTU86", + "outputId": "d8712f47-3773-49aa-88ba-9108268faf76" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ] + } + ] +} \ No newline at end of file From e8fca0cb0ae51c1c73fefe5ac13abde6e6fcb794 Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Mon, 15 Apr 2024 14:34:23 -0400 Subject: [PATCH 06/23] Added notation explanation --- Notebooks/Chap09/9_4_Bayesian_Approach.ipynb | 32 +++++++------------- 1 file changed, 11 insertions(+), 21 deletions(-) diff --git a/Notebooks/Chap09/9_4_Bayesian_Approach.ipynb b/Notebooks/Chap09/9_4_Bayesian_Approach.ipynb index 25eac22..b5d77f9 100644 --- a/Notebooks/Chap09/9_4_Bayesian_Approach.ipynb +++ b/Notebooks/Chap09/9_4_Bayesian_Approach.ipynb @@ -1,18 +1,16 @@ { "cells": [ { - "attachments": {}, "cell_type": "markdown", "metadata": { - "colab_type": "text", - "id": "view-in-github" + "id": "view-in-github", + "colab_type": "text" }, "source": [ "\"Open" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "el8l05WQEO46" @@ -159,7 +157,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "i8T_QduzeBmM" @@ -195,7 +192,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "JojV6ueRk49G" @@ -211,7 +207,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "YX0O_Ciwp4W1" @@ -277,7 +272,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "GjPnlG4q0UFK" @@ -334,7 +328,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "GiNg5EroUiUb" @@ -343,17 +336,16 @@ "Now we need to perform inference for a new data points $\\mathbf{x}^*$ with corresponding hidden values $\\mathbf{h}^*$. Instead of having a single estimate of the parameters, we have a distribution over the possible parameters. So we marginalize (integrate) over this distribution to account for all possible values:\n", "\n", "\\begin{align}\n", - "Pr(y^*|\\mathbf{x}^*) &=& \\int Pr(y^{*}|\\mathbf{x}^*,\\boldsymbol\\phi)Pr(\\boldsymbol\\phi|\\{\\mathbf{x}_{i},\\mathbf{y}_{i}\\}) d\\boldsymbol\\phi\\\\\n", - "&=& \\int \\text{Norm}_{y^*}\\bigl[[\\mathbf{h}^{*T},1]\\boldsymbol\\phi,\\sigma^2\\bigr]\\cdot\\text{Norm}_{\\boldsymbol\\phi}\\biggl[\\frac{1}{\\sigma^2}\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\mathbf{H}\\mathbf{y},\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\biggr]d\\boldsymbol\\phi\\\\\n", - "&=& \\text{Norm}_{y^*}\\biggl[\\frac{1}{\\sigma^2} [\\mathbf{h}^{*T},1]\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\mathbf{H}\\mathbf{y}, [\\mathbf{h}^{*T},1]\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\n", - "[\\mathbf{h}^*;1]\\biggr]\n", + "Pr(y^*|\\mathbf{x}^*) &= \\int Pr(y^{*}|\\mathbf{x}^*,\\boldsymbol\\phi)Pr(\\boldsymbol\\phi|\\{\\mathbf{x}_{i},\\mathbf{y}_{i}\\}) d\\boldsymbol\\phi\\\\\n", + "&= \\int \\text{Norm}_{y^*}\\bigl[[\\mathbf{h}^{*T},1]\\boldsymbol\\phi,\\sigma^2\\bigr]\\cdot\\text{Norm}_{\\boldsymbol\\phi}\\biggl[\\frac{1}{\\sigma^2}\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\mathbf{H}\\mathbf{y},\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\biggr]d\\boldsymbol\\phi\\\\\n", + "&= \\text{Norm}_{y^*}\\biggl[\\frac{1}{\\sigma^2} [\\mathbf{h}^{*T},1]\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\\mathbf{H}\\mathbf{y}, [\\mathbf{h}^{*T},1]\\left(\\frac{1}{\\sigma^2}\\mathbf{H}\\mathbf{H}^T+\\frac{1}{\\sigma_p^2}\\mathbf{I}\\right)^{-1}\n", + "[\\mathbf{h}^*;1]\\biggr],\n", "\\end{align}\n", "\n", + "where the notation $[\\mathbf{h}^{*T},1]$ is a row vector containing $\\mathbf{h}^{T}$ with a one appended to the end and $[\\mathbf{h};1 ]$ is a column vector containing $\\mathbf{h}$ with a one appended to the end.\n", "\n", "\n", - "\n", - "To compute this, we reformulated the integrand using the relations from appendices\n", - "C.3.3 and C.3.4 as the product of a normal distribution in $\\boldsymbol\\phi$ and a constant with respect\n", + "To compute this, we reformulated the integrand using the relations from appendices C.3.3 and C.3.4 as the product of a normal distribution in $\\boldsymbol\\phi$ and a constant with respect\n", "to $\\boldsymbol\\phi$. The integral of the normal distribution must be one, and so the final result is just the constant. This constant is itself a normal distribution in $y^*$.
\n", "\n", "If you feel so inclined you can work through the math of this yourself.\n", @@ -404,7 +396,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": { "id": "8Hcbe_16sK0F" @@ -419,9 +410,8 @@ ], "metadata": { "colab": { - "authorship_tag": "ABX9TyMB8B4269DVmrcLoCWrhzKF", - "include_colab_link": true, - "provenance": [] + "provenance": [], + "include_colab_link": true }, "kernelspec": { "display_name": "Python 3", @@ -433,4 +423,4 @@ }, "nbformat": 4, "nbformat_minor": 0 -} +} \ No newline at end of file From d17e47421b26e8fb3c25334e3ccabd9e2f93e62e Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Mon, 15 Apr 2024 16:01:38 -0400 Subject: [PATCH 07/23] Improved implementation of softmax_cols() --- Notebooks/Chap12/12_2_Multihead_Self_Attention.ipynb | 5 +---- 1 file changed, 1 insertion(+), 4 deletions(-) diff --git a/Notebooks/Chap12/12_2_Multihead_Self_Attention.ipynb b/Notebooks/Chap12/12_2_Multihead_Self_Attention.ipynb index 7e9b0b3..ebbeb68 100644 --- a/Notebooks/Chap12/12_2_Multihead_Self_Attention.ipynb +++ b/Notebooks/Chap12/12_2_Multihead_Self_Attention.ipynb @@ -4,7 +4,6 @@ "metadata": { "colab": { "provenance": [], - "authorship_tag": "ABX9TyMSk8qTqDYqFnRJVZKlsue0", "include_colab_link": true }, "kernelspec": { @@ -147,9 +146,7 @@ " exp_values = np.exp(data_in) ;\n", " # Sum over columns\n", " denom = np.sum(exp_values, axis = 0);\n", - " # Replicate denominator to N rows\n", - " denom = np.matmul(np.ones((data_in.shape[0],1)), denom[np.newaxis,:])\n", - " # Compute softmax\n", + " # Compute softmax (numpy broadcasts denominator to all rows automatically)\n", " softmax = exp_values / denom\n", " # return the answer\n", " return softmax" From 569749963bf93610485622fef1e0a87eb99d982f Mon Sep 17 00:00:00 2001 From: udlbook <110402648+udlbook@users.noreply.github.com> Date: Mon, 15 Apr 2024 16:41:54 -0400 Subject: [PATCH 08/23] Add files via upload --- UDL_Answer_Booklet.pdf | Bin 0 -> 1792553 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