{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian Linear Regression\n", "\n", "In this notebook, we see how Bayesian linear regression algorithm (including the evidence approximation) described in chapter 3 of PRML can be implemented. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.linalg import eigh\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12\n", "\n", "# to make this notebook's output stable across runs\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 Setting\n", "\n", "* Let $N \\in \\mathbb{N}$ be the number of data points.\n", "* Let $d \\in \\mathbb{N}$ be the dimension of the input.\n", "* Denote input data as $x_0, x_1, \\dots , x_{N-1} \\in \\mathbb{R}^d$, and output data as $t_0, t_1, \\dots, t_{N-1} \\in \\mathbb{R}$. \n", "Also, let $\\boldsymbol{t} = {}^t (t_0, t_1 \\dots, t_{N-1}) \\in \\mathbb{R}^N$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Theory\n", "\n", "## 2.1 Model and design matrix\n", "\n", "### 2.1.1 Model\n", "\n", "We assume the following model: \n", "$$\n", "\\begin{align}\n", " p(t|x,w,\\beta) = \\mathcal{N}(t|w^{T}\\phi(x),\\beta^{-1})\n", " = \\sqrt{\\frac{\\beta}{2\\pi}} \\exp\\left\\{-\\frac{\\beta}{2} \\left[ t - w^{T}\\phi(x) \\right]^2 \\right\\},\n", "\\end{align}\n", "$$\n", "where\n", "* $\\beta > 0$ is the precision of the Gaussian distribution, which is a hyper parameter, \n", "* $\\phi : \\mathbb{R}^d \\rightarrow \\mathbb{R}^M $ are basis functions which we specify later, and $\\phi(x) := (\\phi_0(x), \\phi_1(x), \\dots, \\phi_{M-1}(x))^T$ with $M$ being the number of basis functions, \n", "* $w \\in \\mathbb{R}^M$ is a parameter (weight).\n", "\n", "The model means that the output $t$ is the sum of a function of $x$ and a noise $\\varepsilon \\sim \\mathcal{N}(0,\\beta^{-1})$.\n", "\n", "We also assume that, given the inputs $x_0, x_1, \\dots, x_{N-1}$, the output $t_0, t_1 \\dots, t_{N-1}$ are generated independently according the above model with $x$ being the corresponding input data.\n", "\n", "For the later convenience, let tha matrix $\\Phi$, which is called a design matrix, be\n", "$$\n", "\\begin{align}\n", " \\Phi = (\\Phi_{i,j}), \\ \\ \\Phi_{i,j} = \\phi_j(x_i). \n", "\\end{align}\n", "$$\n", "Note that the shape of $\\Phi$ is $N \\times M$.\n", "\n", "### 2.1.2 Basis functions and design matrix\n", "\n", "As basis functions, we use Gaussian basis functions in this notebook, where we set\n", "$$\n", "\\begin{align}\n", " &{} \\phi_0 (x) = 1 \\\\\n", " &{} \\phi_j(x) = \\exp\\left[ -\\frac{(x-\\mu_j)^2}{2 s^2} \\right] \\ \\ (j = 1, \\dots, M-1), \n", "\\end{align}\n", "$$\n", "where $\\mu_j$ and $s$ stands for the center and the width of each Gaussian, respectively, which are assumed to be given." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Bayesian linear regression\n", " \n", "### 2.2.1 Posterior distribution of the parameter $w$\n", "\n", "From the model described in the previous section, the likelihood is given by\n", "$$\n", "\\begin{align}\n", " p(t_1, \\dots, t_N | w, \\beta) = \\prod_{n=1}^{N} \\mathcal{N}(t_n|w^T\\phi(x_n), \\beta^{-1}). \n", "\\end{align}\n", "$$\n", "\n", "As a prior for $w$, we take\n", "$$\n", "\\begin{align}\n", " p(w|\\alpha) = \\mathcal{N}(w|m_0,S_0), \n", "\\end{align}\n", "$$\n", "where $m_0 \\in \\mathbb{R}^M$, and $S_0$ is a $(M,M)$ real positive-definite symmetric matrix.\n", "\n", "With this prior, the posterior distribution becomes (see (3.49)-(3.51) of the book):\n", "$$\n", "\\begin{align}\n", " &{} p(w|t_1, \\dots , t_n) = \\mathcal{N}(w|m_N,S_N) \\\\\n", " &{} m_N := S_N (S_{0}^{-1}m_0 + \\beta \\Phi^T t) \\\\\n", " &{} S_N := \\left( S_{0}^{-1} + \\beta \\Phi^T \\Phi \\right)^{-1} \\\\\n", " &{} \\Phi = (\\Phi_{i,j}), \\ \\ \\Phi_{i,j} = \\phi_j(x_i)\n", "\\end{align}\n", "$$\n", "In particular, if we set $m_0 = 0$, $S_0 = \\frac{1}{\\alpha} I$, where $\\alpha > 0$, we have:\n", "$$\n", "\\begin{align}\n", " &{} m_N := \\beta S_N \\Phi^T t \\\\\n", " &{} S_N := \\left( \\alpha I + \\beta \\Phi^T \\Phi \\right)^{-1}\n", "\\end{align}\n", "$$\n", "From now on, we assume this form of $m_0, S_0$. \n", "\n", "### 2.2.2 Predictive distribution\n", "\n", "From the posterior distribution of $w$, we can compute the predictive distribution of $t$ (see (3.57)-(3.59) of the book)\n", "$$\n", "\\begin{align}\n", " p(t| x, \\boldsymbol{t}, \\alpha, \\beta)\n", " & := \\int dw \\ p(t|x, w,\\beta) p(w | \\boldsymbol{t}, \\alpha, \\beta) \\\\\n", " & = \\mathcal{N}(t| m_{N}^{T} \\phi(x), \\sigma_{N}^{2}(x)) , \n", "\\end{align}\n", "$$\n", "where\n", "$$\n", "\\begin{align}\n", " \\sigma_{N}^{2}(x) = \\frac{1}{\\beta} + \\phi(x)^T S_N \\phi(x)\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 Empirical Bayes approximation\n", "\n", "In empirical Bayes method (or evidence approximation), we determine hyper parameters from our data, \n", "by selecting hyper parameters that maximize a quantity called evidence (or marginal likelihood).\n", "\n", "### 2.3.1 Evidence\n", "\n", "The evidence $p(\\boldsymbol{t}|\\alpha,\\beta)$ is given by (see (3.86) of the book):\n", "$$\n", "\\begin{align}\n", " \\log p(\\boldsymbol{t}|\\alpha,\\beta) \n", " &= \\frac{M}{2} \\log \\alpha + \\frac{N}{2} \\log \\beta - E(m_N) - \\frac{1}{2} \\log\\left|\\alpha I_M + \\beta \\Phi^T \\Phi\\right| - \\frac{N}{2} \\log ( 2\\pi) \\\\\n", " E(m_N) &:=\n", " \\frac{\\beta}{2} \\| \\boldsymbol{t} - \\Phi m_N \\|^2 + \\frac{\\alpha}{2} m_{N}^{T} m_{N}\n", "\\end{align}\n", "$$\n", "\n", "Note that $m_N$ depends on $\\alpha, \\beta$.\n", "\n", "\n", "### 2.3.2 Optimization with respect to $\\alpha, \\beta$\n", "\n", "By differentiating the log of evidence, we obtain the stationary conditions (see (3.91), (3.92), (3.95) of the book) : \n", "$$\n", "\\begin{align}\n", " \\lambda_i &: \\ \\mbox{Eigenvalues of } \\beta\\Phi^T \\Phi \\\\\n", " \\gamma &:= \\sum_{i=1}^{M} \\frac{\\lambda_i}{ \\lambda_i + \\alpha} \\\\\n", " \\alpha &= \\frac{\\gamma}{m_{N}^{T} m_{N} } \\\\\n", " \\beta &= \\frac{N-\\gamma}{\\| \\boldsymbol{t} - \\Phi m_N \\|^2}\n", "\\end{align}\n", "$$\n", "\n", "Note that $\\gamma$, $m_N$ depends on $\\alpha,\\beta$.\n", "As was mentioned by the textbook, later we solve these equations iteratively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 From math to code\n", "\n", "## 3.1 Overview \n", "\n", "We define \n", "* A function that generates a design matrix.\n", "* A `BayesianRidgeRegression` class representing the bayesian linear regression estimator, with `fit` and `predict` method.\n", "\n", "## 3.2 Generating design matrix\n", "\n", "Here we consider how to write a function that generates the design matrix $\\Phi$ from input data and $\\mu_j$ s and $s$.\n", "\n", "In the following codes, we vectorize the calculation of $\\phi_j(x)$, which is a little bit tricky, so let's take a closer look.\n", "\n", "The $(n,m+1)$ component of $\\Phi$ can be expressed as ($X$ stands for 'X', and $\\mathcal{M}$ stands for params['mus'])\n", "\n", "\\begin{equation}\n", " \\Phi_{n,m+1} = \\exp\\left[ -\\frac{1}{2 s^2} \\sum_{i=1}^{d} \\left(X_{n,i} - \\mathcal{M}_{m,i} \\right)^2 \\right]\n", "\\end{equation}\n", "\n", "Because we can apply 'np.exp' elementwise, it suffices to consider the quantity\n", "\n", "$$\n", "\\begin{align}\n", " A_{n,m} &:= \\sum_{i=1}^{d} \\left(X_{n,i} - \\mathcal{M}_{m,i} \\right)^2 \\\\\n", " &= \\sum_{i=1}^{d} X_{n,i}^{2} + \\sum_{i=1}^{d} \\mathcal{M}_{m,i}^{2} - 2 \\sum_{i=1}^{d} X_{n,i} \\mathcal{M}_{m,i}\n", "\\end{align}\n", "$$\n", "\n", "Then, we can calculate the (N,M-1) array A with numpy broadcasting (see the following code):\n", "\n", "* 1: First, `-2*(X@(mus.T))` creates a (N,M-1) array, which corresponds to the third term of the above equation.\n", "* 2: Then, `np.reshape(np.sum(X**2, axis=1), (len(X), -1))` create a (N,1) array, which corresponds to the first term of the above equation. The array will be added to the (N,M-1)array created earlier, where numpy broadcasting take care of matching the shape of the array (Note that the reshape command is required here).\n", "* 3: Finally, `np.sum(mus**2, axis=1)` create a (M-1,) array, which corresponds to the second term in the above equation. When the array is added to the (N,M-1) array, broadcasting takes place too." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def gen_desmat_gaussian(X, params):\n", " \"\"\"\n", " This function generates a design matrix with basis function being Gaussian.\n", " \n", " Parameters\n", " ----------\n", " X : 2-D numpy array\n", " (N,d) numpy array, with X[n, i] = i-th element of x_n\n", " \n", " params : dictionary\n", " Dictionary of parameters of Gaussian basis function with\n", " params['mus'] : (M-1,d) numpy array. params['mus'][j] being the center of the jth Gaussian\n", " params['s'] : double. positive real number, which stands for the width of Gaussians\n", " \n", " Returns\n", " ----------\n", " Phi: 2-D numpy array\n", " (N,M) array, with Phi[n, m] = $\\phi_m(x_n)$\n", " \n", " \"\"\"\n", " \n", " s = params['s']\n", " mus = params['mus']\n", " Phi = np.zeros((len(X),len(mus)+1))\n", " Phi[:,0] = np.ones(len(X)) # the 0-the basis is a constant\n", " A = ( -2*(X@(mus.T)) + np.reshape(np.sum(X**2, axis=1), (len(X), -1)) ) + np.sum(mus**2, axis=1)\n", " Phi[:,1:] = np.exp(-A/(2*s*s))\n", " return Phi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.3 Bayesian regression\n", "\n", "Next, we define our estimator. We require the estimator to be capable of\n", "* calculating the posterior mean and variance given training data and hyper parameters $\\alpha$ and $\\beta$\n", "* calculating predictive variance given input $\\Phi$, and\n", "* performing evidence approximation.\n", "\n", "\n", "### 3.3.1 Posterior parameters\n", "\n", "For the first aim, we define `calc_posterior_params` method, which calculates posterior mean $m_N$ (`self.m`) and posterior covariance matrix $S_N$ (`self.S`) according to\n", "$$\n", "\\begin{align}\n", " &{} m_N := \\beta S_N \\Phi^T t \\\\\n", " &{} S_N := \\left( \\alpha I + \\beta \\Phi^T \\Phi \\right)^{-1}\n", "\\end{align}\n", "$$\n", "\n", "### 3.3.2 Prediction\n", "For the second aim, we define `predict` method, which returns predictive mean $m_{N}^{T} \\phi(x)$ and predictive standard deviation $\\sigma_{N}(x)$ according to\n", "$$\n", "\\begin{align}\n", " \\sigma_{N}^{2}(x) = \\frac{1}{\\beta} + \\phi(x)^T S_N \\phi(x)\n", "\\end{align}\n", "$$\n", "\n", "Assuming the input $\\Phi$ is a $(N_{test}, M)$ array, we want the `predict` method to return two $(N_{test}, )$ arrays `pred_mean` (corresponding to $m_{N}^{T} \\phi(x)$) and `pred_std` (corresponding to $\\sigma_{N}(x)$)\n", "\n", "To vectorize the calculation, note that these quantities can be implemented by matrix multiplication.\n", "\n", "### 3.3.3 Empirical Bayes\n", "\n", "We first define `calc_evidence`, a method for calculating the evidence\n", "$$\n", "\\begin{align}\n", " \\log p(\\boldsymbol{t}|\\alpha,\\beta) \n", " &= \\frac{M}{2} \\log \\alpha + \\frac{N}{2} \\log \\beta - E(m_N) - \\frac{1}{2} \\log\\left|\\alpha I_M + \\beta \\Phi^T \\Phi\\right| - \\frac{N}{2} \\log ( 2\\pi) \\\\\n", " E(m_N) &:=\n", " \\frac{\\beta}{2} \\| \\boldsymbol{t} - \\Phi m_N \\|^2 + \\frac{\\alpha}{2} m_{N}^{T} m_{N}\n", "\\end{align}\n", "$$\n", "Note that we do not need the function for the optimization with respect to $\\alpha$ and $\\beta$.\n", "\n", "Then, we define `empirical_bayes` which performs the optimization with respect to $\\alpha$ and $\\beta$ by solving the following self-consistent equation iteratively.\n", "$$\n", "\\begin{align}\n", " \\lambda_i &: \\ \\mbox{Eigenvalues of } \\beta\\Phi^T \\Phi \\\\\n", " \\gamma &:= \\sum_{i=1}^{M} \\frac{\\lambda_i}{ \\lambda_i + \\alpha} \\\\\n", " \\alpha &= \\frac{\\gamma}{m_{N}^{T} m_{N} } \\\\\n", " \\beta &= \\frac{N-\\gamma}{\\| \\boldsymbol{t} - \\Phi m_N \\|^2}\n", "\\end{align}\n", "$$\n", "\n", "\n", "### 3.3.4 Code" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "class BayesianRidgeRegression:\n", " \n", " def __init__(self, alpha=1.0, beta=1.0):\n", " self.alpha = alpha\n", " self.beta = beta\n", " self.m = None # posterior mean\n", " self.S = None # posterior covariancematrix\n", " \n", " \n", " def calc_posterior_params(self, Phi, t):\n", " \"\"\"\n", " This method calculates posterior mean and covariance matrix from the training data Phi and t.\n", " \n", " Parameters\n", " ----------\n", " Phi : 2-D numpy array\n", " (N,M) array, representing design matrix\n", " t : 1-D numpy arra\n", " (N,) array, representing target values\n", " \"\"\"\n", " self.S = np.linalg.inv(self.alpha*np.identity(len(Phi[0])) + self.beta*(Phi.T)@Phi )\n", " self.m = self.beta * ( self.S @ (Phi.T) @ t)\n", "\n", "\n", " def predict(self, Phi, return_std=False):\n", " \"\"\"\n", " This method makes prediction on the input Phi, and returns predictive mean (and standard deviation)\n", " \n", " Parameters\n", " ----------\n", " Phi : 2-D numpy array\n", " (N_test, M) numpy array. M must be equal to \"M\" (the length in the second dimension) of the training data.\n", " return_std : boolean, default False\n", " If True, the method also returns predictive standard deviation\n", " \n", " Returns \n", " ----------\n", " pred_mean : 1-D numpy array\n", " (N_test,) numpy array representing predictive mean\n", " pred_std : 1-D numpy array\n", " (N_test,) numpy array representing predictive mean\n", " \"\"\"\n", " pred_mean = Phi @ self.m\n", " if not(return_std):\n", " return pred_mean\n", " else:\n", " pred_std = np.sqrt(1.0/self.beta + np.diag(Phi @ self.S @ (Phi.T) ) )\n", " return pred_mean, pred_std\n", " \n", " \n", " def calc_evidence(self, Phi, t):\n", " \"\"\"\n", " This method calculates the evidence with respect to the data Phi and t\n", " \n", " Parameters\n", " ----------\n", " Phi : 2-D numpy array\n", " (N,M) array, representing design matrix\n", " t : 1-D numpy arra\n", " (N,) array, representing target values\n", " \n", " Returns\n", " ----------\n", " evidence : float\n", " \n", " \"\"\"\n", " N, M = np.shape(Phi)\n", " evidence = 0.5*M*np.log(self.alpha) + 0.5*N*np.log(self.beta) \\\n", " - 0.5*self.beta*np.linalg.norm( t - Phi @ self.m )**2 - 0.5*self.alpha*(self.m@self.m) \\\n", " - 0.5*np.log( np.linalg.det( self.alpha*np.identity(M) + self.beta*(Phi.T)@Phi ) ) \\\n", " - 0.5*N*np.log(2*np.pi)\n", " return evidence\n", " \n", " \n", " def empirical_bayes(self, Phi, t, tol, maxiter, show_message=True):\n", " \"\"\"\n", " This method performs empirical bayes (or evidence approximation), \n", " where hyper parameters alpha and beta are chosen in such a way that they maximize the evidence. \n", " \n", " Parameters\n", " ----------\n", " Phi : 2-D numpy array\n", " (N,M) array, representing design matrix\n", " t : 1-D numpy arra\n", " (N,) array, representing target values\n", " tol : float\n", " The tolerance. \n", " If the changes of alpha and beta are smaller than the value, the iteration is judged as converged.\n", " maxiter : int\n", " The maximum number of iteration\n", " show_message : boolean, default True\n", " If True, the message indicating whether the optimization terminated successfully is shown.\n", " \"\"\"\n", " tmp_lambdas = eigh((Phi.T)@Phi)[0]\n", " cnt = 0\n", " while cnt < maxiter:\n", " lambdas = self.beta * tmp_lambdas\n", " self.calc_posterior_params(Phi, t)\n", " \n", " alpha_old = self.alpha\n", " beta_old = self.beta\n", " \n", " gamma = np.sum( lambdas/ (self.alpha + lambdas) )\n", " self.alpha = gamma/np.dot(self.m, self.m)\n", " self.beta = (len(t) - gamma) / ( np.linalg.norm(t - Phi @ self.m )**2 )\n", " if (abs(self.alpha - alpha_old) < tol) and ( abs(self.beta - beta_old) < tol ):\n", " break\n", " cnt += 1\n", " if show_message:\n", " if cnt <= maxiter:\n", " print(f\"Optimization terminated succesfully. The number of iteration : {cnt}\")\n", " else:\n", " print(\"Maximum number of iteration exceeded.\")\n", " \n", " def fit(self, Phi, t, tol=1e-4, maxiter=100, show_message=True, optimize_hyperparams=False):\n", " \"\"\"\n", " This method performs fitting. \n", " The user can choose whether or not to perform empirical Bayes.\n", " \n", " Parameters\n", " ----------\n", " Phi : 2-D numpy array\n", " (N,M) array, representing design matrix\n", " t : 1-D numpy arra\n", " (N,) array, representing target values\n", " tol : float\n", " The tolerance. \n", " If the changes of alpha and beta are smaller than the value, the iteration is judged as converged.\n", " maxiter : int\n", " The maximum number of iteration\n", " show_message : boolean, default True\n", " If True, the message indicating whether the optimization terminated successfully is shown.\n", " optimize_hyperparams : boolean, default False\n", " If True, the hyper parameters alpha and beta are optimized by empirical Bayes.\n", " \"\"\"\n", " if optimize_hyperparams:\n", " self.empirical_bayes(Phi, t, tol, maxiter, show_message)\n", " self.calc_posterior_params(Phi, t) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4 Experiment \n", "\n", "## 4.1 Data\n", "\n", "As an example, we use $d=1, N = 50$ data, where $x_i \\in \\mathbb{R}$ are drawn from uniform distribution over $[-3,3]$, and\n", "\\begin{eqnarray}\n", " &{}& t = f(x) + \\varepsilon \\\\\n", " &{}& f(x) = \\sin(2x) + 0.2\\sin x + 0.1x \\\\\n", " &{}& \\varepsilon \\sim \\mathcal{N}(0, 0.09)\n", "\\end{eqnarray}\n", "The dataset is shown below:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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1EkVWvANtB7httIdoB0yY9L4adubDhhyvk0gYqDDwwoy7wQZg+ANeJ6mdnldA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\nYuVYdhUGEptSO0LncyH3aSg5WOObRe1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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def truef(x):\n", " return np.sin(2*x) + 0.2*np.sin(x) + 0.1*x\n", "\n", "N = 50\n", "X = np.random.uniform(-3, 3, N)\n", "ep = 0.3*np.random.randn(N)\n", "t = truef(X) + ep\n", "\n", "Xcont = np.linspace(np.min(X),np.max(X),200) # for plotting\n", "\n", "plt.figure(figsize=(8,6))\n", "plt.plot(X, t,'.', label='training data')\n", "plt.plot(Xcont, truef(Xcont), label='ground truth')\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$t$')\n", "plt.legend()\n", "plt.show()\n", "\n", "X = np.reshape(X,(len(X),1))\n", "Xtest = np.reshape(Xcont,(len(Xcont),1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.2 Bayesian linear regression with fixed hyper parameters\n", "\n", "First, we see the results for bayesian linear regression with fixed hyper parameters. \n", "We also see that how the results change with different hyper parameters." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def plot_result(pred_mean, pred_std):\n", " plt.figure(figsize=(8,6))\n", " plt.plot(X, t,'.',label='training data')\n", " plt.plot(Xcont, pred_mean, label='predictive mean')\n", " plt.plot(Xcont, truef(Xcont), ':', label='ground truth')\n", " plt.fill_between(Xcont, pred_mean + pred_std, pred_mean - pred_std, alpha=0.2)\n", " plt.xlabel(r'$x$')\n", " plt.ylabel(r'$t$')\n", " plt.legend()\n", " plt.show() \n", "\n", "def plot_prediction_fixed_hparams(s, mus, alpha, beta):\n", " # generating design matrix\n", " Phi = gen_desmat_gaussian(X,params={'s':s, 'mus':mus})\n", " Phi_test = gen_desmat_gaussian(Xtest,params={'s':s, 'mus':mus})\n", " \n", " est = BayesianRidgeRegression(alpha=alpha, beta=beta)\n", " est.fit(Phi, t, optimize_hyperparams=False)\n", " pred_mean, pred_std = est.predict(Phi_test, return_std=True)\n", " plot_result(pred_mean, pred_std)\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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ubnfHGxbXdoNg87bwSekbnJ17BSZD8HeIa3X5KGt0MiQxQiZ7Deky0QOVwD+A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\nV6+oQ73feKYHvSa89WmizU+waf6nOM7fxdTYLEfjSUelOE6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FZ257FNv618LEUkryFSEf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\nwyTRCyGEEB4miV4IIYTwsP8PkwAPxHoqTVIAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mus = np.reshape(np.linspace(-3,3,16),(16,1))\n", "s = 0.5\n", "plot_prediction_fixed_hparams(s, mus, alpha=1.0, beta=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that we are lucky, because, even though hyperparameters are chosen by hand without much consideration, the result looks not bad. However, if we are not lucky enough, we get weird results:\n", "\n", "For example, if we make $\\alpha$ too large, the regularization becomes too large." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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kSMLIUIcRELHGeGKN8Rh0akFvSzQNau1eau1eDHpBfJSRhCijShJaoLorBoDq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\nzx3ysY0xdKV2AXgeCuqiAdobor4Z+Kj8QUSojwU5ojVBa5l/qKgEvjp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+Vkan55kDK/T1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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mus = np.reshape(np.linspace(-3,3,16),(16,1))\n", "s = 0.5\n", "plot_prediction_fixed_hparams(s, mus, alpha=30.0, beta=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we make $s$ too small, then the resulting predictive mean gets wiggling." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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f9l/BypoBDMzO5/BGjqd3+DhFsvHFYr4XRSLbEZimwk4+1HQfJ16/cg+yUbnR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RFbMh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\nGL8AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mus = np.reshape(np.linspace(-3,3,16),(16,1))\n", "s = 0.1\n", "plot_prediction_fixed_hparams(s, mus, alpha=1.0, beta=1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far, we have chosen the value of hyper parameters by hand, but we are much better off if we can determine appropriate values of hyper parameters from data. \n", "That's what we will do in the next section by empirical bayes method." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.3 Empirical Bayes\n", "\n", "\n", "### 4.3.1 Maximization with respect to $\\alpha$ and $\\beta$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated succesfully. The number of iteration : 3\n", "alpha=4.448284052876882 \n", "beta=12.860678264859217\n" ] }, { "data": { "image/png": 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UmgwMJEnq0SINDIy1uzh75yf8Uz+eYXkXd9Co2p/PnMaBmc9gtBWRteouWjuC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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mus = np.reshape(np.linspace(-3,3,16),(16,1))\n", "s = 0.5\n", "params = {'s':s, 'mus':mus}\n", "Phi = gen_desmat_gaussian(X, params = {'s':s, 'mus':mus})\n", "Phi_test = gen_desmat_gaussian(Xtest,params={'s':s, 'mus':mus})\n", "\n", "est = BayesianRidgeRegression(alpha=1.0, beta=1.0)\n", "est.fit(Phi, t, optimize_hyperparams=True)\n", "pred_mean, pred_std = est.predict(Phi_test, return_std=True)\n", "\n", "print(f\"alpha={est.alpha} \\nbeta={est.beta}\")\n", "plot_result(pred_mean, pred_std)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can be seen that credible intervals become smaller than those seen in the previous section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.3.2 Maximization with respect to $s$\n", "\n", "Finally, we determine the value of $s$ from our data (assuming $\\mu_j$s are fixed).\n", "\n", "Because this procedure cannot be carried out analytically, we perform grid search, and plot the value of evidence for each $s$ (Note that the maximization with respect to $\\alpha, \\beta$ is performed for each $s$.). " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s=0.60625\n" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mus = np.reshape(np.linspace(-3, 3, 16), (16, 1))\n", "\n", "\n", "ss = np.linspace(0.1, 1.0, 49)\n", "arr_evidence = np.zeros(len(ss))\n", "\n", "for (cnt,s) in enumerate(ss):\n", " Phi = gen_desmat_gaussian(X, {'s':s, 'mus':mus})\n", " est = BayesianRidgeRegression(alpha=1.0, beta=1.0)\n", " est.fit(Phi, t, tol=1e-4, maxiter=1e3, optimize_hyperparams=True, show_message=False)\n", " arr_evidence[cnt] = est.calc_evidence(Phi, t)\n", "\n", "s = ss[np.argmax(arr_evidence)]\n", "print(f\"s={s}\")\n", "plt.figure(figsize=(8,6))\n", "plt.plot(ss,arr_evidence,'.-')\n", "plt.plot([s,s],[-40,-10],'--')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this optimal values of $s, \\alpha, \\beta$, we obtain the following plot:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated succesfully. The number of iteration : 3\n", "s=0.60625\n", "alpha=3.634825844752948 \n", "beta=13.024570712161763\n" ] }, { "data": { "image/png": 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ErbpIjkjz21ZlowOLUYcSxusrpL43cEJlSZKkw3hVQWNLEHe9QpC64fcopjgS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\netxjR2QxTI8ayTU5tx9xamd53geSM7M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eEW9Xaxs6ee7tCoLbPs3Nz9Tx4aSLcLWsIW+7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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mus = np.reshape(np.linspace(-3,3,16),(16,1))\n", "params = {'s':s, 'mus':mus}\n", "Phi = gen_desmat_gaussian(X, params = {'s':s, 'mus':mus})\n", "Phi_test = gen_desmat_gaussian(Xtest,params={'s':s, 'mus':mus})\n", "\n", "est = BayesianRidgeRegression(alpha=1.0, beta=1.0)\n", "est.fit(Phi, t, optimize_hyperparams=True)\n", "pred_mean, pred_std = est.predict(Phi_test, return_std=True)\n", "\n", "print(f\"s={s}\\nalpha={est.alpha} \\nbeta={est.beta}\")\n", "plot_result(pred_mean, pred_std)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Appendix : scikit-learn\n", "\n", "In this appendix, we see how we can use the scikit-learn library to perform the above analysis.\n", "\n", "Strictly speaking, the implementention is slightly different from ours in that they also consider priors (which are Gamma distributions) on $\\alpha$ and $\\beta$. \n", "\n", "However, if we take the priors to be uninformative, the result closely resembles to the result shown above.\n", "\n", "For detail, see official documentations :\n", "* http://scikit-learn.org/stable/modules/linear_model.html#bayesian-regression\n", "* http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.BayesianRidge.html" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s=0.60625\n", "alpha=3.634829359779728 \n", "beta=13.024559477195034\n" ] }, { "data": { "image/png": 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ErbpIjkjz21ZlowOLUYcSxusrpL43cEJlSZKkw3hVQWNLEHe9QpC64fcopjgS\nZ/2+9zrWmxQNpcc9htDoSf/6NhDtR0ss+hhOy7zAN63QFYdbDe73Jw0JMjCQJGnAaghy0aGm8GOW\nKEV8PvEiVGPPZS3sa57IYZTNfoDIio0k7Hilw2M21azn3f0v+22rsskpCyhJ7cjAQJKkAas+mLoI\nqgdl81O4dUa8I8/svU71kYYxi2jKOIlh3/8ZQ2PhEY/vatjMtxWrcHm7Xo/t8qghZYyUBi8ZGEiS\nNCA53F5aXIEn6okreJcJdft4fMxdjIiZ2Is96yOKwsG5jyK0BtLXHjmlcO6IX/D47H8GNKVQZXWi\nqnLUQGolAwNJkgakenvgd7mK14ln81M0JE3FOuJnvdirvuWbUqj8noQd7acNTNoItBodqvDS4rF3\n3Y5XUCtHDaSfyMBAkqQBR4jgyivH7X6De6NUrk2yhHWGw1C0TSmk5D2B3lbW7jGP6uGu767ijb1/\n9dtOtdWJV44aSMjAQJKkAcjm9ODxBvYhpngcJG1+jsWkcMaY63u5Z/1AUSg79iEUoZK6of1OC51G\nx5xhC8hNOMpvM15VUCvLMkvIPAaDihACp0fFo4rWyF8ACug0CgadBr1WxoHS4BDUaMGeNzHYK8g8\n4SkSkub2Yq/6j9uSSdW0mxmW9xhRB77ElnGi77Gzsi/r4sz2qm1O4iMN6OR7xZAmA4MBTFUFNpcH\nm8OD3eXB4Va73Lql1SiYDVosJh3REXoZKEgDkhpE7gLF68S79TmeS5/AjKTJRPZy3/Q6BYXWqQq3\nt+vXY0+ryb2W2IJ3Gb7uPgrOW43QmXyPOb0OvilfyeyU+UTqLZ22oapQY3MxLMbU6THS4CcDgwHI\n6nDTYHfT2OIO6o3HqwqsDg9Wh4fyRgcWk46EKCNRxtCfBvnF9WzYX8vskQnMyPJfD16SuiuY533s\n3g9Yp9h4UW9igmonkp4toRxh0BIdocNi1GPUadBo/rd+QQiBy6vS7PRidbixOjy9GigIrZGyOX9k\n5KcXk7TlOapm3Op7rNxewku7n0Cr0TNv+OldtlNjc5IYJUcNhjIZGAwQqiqos7uotbmCzgvfESGg\nqcVDU4uHSKOWYTEmzIbgng75xfVc+vcNuDwqBp2G5Ytny+BA6nUNgWbqU70kbf0rZxqyST72FRJM\nKT3Wh+gIHUkWY5evGUVRMOq0GHVa4iMNuL0q9c0uqm1O1O6/hDvUPHwO9aPOJWnLX2kYfS6umJEA\nZFvG8shRL5MVNcZvG0K0TimkxkT0TielsCdDwjCnqoJqq5NdFVbKGxw9EhQcrtnpZV9VM2UNLUGt\nSt6wvxaXR0UV4PaobNhf2+NXmyo7AAAgAElEQVR9k6RDub1qwOWCo4s/x9C4n6opN5AQ0TNBgVGv\nYURSJFkJkUEH0nqthuRoE+NSLCREGXqkPx2pOPoehM7E8HX3tavAmG0ZG3BNhFqbC7e3l6IXKezJ\nwCBMCSGoa3axu9JKRaOjT7YR1dpc7K2yBZw0ZvbIBAw6DVoF9DoNs0cm9HIPpaEu4GkEIUja8jzX\npWXyT6WuR64dF6lndFJUt6beAHRaDcNjIxiVHIlR3/NvwR5zMpXTf4Pl4NdYDvyn3WP/Kf2AJ7bc\n4bcNIVq3L0pDkwwMwlCz08O+ahsH61sC3pLVU1welX3VtoBSpM7IimP54tn8dsE4OY0g9YlAdyOY\nK/PQ12wlMmYsEfqobl1TUSAtLoL0OHO7NQTdZTboGJ0URaxZ32NttqmdcAWOmFGkfvdHFO//Xssq\nAoHA4W3x20Zdc89MW0oDjzIUi2fMnDlT5OXl9Xc3juDxqpQ3OoLaitWbkixGuTpZChtOj5c9FbaA\njs34zw1YDq5l58UbEXpzyNdUFMhKMGMx9fyH96GqrU4qGh092qblwH/J/vwXlB19P7W5i4HWkchg\nSizHRepJjwv99yeFD0VR8oUQMwM5Vo4YhIkGu4s9lbawCQqg9c3qQJ1dVl6TwkJjgK8NXXM5huKV\n7BxzTreDghGJkb0eFEBrEJ4Zb+7RpIzWjJOwps8jZdPTaB2t0yltQUGTq4EmV73fNhrsbpyewOtR\nSIODDAx6SX5xPc99uZf84q5ffG6vSnFtMwfqglv411ca7G5K61tkcCD1u0BzFyT8+DqfRZq4xP4V\nB2z7Q7pW20hBZDfXEwQjxqwnK6Fng4Pyo+9F424mJf8p3/daPHZ+s+5CVhT90+/5QkBVk1xrMNTI\n7Yq9INBtfI12NweD3AnQH9pGMTLi5ZCi1D8cbi8Ot//5bsXjIH7XciYNO4pLxpxKeuSIkK6XEdf7\n0wcdsZhag4PiWnuP5Dxwxo2ldvzlJOz8B7XjL8cZP44InZnLxtzEmJhJAbXR2OIm2ePFqNN2v0PS\ngCBHDHqBv218XlVwoM5OSZ097IOCNg12d4/PgUpSoAIdLYjd/yE6Zz36iUs4PfOioObT26REG4np\nhQWBgWoLDnpq5KBq+m/wGiykfveQ73snpp1JelRgQZMcNRh6ZGDQC7raxtfs9FBQZQ2rtQSBqrY6\nZZEVqV8EFBgIQcKOV3g3eRSbzaFlOIyO0JEc3f8Lbi0mPWmxPZNgyGuKo2raLVgOfk1U6Vrf9yvs\npXxQ+FpA04QNdjcOt1xrMFTIwKAXdLSNTwhBZZOD/dXNuD0DY5SgI+WNDmwBJpiRpJ7gcHtxBjCN\nYK7ciKF2B0stelYf/CDo6xh0mrBagR8XaSAlxtgjbdWNvxxXVDrDvn8UROvvcmfDZt4tfIUye0lA\nbchRg6FDrjHoJTOy4nzrClwelZI6e8CJg8KZEFBSa2d0chQGnYwrpd4X6Oha4o5XEMYYnjzm37QE\nOQyvKJAZb0bbg3kKekKyxYTTrXZ7hFFojVTOuI2Mr35NzP6PaBx1NnNSTmF6wrHEGOMDaqOxpXXU\nwKSXaw0GO/nO3ssa7W4KqqyDIiho41UFJXXNcqeC1CcCmUbQNVcQXfQ59WMvwmhKINYYXBbO5Ggj\nEYbw/MBLi43okb41jD6HlvgJDMt7DMXrwqA1BhwUtKlskuuMhgIZGPQSVRWU1rcuMOytgin9qcXV\nmoxJknpTi8sbUPa9uIJ3qNTALUoJRdaCoK5hNmpJiuqZIfveoNEoZCX0wGiGoqFi1p0YrAeI37Uc\nAK/q4elt9/JB0T8CaqKpxTOobnKkjsnAoBc43F72Vtuobx54CwyDUWtz0eQY3D+j1L8CW3SoErfn\nTfalTKbK00CELvB1AorSekceyu6FvqTXashM6P76B1v6CdhSjyV50zNoXFYKKu2U17upswa+bkiO\nGgx+MjDoYTU2J3urbAEtlhoMSuta8MgqbFIvCSQwiCz/DmNTMZljruCpY94gJSIt4PaTLcYBM2ce\nZdSREt3NkQ1FoeKou9A56mD9X7hnxXZ2bTuTT77NYVd5U0BNWB0e7C65AHkwk4FBD/F4VYpqmilv\ncPRIYpKBwqsKyhrkHYTU8xzuAKcRdr+B1WChIfu0oO78jXoNSZbwnULoSHK0iUhj9wKZlqQpNIw4\nndH7XiPWW4cqWt+/1pX8GHAblXKHwqAmA4MeYHN6KKiyYXUMzSi6scVNg91/NUZJCkYgowUaZyMx\nRZ/yaOYE7vjhelQR+OjV8AEwhdCR1iqP3Wujcubv0AsXt+g/QKOAIS6f1bbbONhcHND5NoeHZrlt\nedCS2xV7QH2zq8/LIx/Ko3rwqC5MOjN2j41397/CtMRjmBTfWkjL4bFjCmLeNRRlDQ6ijDp0Whlr\nSj0jkMAgdt8KNF4nY9NPJ1KvR6ME9vyLidAT1Yd1EHpSW76Fklp7yG24YkZQn3MJF+/6N9UTryYm\n8xxqSScuiN0clU0ORiZ1r6S1FJ7ku/gAZ3U3csPXZ/HFTwldvMLLmrKPaHC2pmGuainj2rWnsbb8\ns17th1cVcpeC1GMCTWoUv/sNWhImMn3UlZyZdWlAbSsKA76ceEyEnthupm2umnYLaPX8wvE6MzOy\nWJhxHmZd4B/0zU6vTHY2SMnAYADa17TT90Fv0cdwcvq5jIud7Pv6pXmrmJu6EACdouf0zEvIjZ8F\nQLG1gLXlnwU15BqoBrtbvlFIPaIpgNECU812Imq3szprDg5vS8BtJ0YZB0VyruGxEei0oU+FeMzJ\nVOcuIbbwE0w121GFl++rvmJn/eaA25A7FAangf/qGII+LPon7xW+gldt/RC+YNS1jO2kUlq8KYmL\nRl9HnDERgDVln/DPgmdp8TT3St/KGmSJZqn7AplGiN/zJtX6CO6pX8WK4tcDalejYcAtOOyMVqOQ\nFte9ego1kxbjMcaQkv8kAK8XLOWL0vcDPt/u9Moty4PQwJxkG4JKbfuJNSYSpY/mmpzb0WsMaDXB\n//kuH3szCzMWEam3IIRga91GJscf1WOLsJxuldpmF4lhnDBGCm9Oj/8Sy4rHQeze92nMWMD9068l\nwZQcUNvJFlPYpT3ujmhT65RCqCmTVWMMNbnXMSzvMSKrt3D3tGdIMg0Lqo2qJgfR/VCiWuo9csRg\nALB7mnko/yb+secZAKINsUElcTmURtEwzJwOwObaDfx5863k1XzdY32F1uFFmdtAClVTi//pKEvJ\narSuJhrGXcC42MkkBvBhptcpJEQaeqKLYSU1pnvBTu3Eq/CYEkjJe4Jh5vSgbzhaXGrAZbGlgUEG\nBgOAWRfJkgl3cfHo63u03SkJR3P9hHuZkTi3R9v98WATj3++m/zi+h5tVxoaAvmQidv7PsVRKbzm\n2E2jsy6gdpOijGgG0WhBG51Ww/DY0BdTqvpIqqbciKXsGyLL1pNf/Q0P/3CLb6oyEFVNDjmFOIjI\nwCCMfVLyBjvqfgBgZtJxvnUCXVLd6K0HMNVsI6LqByKqt6C3lqB4jlwkpFE0HJd6KhpFQ5OrgVd2\nPYnT273FRLvKm7hnxXZe/Ho/l764QQYHUlDcXtVvLn6tox7LgS/5Jn0mHxS/jkv1n0NDr1OIH4Sj\nBW1izQaiTKHPDNeNvwy3OYWU/CdACJzeFhpctQGf73DLUYPBRK4xCFNOr4M1ZR8zJmYSE+Ond3yQ\nEBiaCrHvWImubCMjXAVE2ktRODJyFyi4orOpjMohXzsN7dgFjBgx0vf47satrK1YyXGppzI6ZmLI\n/d52sBGPV0UV4PKqbNhf6ys/LUn+BLIbIabwYxTh4ajxN/G8JY1oQ6zfc5KijAMymVEwhseaKKi0\nhZR5VehMVE39FWnr7uV4p8qMWcuCbqOyyUlMhH7Q/56HgrAMDBRFiQdeAhYANcBdQoh/dXDcg8A9\nwKH5OScLIfb3RT97k1Fr4oEZzxOhPXItgd5aQtze94nZ+wGmxn0AHBSJfCNGkjHudGKGjcRjikdo\n9CiqG52zAb21FHf5DowHN3Cu8hnekj9RmXI8rqlXYs2Yz6yk43n62LeIMXTvQzw3LQadVoPHq6LT\napiS4f9NW5LaNAWQPTR27/s44sbiiJ9AdAAfQoN9tKCNUacl2WIMOV1x/bgLSdr6AsN+eIJ96cfj\nUl14hTfg9Uwuj0q93T0kfteDXVgGBsBzgAtIAaYCnyiKskUIsaODY98UQlzWp73rRbvqt5BXs5aL\nR11PlD663WORZetI3P53LCX/AaA59Rg+spzDE/vSKRYpaBS4LDKL88dldNj223kH+GdxETkUc4Z2\nA5fXfYtl1dW0JEyicsZvIWM+AHnVX7O/aRcXjLo26P7npEbz8NmT+O+uKgDqbDKnuhQYryr8ptnV\nW0uIrMzjyQmns3/nI1w3/m6/d6iJQ2C0oE2SxUi93R1QjYnDCa2Rqmm3kP717WiLPuZXB/7GgvSf\nc97IqwNuo7LJQWyEflCu5RhKwm6NgaIokcB5wH1CCJsQ4hvgQ+Dy/u1Z79tV3sRbO/7LdxXf4FT/\nN9dvrsxnxCcXMfLTizBXbaJ66q/YfdF6Ck9/A8eUqyjXpqJRWhch5abFdNp+6928ll1k8zSX8Pkp\nqzlw/JNo3FayV11N1qqr0VtL2VGXz9a6jd1ab/Cf3VV8/mMFt72zlbV7qkNuRxo6mlrcfofBY/eu\nAMAaNwaP6vb7ga/VKMSbh84drKIo3VqIWD/mPJzR2YzY9CynZSxiYvyMoM73eAW1za1rPvKL63nu\ny71yndEAFI4jBmMBrxBizyHf2wKc0MnxZyqKUgeUA88KIf7a2x3sDW2L9jzeWej0UygZrTLVsJOU\n/MeJLlmN25RI2ewHqMu5FKH73wu/7Q5928FGctNiyEmN7vQahx87LjWaBs6nYfQ5JO54laS8Jxjx\n9nx+PukeTDOfQ68J7Q310HUGHq/Kmt1VHD82KaS2pKFj3b4avttf1/nzWAhi976PbdjRnDf+twG1\nmRhlGHJ3rxaTnugIXUDbPo+g0VE5/bdkrrmZK0UCjbFTgm6i2uqkqLaZy1/6DpdHxaDTsHzxbLnW\naAAJuxEDIApoPOx7jYClg2PfAsYDScC1wP2KolzcUaOKoixRFCVPUZS86urwu4N9b/9yvJoqVAEG\nt0raxocY/cFpRFZspGLm79hz4dfUTrqmXVDQJic1mvNnZnQZFHR5rEbPN4kXcrLzMTZ7sjh2673E\nrboNt6uJN/a+gM0dWJ32Nm3rDNpGMcYPi5bVF6Uu5RXV8Zu3tvDP74q5Z8V2dpUf+Zwz1W7D1LiX\ngyNPC6hNRWHIzncPizER6uxJ48gzccSNJTn/KRpaKtlYtSao872q4L+7qnB5Wm8O3J7WRcjSwBGO\ngYENOPwTLhqwHn6gEOJHIUSZEMIrhFgHPAMs6qhRIcQyIcRMIcTMpKTwunttcNay17UCQ9wPnKLN\nZ5Xhdo6pfpu6nEvZdeE3VE+9CVUf2at92HawkRJvApe47mGp51xGlH6AWHUJn5S8wZbaDUG11TYy\ncdnRWTx89iRyUqOpsjrlPmepU2sLqtuNMm07ePi9QWvuApfGwDU17/HWPv+r5uMjDUO22qdRpw09\n9bNGS+X0WzE17uM/2x7hL9sfCPrmYGRiJAadBq0Cep2G2SMDr9oo9b9wnErYA+gURRkjhCj46XtT\ngI4WHh5OAANu3DDWmMBT054h45tHyda/SqNlDPvn/R17SnDze93xv90E8CwXMnP6cczechcrLCm0\nRI4n2B3KOanR7UYlnD/tc44dQvO9UuAmpEa3281yxFoZ1UPMvg+pzZjHaZnzGBU9wW+bCVFD+7mW\nFGWkLsSS8E3Zp9KSMInFxfkcc9prRyyE9idnWDTPXDSNvVU2Zo9MkNMIA0zYBQZCiGZFUd4DHlIU\nZTGtuxLOBo49/FhFUc4G1gINwCzgZuDuPuxutwgh+LH+B45ubiJn7W1oXU1UzLqD6twloOnb3OOH\nrz+wpB5LYdoIslb9AvWTC/jqxCfQRo8iKSK4POqHqrI6ZWAgHUEIQWZ8ZJdrZSLL16NvqcY5+uec\nlf2zdo/tKm864rzoCB1GnbbPfoZwpNEoDIs2UVofeOVJH0WhcsatZK+6Ckq/oz5nVNBNpMVGMG9c\n0pD/OwxEYRcY/OQG4GWgCqgFrhdC7FAU5TjgMyFEW9Hwi346zgiUAn8WQrzWHx0OxXfln7N05x/5\na0UVqaYsCk9bjjM+p9/6c/hdvj1lBoWn/Zvhn13CH7b+jpzE2fxq2pMht+90qzTa3cR0s468NLjY\nXV68qjji+Xeo2P0f49SZWR8VR47q8eXz/9+i3daRhrapK1nEq1VcpIHaZpffbJIdsWachD15OrrN\nz/CyWsLxaWcGlfxMCKhqcpIRH1pdF6n/hOUEnBCiTghxjhAiUgiR2ZbcSAjx9SFBAUKIi4UQCUKI\nKCFEjhBiaf/1OjjG+j1cvO4xHqmqYdyIi9l79kf9GhR0xpE4ibKfvcHDdc08uC8PrSOwvPSdqbLK\n+u1Se37L9qpuootW8nXmbB7eejs/1K7zPXT4DphtBxuJMGiINIbrPU/fS40JcfuiolAx4zaimyvI\nq1zNAVvweeMa7G4c7uCDEql/hWVgMNhFF7xP1oozMToamHTc36g49vcd7jYIF46ECQw/YRnDrGVk\nf/4LvK7gFiK1a8utyvrtUjv+ttVFla1H56wnI3sRv879I5Pjj/I9dvgOmNy0GOIj5WjBoSKNOqIj\nQguUmofPQU05ms/L6jkp5eSQ2ihvlDcDA40MDPqQ4nUy/Nt72fv9nZybNox1p72KLb2z9AzhxT7s\nKErm/YX7KeX1ry8lpITsP6mxymyIUiuH2+s3S19M4cd49ZG4M0/mqOR5GLVH5vFo2wEzIS2a2Ag5\nVXW4kLcvKgqVM2/F3FJNwo//wBNExcU2NocHq7wZGFBkYNBH9LYyRn68iISd/0DNOp1hyccSHed/\nZXU4sY44leHJxzCxbj+JW54LuZ1mpxe7K4TkK9KgE+g0wvcZc/miYmWH2TgPzc0RHzn0EhoFwqjT\nhpzTwT7saKxpx/NS0Us8kn9TSG1UNslRg4FEBgZ9wFyZx6gVZ2Js2EfxycsYNucpfjPlT+g0A28e\n9JTZz/LzhBMZlvc4UaVrQ26nWo4aSAQyjbAOnbOB1bGJLC941m97QzWhUSCSLUY0Ib7jV864jQl2\nKzNcKqoIfs1Ai0uVSc4GEBkY9LK43W8y4pMLUfWRfHfqy7ypacKjDuBhNUWh9PjH+TppJLs23IrO\nXhVSM00tHrkoaYhze1W/q+Vj9n+MV2/h7Nz7eeKY5e2mEQ4XZZJbFNt0VKdAp9WEnPSoJXkqJ8cf\nw+371qFz2UJqo6LJgarKJGcDgQwMeovqIXX9A6R/fTvNqbPZe/aHrHHs4419L1DvHNjpQVWtiRdS\nR/OaWUPamltAdDxHvKu8ibfzDnSY3hbwFVuRhiZrFyWWd5U38d7G/UQVfkZT1imgjyDBlNJle3K0\noFV+cT2X/n0DT67azaV/39AuOEiMNKLThjbVUjnjVjSuJqo2/zmktQZuj6CmWY4UDgQyMOgFWkcD\n2SuvIHHHK9RMWkzRwtdQjbGckXkJjx79WreSBIUDRVG4bvIjPDLyV0SXfUvithePOKZtf3lXue/r\nm114vMGXh5UGh6aWjkfO2p47RfmfYnA38bjBxNv7/t5lWzqtQrRp4E3N9YYN+2s7rVOg0SikRIe2\nA8qRMJHVI47jZttatpavCqmNaqtTvuYHABkY9DBj/W5GfXgmkRUbOXD8k5TPvh+haLF7bCiKQqo5\no7+72CPiTUk0j7uUuqwFWH54EmP9nnaPd7S//HBCQJ0cNRiSVFVgc3Z819n23PmZsgGriGCbR0OV\no6zL9uLMBr8lmIeK2SMTuqxTEGfWY9SH9tafPu1e/lBdy7zSvJDOV1WolOuLwp4MDHqQpfgLRn14\nDhq3ncLT36Rh7PkA5FWv5ZZvz6fEtq+fe9izVFSutnj4c3ws6WtvhUOGFzvaX96R2maXLK40BFmd\nnk53vOamxRChVVmozWO1mMUVY+7khgn3ddleXKTcothmRlYcyxfP5rcLxnVY7lhRQh818MSP54SU\nBWT8+M+Q1xfV2VxyfVGYk4FBTxCCpM3PkvXFYpwxI9l7zsftCiClmjOYnXISaeasI071Nw8fzjSK\nlqNSFzAu+3zM1VtI3Pa/incdVVjsiMcraOxkSFkavLra156TGs0LxzQRrdiJn7WInNToLkcDIo1a\nuejwMDOy4rjxxNGdFi+KidATYQjtd1Y57RY+jdCxPf+BkPsnkx6FNzkp110uOwkrr8dcsIKGUedQ\netxjR2QxTI8ayTU5tx9xamd53geSM7MuAaCxcg8pPzxN48gzcFsygSNrL3SmxiaLKw0lQgi/2xQn\nNq7FrY/iIftyTiqycVb2ZZ0eKxcdhmZYjInC6uagz3PHjuRfyVlENuYxqbkcT2Rq0G3YHB6aHG6i\nTXKkJxzJEYPuyn+ViIIPKZ91FwfmPdMuKHCrLt7Z/xKNrvoOTw1kHn4gUIWXf446gR9MRtK+vTfo\nrIgtLlUmPBpCWtytRZM6pXqJLllFdcY8ZiQdR0bUyE4P1WiQHy4hijLqiApxwebNUx/jr1V1JG/6\nS8jXL29wyGnEMCUDg+46+jqqzv+QminXc3jO0V0NW3i/8DVKbHs7PDXQefhw51E9vHHwbd7NOhpL\n6RqiCz8Juo1am1yEOFT4Gy2IrPwenaMO94jTuXzszUxLPKLiuk+sWWY67I6U6NDyGkTG59I47iLi\n9ryJ3loSUhsuj0q1TS5EDEcyMOgujRZX6swOH8qNn8XTx77JpLiOHw90Hj7cGbRG/jBrGRcf/QIt\n8RNI/e6PKJ7gasA3trhxy21MQ4K/vPnRRZ/h0RrZFTfCb1txsoR3t5gNoRdYWpk1hwtSE4n64f9C\nvn5Vk1O+7sOQDAx6iVttvQNOikjtcuHUoXneB7IEUwqKVkfx0fdhaC4jactfgzpfiNa8BtLg5vR4\ncbi7+CAQguiiz9mQNpPb8pfwfXXnabeNeg1mg1wm1V2h7lCIsGQSYUrGW/QRhsbgSzJD6+u+Qi5E\nDDsyMOgFLq+T29Zfymclb/V3V/rUvqadLN7/Z74dcRJJW/+K3loa1Ply6+Lg11W2Q4CImq0YmsuI\nzTiNq8bdysS4GZ0eGytHC3qESa8N6Xc5JmYSdx/9MhlCS8oPT4d8/Qa7m+ZOclpI/UMGBt2UX1zP\n6xuK2203dKsupibMJjNqVD/2rO+lmbMYG5NL06QlAKTkPx7U+R6v/9Xq0sDWWbbDNtFFKxGKFs2I\nszgl/VzMushOj42NkLsRekpytDGksswecxIHxl8GhR9hrN8d8vXLGlrkTUEYkYFBN7TlJP/71/vb\npf2N1Fu4KudWJsZ3frczGJl0Zn4z+WHSU46lduJVxO79AGPdrqDaqJW51Actryqwd1U0SQhiij6j\nIHUmG6xbcXk7fy5EGrUYdPLtq6cYdaGNGji9Di5yrOPv8fGk5D8V8vUdbpUauQA5bMhXVjccmpO8\nbbvhjrofKLWFNt/WHYoCEQYNsWY9ydFGUmNNpMVFMDzWREqMkfgoA5FGbchlV4NJxGRzN/F+6gRU\ng4VheY8FdZ1mp1dmRRukbI7Osx0CGBsKMDbuZ0VCGk9vvYcWT3Onz7s4mfeixyVbTEGPGhi1Js4b\neQ0zUk8lpugzTDXbQ75+ZZNDLkQME3LlTje05SR3eVTfdsPXCu5Dp9Hzh1lHFhbqaXqdQrRJj8Wk\nI9KgC2jblhCCFreXphYP9XYXHq//4btgEzF9Ufoe7+x/iVkTL2PapucxV+ZhT+l4Z0ZH6ppdDI+N\nCPh4aWBo8rsbYSUAp064jdFqE+V1ug6fd4oC0RFyfUFPM+g0xEcagt46vDBjEZrkU/Ds+ZCU/Ccp\nXvhKSNcXojW3QWaCOaTzpZ4jA4NuaMtJ/vmOCsYkRZGTGs1dCU/T5KrrtWsqSmtCl/goA1HG4P98\niqJgNugwG3SkRBtpcniotjpocXUeqXeUiKmrwGBB+nlMT5yD3pSGe9fbpHz/ZwpPf+uIPA+dqbe7\nGBZtkvvTBxEhhN/AIKZoJc3JM8CSzmjg7YIDHT7vYiL0aOVzo1ckWYzUNbuCzVFGpdrClrELuWTb\nW0RUbaIleVpI129sccuMiGFATiV004ysOC6fneX7oIw2xJLeRaa2UCkKJEQZGJtiITPBHFJQcGSb\nCjERekYnW8iMN3dapz3YREyRegtZljEIvZmqaTcTVfEdUaVfBdwvVUXWTxhk7C4vahejxHrrASJq\nt/PRsBw+Kv4XqlA7fd7FyN0IvUav1ZAQFfw0zeqD7/NYcx51EfGk5D/RrT6UNbSgdpUZU+p1MjDo\nIbvqt/DY5tupdXRecSzUgkmxZj1jUywMj43otQVXMT9dI76DN4VQEjEJIVhe8CzLDE5clozWtQYi\n8PnDOrtciDSY+J1GKF4FwAajhnUVX6BRNB0+77QaBUsPBMVS55Kigt+hcFrGBTx1zBs4c2/AcvBr\nzOXfhXx9t0dQaZW5DfqTfIX1kAZXLdWOcqL0HX9ohlIwKcKgJS02IuQqaMHSahTSYiOIMuoorbe3\nu8MLtCBSG0VRaHI1YNKZqZx+Kxlf/ZqY/R/TOOqsgM63/7QI0aSXVfMGA3/5C6JLvsARO4ZrpjyM\nw/u/rJmHP+9izPouE4ZJ3afTakiMMlJtDXyHUKwxAYDaCVeQuP1Fhn3/KPvPfC/g6cPD1VhdxETo\nZQKrfiJHDHrI7JSTeOzo1zFqO84iFkzBJI0GhseaGJ0c1WdBwaFapxeiMOq79/T45YR7uGrcb2kY\ndTaO2DEkb/5LcKMGMhPioOD0eHF2ke1Q42wksnwjTZknA2DSdr7wNFYuOuwTiVGGoHcwNThr+eue\nJ1kz8RIiq/J9o0ChOrcjFLgAACAASURBVFgvcxv0FxkY9IBSWzFCiC7vZAKdp480ahmTbCEhKrTi\nJj3FqNMyKimKSGPogUnb76PaWU355F9iqt+NpeQ/AZ/fYHfLucZBwF/SKkvpVyjCwx+1Vbyz/6VO\nj9PrFCLlNEKf0Gk1JAX5HmTSRrCt7nv2JI7BETOalLw/gxp6wjKHWw1q1ELqOTIw6KbK5kpuWHMJ\nHxUv7/I4f/P0igKpsSZGJkWFTeIWrUYhOyEy5NKsAIVNu/nN+gv53GLBFZVB8uZnAy7L7FX9r2SX\nwp/fokklq3Gb4vGY4lHoPLiOkaMFfSohyhjUqIFJZ2bpse9wfNoZVM76HaaGvcQVvNOtPlRZnTKv\nST8Ij0+gASzGGMMvJ93K7JST/B7bWcEkg07DqKQoEvt5lKAjGo1CVrwZS4jBQZZlDOePXExO3HSq\np/wSc/UmIsvXB3y+nE4Y2PxmO1TdWA78F2vGfK6feB/njby600NlCuS+pdUoJFmCe0/SalrfJ2rS\n52FPnk5K/lNBV1o9lBBQWm+XUwp9TAYG3WTSmfhZ9s9Jjhge0vnREbp+W0sQKI1GITPeHFIfNYqG\ns7MvJ8GUTP2Y83FHJJG0+dmAz292enF65B3DQGV1uLscIIqsyEPraqI6/fgu2zHoNGH9GhmsEiKN\nQeeMWLbzUR7Z/BvKZ92F3l5Bwo7QEh61aXGpVMkphT4lA4N+lBJjJCshckAka9FoFLITzCEvSCxs\n2s2nZR9Sk3stlrJviKjaHPC59c1yOmGgCmQ3QovGwBUHnuej4n91epycRugfWo1CoiW4kZqc2ClM\nSzwW27BZNGWcRPKW59E6GrrVj2qrE7tLFljrKzIw6AcaDWQnmkm2hFYHvb/otBqyEswhBTIbq9fw\nbuHLlI4+F68hmqQtz7V7vKscD/V2WY55IPKb7VAILCVf0DB8NgszzmdszKROD5UllvtPYpCjBsen\nnsbZ2ZejUTRUzLoTjct6xOs9WK1TCjLxUV+RgUEfa1tPYBmgKT+NOi2ZCeagtyefnnkxS+e8i8mc\nQs3Eq4gp/txXprUtx8M/vytuV6WyjccrsMp67QNOs59sh8aGvRibilEzF3L+qMWMi53c8XF6jcxn\n0Y80Iaw1UIXKjrofaI4dTcOYn5Pw46vobWXd6ofTrVLeJBMf9QUZGPQhs1HLqKTIAf8mF2XUMSwm\nuNGOKH00Zl0kADUTrsKrM5O09QUgsBwP9XIR4oDjbzeCpWQ1XuCH+EzULvJbyGmE/pcQaeg0ZXpH\nttVt5OFNN7Opdh2V028FIUj+4f86PDaYjLB1NpdMl94HZGDQR2LNekYmRqLTDo5feWKUkeiI4HYq\n2NxN/PGHm/myfgP1Yy8gZt+H6OxVAeV4sDo8eGRJ1gHFX/6C6JIv2JCcw9077iGv+utOj5OBQf8L\ndtRgUtxMfjXp90yJPxq3JZ3aCVcSV/C2b5Swjb/Rwo4crG/B5ZHvBb1pcHxKhbkki5GMePOgS+Wa\nFhuBXhf4zxSps6DXGNAoGmonXoVGdRO/858B1WIQAhrkncKA4XB7u3zz1rbUYq76gWHDT+KGCfcx\nOX5Wh8fJaYTwEW82BPx612p0HJMyH4O2NZionnoTqj6KYRv/1O64YDLCtvGqggNyC2OvkoFBL0uN\nNQU97D5Q/D979x3eZnU2fvx7Hm1ZlizPOE7iLIcAGUAChL3KLqNQSkugP9pSOqCLUqClb0tLKeVt\noeOFtlAodISWsimrhE0IARJWCGQ6sR3Hcbxt2do6vz8cuxmW9MixLdm+P9eV6yLy0aMTYUm3zrnP\nfVstBpP95nunK6W49qBfcUz5aUR80+icfCKFH/8dFQslrfGwK9lOGD3SnUbIr3sRpRMkpp7B0eWn\n4rQO/HskqwW5wzBURtUQtda8vO1Jlm9/nrjTz46DvoG37kU8W1/tH5Np59Y+PeE4jZ1yhHG4SGAw\nTJSCKYXunCxaNJTyHNaMjzNprakLVNM850vYQs34qv9t6n6haIJgqmI5Imek7aZY+zwb8yfwXKR+\nt6ZJe5LAILcU5plfNVBK8WrDMyxvXApAy4GXEsmfTPmbN0Ki93U8mM6tfZq6wlIZdZhIYDAMlIKp\nxXnjpm98Wb4zo/oGd62+k+ve/AKvxCcR8s+ieM2fTZdJbpN2zDkvFk/QE04ewKl4GE/9qzxVVsWd\nH99MJD5wprlsI+QepVRGx6yvmncz3533CwC0xUHDYT/A2bYO//oH+seYWS1Mpq61Z9QVQFtV08Yd\nL21kVU1btqeSlAQGQ8xiKGaUePCMo2YvhqGY5E/eEW9Xaxs6ee7tCoLbPs3Nz9Tx4aSLcLWsIW+7\nuf7t7T1R2VvMccm2Efqyz1vXvIgl2s1Z07/ALYf/Ba/dP+B47yg90jvW+d020/1cPDYvSqn+12zn\n1DPoLjuUspW/wogE9nkuiQTUtvSMmvoGq2raWHz3Cm59bh2L716Rs8GBBAZDyGZVTC/JG5elW912\nK4We9FsKq+s7iIX8RDsOJhYzeFodS8zhp+jD5F31dhVP6LTZ7iK7BgoMds0+r1vxMDGLi56JRzPJ\nMy3pdWQbITf1rhqY3yJd2fQa31txMcFYDyhFw6IfYQs173PRoz6haIL69sH3YxhJK6pbiMR6ky2j\nsQQrqluyPaUB5WRgoJQqVEo9qpTqVkrVKKUuSjJOKaVuUUq17PzzvypLqf92q8H0Ys+4Xvqc4HWm\nPev832SjGHb/KjxFzbTOXoy35jlsnTWmHke2E3KX1pqu8N77vv/NPtecoFbxp8L9eaDmb0nrF9is\nalwG2KNFgdtmevvQZ/dT4ppAZ7T323GwZD5tMz9F8Yd3Y+vaOiTzae+JsqMr94sfLZpehN1qYFFg\nsxosml6U7SkNKCcDA+AOIAKUAYuBPyilDhxg3OXAucB8YB7wSeArIzXJPk6bhekleTnTLnk4mNkX\nsxiK8jQnMPqSjS46rJKCiUvZGn2dlgM+D8pC8Ud/MTWXQDhGVGoa5KRAODZgtcO+gPBAo4aJqoV1\n/lI+aH0LQw38mpHVgtyWyapBlW8O1x50K2Wuiv7bth96HaCY8NbPh2xOjR3hnC9+tKDSz5LLFnHV\nKfux5LJFLKgceBst21Su7dcqpfKANmCO1nr9ztv+BtRrra/bY+xy4D6t9V07//4l4Mta60WpHmPh\nwoV65cqVwzL/sahvXywSS2C3Gml/oTc1BVImn/VpDm2nyFGGUorJL15B/tZX+Piit9HW9PkKE3zO\njMu0iuG3rT1IS2DgFZ21DZ0UrvoNJ26/h7UXrSTk9GM1Bs7FmV6SR944ytMZrTY0dhGKmgvSe2IB\nYokYXnsBAKXv/Iayd26j+ox/0j3xyCGZj1K9vztuu/zu7EkptUprvdDM2Fz8ijsLiPcFBTu9Dwy0\nYnDgzp+lGyf2Qab7YhN95hIRi50T+os+te5/CZZIJ77qJ03dt122E3JSquNjs8u9HBF7i2DpwcTc\nJUmDAqtFSVAwSpg9oRCKB/nGsvN5fMvf+m9rmvdVIvmTmfjGjyAxNN/0tYaalh6pjLiPcjEw8AB7\nlr/qAPJNjO0APAPlGSilLldKrVRKrWxqahqyyY4Hme6LuewWU4mIAMu2P8dPV11BV9mhhApmUvTx\n39LfCalpkItC0TjRWPIVSGv3dtzNH3C138n9G36fdJxXthFGDZ/bhsue/mPEaXFx0cyvcUz5af23\naauTbYt+jLNtPUUmtxHNiMU1W1q6pYT6PsjFwCAA7Hmg1Qt0mRjrBQJ6gP0RrfVdWuuFWuuFJSUl\nQzbZ8WAw+2Jl+Q5THRhtyobdcBCIddI6+2LcTe/hbF5tal6ShJhbOtPs7+bXvYAG8ryz8NiSn1n3\nOmW1YDQp9ZpbNThp0rlMza/a7bauKSfTNel4ylb9GmvP0H1hC0cTbBlFxxhzTS4GBusBq1Jq19+g\n+cCaAcau2fmzdOPEPlpQ6eeKE2aaTpaxWgxTyUmHl53AdQffhtfup63qfBIWJ0Uf/93UY0hNg9zS\nmaYMsrfmeaL5k/n8vJ9w9tSLBxxjGIyrGiBjgddpM32CpLGnnqdr/1vcCKXYdsQNqHiIsrd/MaTz\nCkbibGnpluBgEHIuMNBadwOPAD9VSuUppY4CzgEGWmP+K3CVUqpCKTUR+C5w34hNVqRU7HGYbtXa\nEwsQsFhon3EOvk2PY0TSd1mLJzRdYalpkAui8dRbOyoWxLNtGXWTjyPVUpLXaRtzzcbGA7P9YN5r\neYN/bPw9O4Lb+m+L+KbTPOcyCjc8iLtx1ZDOqzscp6ZVGi5lKucCg52+DriAHcA/gK9prdcopY5R\nSu1aLutO4N/AauBD4Kmdt4kcYBjmjjR1Rtq5YtmneG7rI7TufzGWWA8FGx8z9Rjt3bl9PGm8SLeN\n4Kl/jXAiwoWhN3hsy1+TjpNqh6OTx2Elz5F+1eDY8jP43VEPU+qauNvtTQd/k6h7AhNfvx4SQxvs\nB0IxamRbISM5GRhorVu11udqrfO01lO01vfvvP01rbVnl3Faa32N1rpw559rBsovENlTmGdPW9/B\nay/g/Glf4KCiIwgWzyNYNKc3CdHE/8rOUFSSjHJAum6K3prnido8nD/tC8xN0mJZKciX/IJRq8xE\nroHL6sbvKN7r9oQtj21H3ICr9SOKTVZBzURXKEZNqwQHZpkKDJRSq5VS5vphCrELs4VQPll5UW9i\nklK07H8JzrZ1uBvT15rQmpwvajLWJRKaQKotHZ0gv+4FEpOO55PTPs8M7/4DDvM4rBiGbCOMVnkO\nq6nALhIP87vVP2Lp1kd3u71z6ul0TvkEZe/chq2rbsjnFwjF2NzSTVyCg7TMrhgcCOz17q6U8iml\nhqbgtRizzJZP3d6zldcanqV9xjnEbfkUmk1ClMAgq7pCsZSLO66m9yHYxKslVcRSLBPLMcXRz8yq\ngd3iIBjv3rurplJsO/JGNIqJy//HdMfVTPSE41Q3BaRyahop362VUk8rpW4ANDB5gCFuslCCWIwu\nZlcNXqh/jLvX/i/dStM+81P4tjyNEW5Pe7+ecHzUtV4dS1IVNQLw1ixlpcvN9Tse4t2W5cnHyTbC\nqOeyW0yVs772oFs5s/Jze90e9VTQuPBqvHUv4ttsrthZpkLRBJuaAlIHJYV0X+PWAMcDCnhLKdWu\nlHpFKfUbpdQXge8ADcM8RzEG+FzpVw3OnPI5fnPkv3Bb82jd70KMeJiCTY+bun57j6waZIPWOm1+\nQX7t81T55nLVvJuZV3jYgGPcDgtWS06mPIkMlXrN1TABaAru/fHRcsClBIvmUP7GDRjhPWvdDY1o\nTLOpKSDbkEmkfCVqrb+ntT4eiAKHAhcDS4FJwPeBC4BrhnmOYgxQSlHiSb1qUOAo6k9MChXPJVh0\nIIXrHkh5nz4SGGRHdySecs/W1lWHq20t0cpTWFhyDA7LwEvNchph7HDaLBS40///XLr1Eb69/EKa\ngtt3/4FhZesxt2ANtTDh7ZuHaZa9OxW1LT1s7wjJccY9mF27y9Nax4B3gOFZ3xFjXoHbxo6ucMo6\n5m3hZpZsuJ2TJ51H0awLmfjGj3A2f0ioeE7Ka0diCbrDMamxP8LSHVP01j7PRpuNp5xwRKwHl9U9\n8DiX/H8bS0rznTsLkCUfc0jxUUQSEfJse1e7DxXPpXnOlylZfSedU88gMOnYYZtrU1eYnkiMyYVu\nbLJqBZhMPtwZFAixT5RSaTsiuqx5bOhYQ1NoO20zzyVhcVC43tyqgZRIHnnp8gvya5byQuEk7q37\nO/EkbyMOm4HDaq5ynhgd7FaDojT9UoqcZZw55bO4rXkD/rxxwXcJ+WZS8do1pgqe7YvucJwNjQE6\nZOURyNE6BmLs8rttKashOi0ufn3kAxw94RQSjgI6p55OwcZHUbFQ0vv06QhG5ZzyCErXNMmIdJK3\n/U3OKzuVXx/5QNL+CLKNMDaVeBwYaT5htNa827ycd5pf3/tnVidbj7sVW892ylfcOEyz/K94QlPb\n2kNtS8+4P7UggYEYUUqptN8kDNX7axmKB2nd78Ledsxbnkl77UQifaEdMXTSNk3a+gpGIkrnlE9Q\n7JyQdJxsI4xNVouRNq8I4OHN9+7eP2EXwdKDaZr3VQrXP0B+3YtDPcUBdQSjrG/sojkQHre5BxIY\niBFXlJf+m8Tv19zIL969iu7yI4jkT8ZvMglRthNGTtpthNrn+Ye/lDs73iChB/4GZrUo3HYJDMaq\ndP1SlFJ8a86NXHfQbUnH7DjkO4T8s6h47VpTx5eHQiIBDe0hNuwYn9sLEhiIEWcxFIV5qVcN5hYe\nyqGlx6FRtM66EE/DcuydW9JeOxCOSYnkERCJJQhGUjzPiRj5dS+yyV9JTfem/lWgPUkJ5LHNTL+U\nEtcErIY16bdzbXFQd9xtWIPNTFz+4+GYZlLhaILa1h427uiivScyYisIWuusrlZIYCCyotiT+qzz\nMeWnceaUz6KUom3WBWhl4F//YNrrai2VEEdCutUCd+MqrOEOLpn2Ja4/+LdJx0m1w7GvMM+etobJ\nlq71XPfWpdR3bxnw56Hieew4+Jv4Nz1KwYaHh2GWqQUjCepag6xr7KKxMzRsBdVC0TjbO0Ks3d5F\nOMXpreEmgYHICpvFSFshLaHjvN+ygrCrhEDFcb2BQSL9C7JdthOGXbrCMN7apcQNO4GKY5O2UVYK\nPLKNMOYppdKWSi50lOAwHHRHu5KO2XHQN+iecBgTl/8Qe8fmoZ6mKdGYZkdnmPXbA2zc0cWOzhA9\nkdigv93HE5rOUJRt7UHWbe9iQ2OApq4wsXh2cxskMBBZU5wmMem9lhXc8t7VfND6Fm2zPo2tZzue\nbXtnL+8pGEkQikq50+ESiyfoCad+fr21z3P55Gncu/nupGPyndI0abzwuWy4U7Rl9tr9/PTQu5hV\nMDf5RQwrdcf/Dm1YmfzSlah4dr8ABCMJGjvDbNrRzZptnWxqClDfHqSpK0x7T4SuUJTucIzucIxA\nOEZHMEprd4TGzhC1LT2sb+zio22d1DT30BKIpKzvMtIkMBBZ47JbUvZwn1d4ON+ZexNzCw+lc8rJ\nxO1e08uIUglx+HSmOflhb9+EvaOaKflVlLsHarHSK1+OKY4rE0w0WIomIlR3rk3+c89E6o/5Fe7m\n1ZS9fctQTm+faN3bs6U1EGF7R4i61iBbmnuobuqmuqmbzU3d1Lb0UN8WZEdnmI5glHA0dwKBPUlg\nILKqKMWqgdWwcmjpcVgNG9rqpH362fi2PIMRSb7c2KdtBBOFxhsz1Q4VcOGc6zll8vnJx0ni4biS\n57Cm3T786/rfctM736In1p10TOfUU2nZ//OUfPgnPHUvDfU0BRIYiCzzOq3Yrcl/DbXWLN36CMu3\nP0/brE9jxEP4Nj+d9rqxuCYQlpoGQy2eSP+8emuXsrloNpG8iUnHuOzSNGk8KvOlTjo+bfIFfGvu\njbgsA5fO7tNw+A8J+mcz+eVvY+vamvZx1zZ08uDKOtY2DG8FxbFCXpkiq5RKfXRRKcVrDc+ysulV\ngiUHE/ZNx78h/ekEkO2E4dAVSl3/3hJqQ+9YxfneEI9uvi/pOClqND45rJaUr/eKvKnMKzosacJq\nH211UvuJP6ISMSqfvxwVCyYdu7ahk+sf/5C/v1nD9Y9/KMGBCRIYiKwrzLOn/BZx7UG38s25PwWl\naKv6NHnb38LWWZP2uh3BaMrOfyJzncE0LZbrXsTQCb5U8RkWlhyTdJyUQR6/SvNTFziLJ2L8u2YJ\nr29/LuV1Ir7p1J3wO5wta6h47TqSRayr6zuIxRMkdG/i7Or64WnlPJZIYCCyzmKolG1a+7qvaa1p\nn3keGoXfRBKi1un3w4V5iZ1Hq1LJr30em6uEY/f7OlPyZw44xmZVOG3SNGm8slqMlMcXDWXh7R2v\n8FHbu2mv1TXlJBoXfBf/pkcp+vCeAcfMrfBhtRgYqvex51b4Bj33kRCO9662tY9QlceBSGAgckK6\no4tvNL7A1SsW0+0qonvikfg3PgxJyuzuSkokD52ucCzlNoKKh3FsfZknKw4ilAgnHSerBaIoRdEj\npRQ/OOS3fHn/a01dq+mgK+moPI3yt24ib4DjzLPLvdx0zhwuPrySm86Zw+zygZt55YoPW1fyYPXd\nVHdsytocJDAQOcFps6Q851xgL2Siu5KuaAdtVZ/G3lWHe/vbaa/bHY7n1Png0Szd6ktewwretsb5\nUWwta9veSzpOyiALpRQTfMlXDZwWFwBd0Q4SOk1NEmWw9bjbCPumM+WFr2Fv3/sDdXa5lwsWTs75\noABgQcnR/PqIBzikdEHW5iCBgcgZRSmSkvb3H8x3599MkbOUjqmnE7fl4d/wkKnrSiXEfad1+m0E\nb81SFkUV18/7JQcWDvymZhjgcUhgIHpXjjwpgsStgWq+/foFrGhM31UxYfdQc8o9aGVl2rOfx9rT\nOJRTHTGxRO9rrMxdkdV5SGAgcobPZcOSphJeV7SDTqJ0TDsT3+anUmYj92mT0wn7rCscI5Fq4UVr\n8muXEqw4jgNLjsBmDBzk5TtsaTPOxfhR7nMmTTyemDeVEyrOojK/ytS1It6p1Jx6L5ZQC1P/c6mp\neie5JBIPc/WKxSzd+mi2pyKBgcgd6Y4uBqKdXLnsU/yn7iHaqz6NJRrAt+XZtNeNxBJ0S02DfZKu\n9ayz5UM+jrVwt7+AYKwn6TjZRhC7ctosFHkGfs0byuDiqm9QkTfV9PWCJfOpPemPOFvX9R5jzHLZ\n5ExEEmEOKDiYSXnTsj0VCQxEbkkVGHhsXi6u+gaLSk+ke8JhRDyTKTC5nSBJiIPXt42QqkiMt2Yp\nK1wuHgi8i0UlzxWRwEDsqTTfmXKlsC3czD833kk0Ye41HJh8PFuPuQXPtteZ9OrVppKUc4HH5uXy\nA77P/v6Dsj0VCQxEbrFbjZQfHidP+hSTPNNAGbRVnYenfhm2wLa01+0IRklITYNB6QrH+Kg+dZEY\nb+1SLnbM4rdHPYzdMvAJE7dDqh2KvVkMRXmKRMTawCaeqr2fDR0fmr5m+6wL2H7otRRseqw3ODDR\nlTWb3mx8icae+mxPo5+8SkXO8adYNQCoC1TzasMztFedj0JTsPGRtNdMJEibPCcG1tETTVkkxhao\nx9Wyhs7Kk/HYkmd9y2qBSMafZ096Kmle4WH85sgHOcB/SEbXbJp/BY2HXIV/w0NMevW7ORUc7Lr6\nFomHuXfdrTxY/adsT6ufvFJFzvE6rVgtKmlP8hfqH+e1hmdZdMwTdJcdSsGGh2mafwUpyyfSm4RY\n4E4ddIjd9W0j9BWJicUTexWJya99nl/7fTSqHSxOcS2pXyBSmehzsXFHYK/blVIUOUsBCMV6cFpT\n91HY1Y5Dvo1WFias+iVKJ6g77jYwsvux11eiue+1dNM5c7j58PtI7LLlsbahkxfXNnJ0VQkLKv0j\nPkdZMRA5J10S4jlTL+HXRz6A3eKgrerTODs24Wp6P+11A6GY1DTIUN9phFRFYrw1z9Hj9BO0Jl8O\nlmqHIh2XPXkiIsAztf/i28svJBDNrNdB08Hf6N9WmPzyt7KekLj76lvvapzfUdwf/PQFDr99YQOL\n717Bqpq2EZ+jBAYiJ/lTfLP3O4rx2gsA6Jh+JgmLo7cSoglS0yAzu55GGKhIjBHpJK9hBZcXn8pl\n+1+T9DqyWiDMKPM6sVoGXvk7wH8wR004GUNl/rHVNP8KGg77AQXV/2bqs5/HyGK54V1LNDsnPswG\nfeduLeJ3DRyisQQrqltGfI4SGIicZLcaKYufNAbrue2D77M53Ehn5an4Nj1u6puA1DQwL5HQdKSp\ndpi/9RXCOkZn5Smpx0l+gTDBYigm+lwD/qwyv4pLZn0Tt9UzqGs3z/sqdcf9Gnfj28x44lPYO7fs\nw0wHr2/1bfFhU/jEjDnMLp65W22PvsDBosBmNVg0vWjE5yiBgchZhSlWDfKs+WzpWk9TaDttVedj\nDbeTX/dS2mtKTQPzukKpeyMAuLcs5YzJFfy1O/lWjlJS7VCY53PbUgaStV0bU7b0TqW96nw2n34/\n1lALM54411RZ9eEwu9zLZw6dwpfnXc550y7d62c3nTOHb55UxZLLFkmOgRC78rqsSc83e2xefnvk\nQywsOYZAxTFEXSUUmOi4CNDaLdsJZqRbLSARxVn/ImfZJrOff37SYflOq1Q7FBmZWOBKmkv8bssb\nPFP7L9rCzYO6dk/54Ww6+3Hidi/Tnv4cRWvuS9qyebi827yctW3Jg+nZ5V6+ctyMrAQFIIGByGFK\nKfx5yfem+z5sQokI7TPOJb/uBSyh9Ik6HcEocalpkFLcRIvlvO1v4wl3cv60LzK38NCk4yS/QGTK\nbjWSNlk6Y8qF/OqI+/E7igd9/YhvGpvOfpxAxdFMfONHVD73RSzBkdnL11rzyOZ7uX/jHbvlFuQS\nCQxETkuVhAjwq/ev5Terf0h71fkYiSi+6n+nvabWJr4Nj3OdwWjaL1F5Nc/xjstDx8SjUo5LlSsi\nRDJFeXZc9r1PstgMO157AVprGnpqB339uNNPzSn3sm3RDXjqX6Pq0VPJq39tX6ZsilKK6w/5Hd+Y\n89OcXUmTwEDkNKfNMuCbQ58FJcewsORYQkUHECzcH79sJwyJ9nSBk9ZsaljK/5tQyNvtq5IOc9kt\n2KTaoRgEpRST/Mm3FP5d83eue/PSfasYqBQtc77IpnOeIG73Mv2ZxUxcdt2wnVpoCzeT0HGcFhcl\nrgnD8hhDQV6xIuelqmlwwsRP8olJ5wLQPvN83E3vDtiPfU/BSJxQNHcqoeWSaDxBIJQ6QdPRtp75\nbVu5xv8J5qXcRpDVAjF4TpuFUu/AJbaPLT+Dz8746pB8wIaKDmDjuU/RNOfLFK57gFkPnoh/7f2Q\nGLpE5Vgiys3vfoffrf7xkF1zuEhgIHKez2VLWdQwloiyqmkZrTPOQisDv4kSySCrBsmY2Wbx1i4l\nT2sWzv5aykp0OeVeugAAIABJREFUXpfkF4h9U+Jx4LLv/VFV4Cji9CmfwVCWIdmr11YX2xf9DxvP\nfZKIt5JJy66j6tHT8G5+ekgaMVmUlXOmXsKJFWfv87WGW84FBkqpQqXUo0qpbqVUjVLqohRjb1BK\nRZVSgV3+TB/J+YrhZzEUvhQfMG/ueIlbP7iONZHtBCqO7e2dYOKF3N4jjZUG0m6i1kNj3VP8q3x/\nehwFScdItUMxFHq3FNxJvxxUd67l+29dSkNP3ZA8XqjoQKrPeoSak+5EJWJUvvBVqh45Bf+6f6Ji\noUFdU2uNUoqjJpzCvKLDhmSewynnAgPgDiAClAGLgT8opQ5MMf4BrbVnlz/VIzJLMaJSNVY6tOQ4\nvjf/l8zyzaWt6tPYA/XkNbyZ9ppmMu/Hm3AsTjCSeovFFtjGK5Gt3OIMkdDJx+bLaQQxRJw2C2Xe\ngU8p+OyFWA074Xhw6B5QKTqnnc7681+g9oTb0crCpNeuYfY/DqV8+Y9w7XjH9BHHYKyHG1Z9jVVN\ny8w9diJKXsMKLO/+dR/+AfsmpzYAlVJ5wPnAHK11AFimlHoCuAS4LquTE1nlcVixW40Bex3YLQ4O\nLj4CgM7KU4jb8inY+DDdE49Ie93W7og0VtqFmdUCb81/+EZbB/OOvivlNoJUOxRDqSTfQVcoSnd4\n92C0yFnKjQvvGp4Mf8NCx4yz6Zh+Fu7tb1H08V8pXPcPij+6j6h7Ap1TTqS7/Ei6JxxGLG/gXIee\nWACtE7iteQM/RKQLV9N7uHe8i3vHO+RtfxtLtAtt98Ahi8E68u9PufbKnQXEtdbrd7ntfeC4FPc5\nSynVCjQAt2ut/zCcExTZ43fbaOwMD/izeCLGs1sfosQ5gYnTzsS3+d9sO/JGtHXg8qp9usNxwrE4\nDqsseQO0megl4d3yLGH/LIrKkgdeSoHHnmtvL2K0m+R3s2FHF4k9vh8opUjoBI9v+SvT8vfjoOL0\nXwoyohQ95YfTU344RqQL75Zn8dY+T8GmJyhaez8AUVcJIf9+RLxTiXomEnMWkrDn41UWflNwOkbT\nRozta7CEWrF31WEP1GHvqsPWtRVF7+pDqKCK9hlnEZh0AmUHnYIzC0EB5F5g4AE69ritA8hPMv5f\nwF1AI3A48LBSql1r/Y89ByqlLgcuB5gyZcqQTViMHF+KwMBQFl5teIaZ3gM4vup8Ctf/E9+WZ2mf\n+am0123tjlCepD77eNIdjhGNpV4etYRauS/0MfEJizgxxTiPw4qRpGqlEINltxpMKnBT29qz189i\niShv7XiZ9kjr0AcGu0jY82mfdQHtsy6ARBRXy0e4G9/G2fIxzrZ1+DY/hTXcxkd2G4/ke7i2pY09\nN9WirhKi+ZPpKT2EcNUF9JQeQk/JfBKO/7YzL3MMrifEUBjRwEAp9TLJv/2/DnwD8O5xuxfoGugO\nWuuPdvnrcqXUb4FPA3sFBlrru+gNIli4cKFknI1CDquFPIdlr6VE6P3GcMOCP+CyuunRCSKeyRRs\neNhUYNDWHWWC15mzxUZGiqnVgpqlVNusJNzJkw5BTiOI4eNz2/CHbbR1777tZbc4+OEh/zfoJkuD\nYtgIlswnWLJ7SXAVC/LMlr/xYsNTnHrk3XgdhWiLHW3YiDt8aVcys21EAwOt9fGpfr4zx8CqlKrS\nWm/YefN8YI3ZhwDG97v7GOd32+kOD5xk5Nq5361RtFWdR+l7/4e1e3vSvb8+8Z1dBMdzroGZTooA\n3i3P8IseJx/PvznlOMkvEMNpos+1sxbJ7nsKebbexeX2cAtP1f6Tz874ChZj5H8XtdXFaTMv59ip\ni3Fa8xhtB6Nz6lSC1robeAT4qVIqTyl1FHAO8LeBxiulzlFK+VWvw4BvAo+P3IzFSEtX0+DlbU9x\n9YrFNE0/G6UTFGx6zNR1W8Z5TYPOUHSvfds9GZEAjvpldE49DcNInpPhshtS7VAMK8NQTC5MfoTx\ng9a3eL7+Meq6N4/ovGKJGH/6+Bbqu2sAkiYc5rpcfPV+HXABO+jdEvia1noNgFLqGKVUYJexnwU2\n0rvV8FfgFq31X0Z4vmIEGWlqGhQ5SpmaX0V7XjHdpQvwb3jI1LGinvD4roRoptiTpeYZPjGphEd8\nhSnHSdMkMRKcNguT/AMvyR9bfjq3HfEPpuZXjeicWkKNvNP8Ohs6PhzRxx1qObfep7VuBc5N8rPX\n6E1Q7Pv750ZqXiJ3+PPsSY/VzS06lLlFvSV626vOo+L163G2rCFUPCftdVu6I1QU5Pbe33AIx+ID\n5m3syVb7HCeHEpSWH59ynNQvEMNhVU0bK6pbWDS9qL8dcYHbTk8kTktg78C2r/viWzteZl37ahZX\nXYGhhue7cELHMZSFMncFtx5x/8jmOQyDXFwxECIlj8OKzZo6laQt3ExtxTEkDDv+jeYaK7V1R8Zl\nO+Y9k7gGomIhpm5dxhWFJzCjIHmQZbWolE2vhBiMVTVtLL57Bbc+t47Fd69gVc1/26uX+5y4Hcl/\n5zZ2fMSmzo+I66Hre7CrUDzILe9dzbN1DwKM+qAAJDAQo1SBK3miYCDaybeXf4YndzxL15ST8G18\nHBLpP/y0NpeZP5Zorc39m+uWslWH6aw8LeUwSToUw2FFdQuRWIKEhmgswYrqlv6fKaWoLHQn/bLw\nuZlf47qDb8Nm2AnGemgObR/SudkNBy5rHk5L8mJfo40EBmJUKnAnX6722Lx8cb+rOX7iJ2mrOh9b\nqJn8ra+auu54a6zUFY4Ri6dfJXlzywN8cvJENhZMTjlOjimK4bBoehF2q4FFgc1qsGh60W4/t1oM\nphblDZiMqJTCaendIvzHxt/zgze/SHd0wBPwpiV0nP/UPUxHpA1DGXxrzo0cP/HMfbpmLpHwXoxK\nTpsFl92StK7/cRPPACAwqZSYs5CCDQ/TNeWktNcNRxN0haLjZp+8dYC92b0kopy+bTX28jlMyJ+R\ndJhUOxTDZUGlnyWXLdorx2BXTpuFKUVuapr3Ln7U58wpn2Oad3b/sca2cHN/LkImGoPbWLLhdiKJ\nMGdVXjTmaqDIioEYtfwpVg0Aaro28HT9Y7TPOAdv7VKM8J5FNfe2tqGT372wYbc9zLEqEkvQFUq/\n7+rZtpyJwTaOmfH/Uo+TaodiGC2o9HPFCTMHDAr6eJ02JhYM3GwJoMxdwQkTPwnA1kA133z9fF5t\neMbU47+142Ue29Lb2KjcPZmfH3YPn5wyNvPfJTAQo1a6mgYrm17jweo/UTvtNIx4GN/mp1Jeb21D\nJ9c//iH3LNvM4j+tGPPBgdl8inc3/oXXPX4CFcemHCfbCCIXFHkclOQ70o7zO0o4b9oXmFvYe4rp\n3ebl/Ojty2kP9+YvfNDyFnd9dDN653HnTZ0f8VrDM4R2dnGc5Jk+5lYK+khgIEYtq8VImex22uQL\nuP3oR7GVLSJUUIV/Q+rTCavrO4jFexOcIvHdE5zGGq21qXwKFY9wf+hj/lxSgbYm/yYGkngocscE\nnxN/XupANc+Wz6emXdq/laDRWA17fz5CU6iBD9tW0h7pfR84f9qX+NWi+/t/PpbJK1mMagVuO53B\ngZfD+/YRAdqqzqf87V9g79hCxDd1wPFzK3xYLQaxeAKrxeDQqcmXLEe7zqC5pMO8ba9z/9Z63j/+\nuynHuewWqXYockpFgQutzbUSBzik+CgOKT6q/+8nVZzDSRXn9P/dbkm/CjFWyCtZjGpepxVLin3t\njkgbN797Fc/6J6KVgX/Dg0nHzi73ctM5c7j48EpuOmcOU4tHZzlTM5q7B+5SuSdf9ZNYbPm4pp2V\ncpxXVgtEjlFKMcnvSlkpVQxMAgMxqiml8KVIQsy3eYnEQ4TsbgIVx1Gw4SFIJK/yN7vcywULJzO7\n3EtLINK/vziWBCNxekxUOgyHO/heYBmvVi5Cp/m2JPkFIhcppZhcKMFBpiQwEKNeqtMJhrLw44W/\n5+gJp9C632ewdzfg2bbM1HVjcU2byWXI0aQ5YG61oKf2aVoNTU/5USnH2awKp02qHYrc1BccpMs5\nEP8lgYEY9dx2K3Zr6l9lrTUbSw4g5vDjX/eA6Ws3B8JjatUgGk+Yaq8MMHfbWzzY1MOUGYtTjpOm\nSSLX9W4ruCnOH7+t1TMhgYEYE9LVNPjnpj/y/ZVfYduMs/DWPIclZO4oYjiaoNPEWf/RorU7YqbZ\nJJFIB3lbnqOz8lSwpt5GkNMIYrQo97lS1jkQvSQwEGNCqjwDgCPLPsEls75FoOoCjESEgk2Pmb52\nU1doX6eXExIJPWAXuoE8v+ZXnD4hn4apJ6ccZxi9hY2EGC2KPA4qi90Y8umXlDw1YkxwWC0pO6xV\n5ldx/MQziZfMJ1g0B//6f5m+djDSWyZ5tGvtMd898uD2rZwdjKEnnZhyXL7DNmaLvIixy+u0MbPU\ng9MmH4EDkWdFjBl+d+r9w1giyrKG//Dm9BNxtazB2fyh6Ws3dppL2MtVWmvTSYcqFuSk2je5pPB4\ntCX1c+p1yWqBGJ0cVgszSjySlDgACQzEmJGuRHJCJ/jL+t/wlC1OwuLIcNUgTiA8enMNOoJRojFz\nqwXrPv4j3fFu2md+KuU4pRg3zabE2GQYvUmJUwrdKeuhjDcSGIgxw2KolBnydouDnx16N5fsfw2d\nladSsOlRVMx8/kBj5+jNNdjRNfBqwdqGTh5cWcfahk4AuqId3Nj4MH8snkj3hEUpr+m2W+TNVIwJ\nPreNWWWelO3cxxMJDMSYki4JscxdgVKK1qoLsIY78Nb8x/S1e8JxOkdhrkFHT5RwNLHX7X1No/7+\nZg3XP/4haxs6KYjFWNLQxBklJ4GRujaBFDUSY4nVYjC50M20krykuQd7BtJjlQQGYkxJVyIZYFXT\nMr657T468idT+PGSjK6/YxSuGuxIcqpi16ZRsXiC1fUd+DY/yYHhIPb9Lk57XalfIMYij8PKzFIP\nkwtdu9VHGSiQHqskMBBjSroSydDbXCnP6qF65ll4tq/A3r7J9PWDkQQdo6gaYkdPlNAAqwXw36ZR\nhur9tuQtqOWvtX9nR+FswoWzU17XZTfSFpUSYrRSSlHgtjOrrDdAcNmNAQPpsUpe2WLMSVfsaHbB\nfH644P9w7v9FtLJSuPb+jK7/4tod3PHSBlbVmCuSlC1aaxpT1GDYs2kU8fd5TgUIzjgn6X36yGqB\nGA/6AoSZpfmcNmcCtl0C6bkVvmxPb9jIWSMx5rjtVhw2Y8B99V112vP4eOpxzNrwII0Lv4e2pq+I\n1recGIsnsFs3suSyRSyozM32zG1Jcgt2Nbvcy+xyLwDHbgtxxdYGthx9XtprS36BGG+OnFnM/V9e\nxIrqZuZNKmBGiYdAOJb2NTYY2S4NIoGBGJMKXDYao8nP7Wut+cnKr+F3K5aE2/FteSbt8TzYfV8+\nGkuworolJwODREJndIoiFo9SsOlRouWLiOWVpxxrtxrSNEmMSwsq/Xu93mPxBD3ROKFInHAsQTiW\nIBpPEIunPh6sFNgsBlaLwm7p3ZpzWi04bAYOq5HVwmESGIgxqcBtT1mUSCnFhTO/gs9WQLiumsK1\nS0wFBn378rF4AqvFYNH0oqGc9pBp7g6nfWPqk9Bxrlt+IecZbZwx85tpx0tRIyH+y2ox8FqMAbfX\n4glNQvf+AVAoDNV7tDqXK4bKK1yMSavrO3hmdQP7leX3L5Xv6ZDi3nbCrftdRPnbN+No20DYX5Xy\nun378qvrO5g7yccBSa6dTZFYgh0ZVGqMxMMcFbdTFdN0Tj0t7XjJLxDCHIuhsJC7AUAyEhiIMWdV\nTRuL715BJNb7rf6mc+YkDQ46Im084Ahypc1B4br7aVj047TX33Vfvr49yIySvJyK/rd3hEx1UOzj\nUhZ+UPcxgYnHUWfPTznWYijcdtlGEGIsk1MJYsxZUd1CJGbuWFEo3sNT2/7Na5MOpWDDQxlVQoTe\nUsmt3eY6Fo6EQDhGR9D8ccqGnjqa1v8Na7iNtlmfSTve67LmVBAkhBh6EhiIMWfR9CLsVgPLzuSe\nVMeKylwV3H70IyzY/0qs4Q581f/O+PG2d4aIxIY+MzlTiYRmW3swo/s8vuVvXFf/Fzo8FQQqjkk7\n3ienEYQY82QrQYw5Cyr9LLlsESuqW5g3yUeBK02HQLuf7vIjaC+YSfGae2mv+nRG54USid4thWnF\nefs69X3S2BXK+OjUFyacy+ffuZfQgVemLYFsGL1V4YQQY5usGIgxaUGlnytOmMnRM4uxWtJ/yC+t\nf4yziizEW9fgbnw748cLhGK0mGxrPBx6IjGauzLf0piy6UkOC0dpNbON4LTJNoIQ44AEBmJM661c\nln75e4Z3fw6bcAohh4/iNX8e1GM1dIQIReODuu++iCc0da2ZbSGE4kF+88EPaNj8IF2TTkhbuwCk\nqJEQ44WsC4oxz++2p/02Pd07m+ne2ejOCN4P78YWqCfqqcjocbSGmpYeZpZ6RrQdcX1bMOMch4bu\nWja2vkMi3Ebr7M+lHa8U5Ms2ghDjgqwYiDHPabPgspv7VX9v6om87rRT+NFfB/VYkViCrW09g7rv\nYLQEwhmdQugzzbsfj4TLONDip2vyiWnHe502jBEMdoQQ2SOBgRgXCtypExD7/GnrEm4uq8C/7h+o\nWGbL8306gzG2dwx/e+auUJSGQTxOR6QNS2AbhVtfoX3WZ8BIvxIg1Q6FGD/k1S7GhQKXzVThn8v2\nv4aSlo3YtlxKwcZHaZt90aAer6krjNWiKPY4BnX/dELROLWtPRkVMoLeHhG3vPddpoR6uEMnaN3v\nwrT3UQrypdqhEOOGrBiIccFqMch3po+Dy91TsE46gWDhARSu+TMZf/LuoqE9NCzFj0LROJubu0kM\nonSCRnNqxXmc1VxDV8UxRPOnpL1PvtM6ojkTQojsksBAjBtmtxOiOsrXy4r4e2I7edte36fHrG8L\n0tQ1dMcYQ9E41U3dphsk7clQBp+M2TmttZ7W2YtN3UeKGgkxvkhgIMYNr8lvvjbDTl7BbPIsbko+\n+MM+P+72jhD17UESicGvPgB0BKNsagoQH+R11ra/z7KG/+Bfcw+RvIl0Vp6S9j6yjSDE+JNTgYFS\n6kql1EqlVFgpdZ+J8d9RSm1XSnUopf6slBqeDV0xJiil8OeZ+5D7yoH/w4kzvkB+/Wu4mt7f58du\nDUSobg4Mqs5BIqFp6AhS29IzqO2DPq9se4p/bbgD17Y3aD3gElNJhx6HbCMIMd7kVGAAbAN+BqSt\nMKOUOhW4DjgJmApMB34ynJMTo5/f5HYCQMvsxbyWX0j8vd8MyWMHIwk27giwrT1INJ7+E15rzSvr\ndvDTJz9i2frmfX78L+9/Hf+nZmC1OGjdL33tAsBUcSghxNiSU6cStNaPACilFgKT0gz/f8A9Wus1\nO+9zI7CE3mBBiAH11TQIRtJ/MLcT41vFXj7XsYq5699leWcxcyt8SVs4m6E1tAQitHZHyHda8Tpt\nuOwW7JbeGD2uNaFonO5wnOWbmrnukdXE4unbR6eS0AliiSiuaJDZG5+ifcaniDsL095PthGEGJ9y\nKjDI0IHA47v8/X2gTClVpLVuydKcxCjgd9sJRtKf//c5Cvnh3J9z+lNf4j8v/4q/R7+2Tx/Qu9K6\nt95BZzCWdMx7te3E4ru3jx7M465ofJH7N97Brc6FGPEQzXO+ZOp+chpBiPEp17YSMuEBOnb5e99/\n5w80WCl1+c78hZVNTU3DPjmRuwrcdtPNE6tKj+bdwrM5Tb1OOY39H9AjYW6FD6vFwFC9xy1TtY9O\npcQ1gbkFhzB37UN0TTqBcOF+pu6XriulEGJsGrHAQCn1slJKJ/mzbBCXDAC7fn3q+++ugQZrre/S\nWi/UWi8sKSkZxMOJscJiqIyO4G064HwunFTGib5/7tMHdKZml3u56Zw5XHx45T6tUlT55vB9yzQc\noRaa5n3V1H16txFG84KiEGKwRuyVr7U+fogvuQaYD/xr59/nA42yjSDM8OfZae8x12Ng7oyFvLKl\nhFPUGg47tYyp+7iNkInZ5d5BBwSdkXZe3PYEp1WcR/Hqu+gpnkd3+SJT9/W5pDeCEONVTm0lKKWs\nSiknYAEsSimnUipZ8PJX4EtKqQOUUn7gh8B9IzRVMcp5HFbsVnO//hbDyvcOu52jQz0c0bhkmGc2\ndFY1vcbD1fcQ2vgvHJ1belcLTO6h+OQ0ghDjVk4FBvR+uAfpPVlw8c7//iGAUmqKUiqglJoCoLV+\nFvhf4CWgZuefH2dj0mJ08mfw4RfxTaV5xnn8p+4htjW9OYyzGjonVJzFrYuWcOhH9xMqqKJz2hmm\n7mcY0mJZiPEspwIDrfUNWmu1x58bdv6sVmvt0VrX7jL+Nq11mdbaq7X+gtZ66GrPijHPn5dZct2W\neZfxR5+HlWtuG6YZDY2EjtMW7q17MLPxfZxt69lx8DdBmXu5+1w2lNnsTCHEmJNTgYEQI8lmsrFS\nH2fhAfzBfRTf3/QW9o4twzexffTc1ke46o3PsS2whdJ3fkvIN5OOaZ80fX+zPSWEEENrVU0bd7y0\nkVU1bVmdh6wXinGt0GOnK5S8lsCeLId8DzY+gWPlTWw98ieUuiYO4+wGZ2HJMfREA8xu/ABX21rq\njv8tGBZT97VaFHl2c2OFEENnVU0bi+9eQSSWwG41WHLZIhZU+rMyF1kxEONavsOK1WJ+2TzmLqVx\n7lf4TuR97nzvWvQ+tGUean1zKXZO4LypFzNh1S8J+mfTPv1s09fwu+2yjSBEFqyobiES6y1oFo0l\nWFGdvQN2EhiIcU0pRWGGuQYt877Kt7vh+uZmFLkTGDxd9wC/X3MjkXiYwrX/wNFZQ+Nh15leLQDp\njSBEtiyaXoTdamBRYLMaLJpelLW5SGAgxr1MGisBaJub6fOvYX7jGgo2PkYg2jlMM8tMPBElkgjj\niEcpfec3BCYcTtekE0zf32U3cNpkG0GIbFhQ6WfJZYu46pT9srqNAJJjIAR2a28SYia5Bu0zz6Po\no7+wbPUv+L9td/Pzw++lyFk2jLNM7+ypl6C1pnTlLdhCzdQcdo/pugUgSYdCZNuCSn9WA4I+smIg\nBL1JiBlRBvVH3cQRXa2cpPPJtxUMz8TSSOg4d3/8v2zuXAeAo3Mzxav/RGvVBQRLDzZ9HaXIqEy0\nEGLsksBACHqTEG3WzJLuQsXz8FRdxE83rsDXupZIPExCx4dphgNrCzfzfssKNnZ+BFoz8Y0b0BYn\njYdm1n3c47Bis8jbgRBCthKEAP6bhNjYkVmNrMaFV+Pb8jRFr17NNVOmMt17IP9vv28P0yz3VuQs\n45ZFf8NtzcO7+Snyt77MtsN/RMydWaOwTIs9CSHGLvmKIMROhRm0Y+6TsHupP/oX+NvWcVgoxgF+\n88v3++L17c/x6Ob70FrjtuZhCbVS8foP6SmeS8uBl2Z0LYuh8EonRSHEThIYCLGT1WIMap+9a8on\naJ11Ideuf4ljd3b/rg1sIqETQz3Ffmva3uHD1pXEdW/C5MTlP8KIdLL12NvAyOxD3p8nJZCFEP8l\ngYEQuyjKNAlxp4ZFPyKaV86Ul66kpWM9P3r7ch6u/vMQzw5C8SAAl82+hmsO+hVWw4Zv0xMUVD9B\n08HfJFy4X8bXzPS4phBibJPAQIhduO1WXIMoCZyw51N74h3YAg0c9NYtXFL1DU6ZdN6Qzu0fG3/P\nT1Z+nWCsB0MZOCxO7B2bqVh2Ld2lC9gx/+sZX1NqFwgh9iSBgRB7KB7kqkGw9BAaDr+egpqlfLal\nHp+jEK01d370c15teGaf5zW74CDmFx2Ow+IAQMVCTHnha2jDRt2Jd4CR+TZIYZ5jn+clhBhbJDAQ\nYg8+ly2j/gm7ajnwi7RPP4sJb9+Ct/pJwvEgTcEG2sO9dc8TOmE69yCh4/xhzc94futjABxcfCSf\nnflVDGUBnWDSK1fhav2Ircf9mqgn82ZOhgEFUrtACLEHCQyE2INSiqLBHt9Tiq3H3kp32UImv/Id\nCptXc/0hv+PMKZ8FYHXrW1z1xmfZ1l0LsFeQsL1nK+81vwGAoSy0hpvoiXXt9TAT3rqZgs1P0nDY\n9XRNOWlQUy1w2zEMSToUQuxOAgMhBlCYl/nRxT7a6qTm5HuIeiqY+p9LyWt8C8vOkwJ2w8kUzwxK\nXeUAPFz9Z7748sn9AcK/a5Zw+5qf9BdK+v7Bt3H21Et2u37Je7dTsvpOWvb/PM1zLx/kv5DBBz9C\niDFN5VLb2JGycOFCvXLlymxPQ+SgVTVtrKhuYdH0Isq8Dtq6o4O+lrV7O9Oevgh7YCs1J99NYNKx\ne415v+VN1rV/wGdmfBnoXTHQaCa4Ju19hFBrylb+ktL3b6d9xjnUHffrjI8m9nHZLcws9QzqvkKI\n0UcptUprvdDUWAkMhOi1qqaNxXevIBJLYLca3HvpoXgc+7YHb+1pYuozi3G2b2D7od+nee6XM2ps\n1EdFe6h4/Qf4Nz5C636fpf6omzNqp7ynyYUuaZokxDiSSWAgWwlC7LSiuoVILEFCQzSW4J3adryu\n3m/kaxs6eXBlHWsbMmuxHHOXUH3Ww3RWnkL5Wz+jcull2AL1GV3D2byamU+cTcHGR2k85Crqj75l\nn4ICq0VJwyQhRFJSB1WInRZNL8JuNYjGEtisBoumF1HscfBWdSvXP/4hsXgCq8XgpnPmMLvca/q6\nCXs+tSf9keIP76Zs5S+Z9dCJNM29nNbZi4nlTUh6P3tHNaXv3U7BhoeJOYvYfPrf6a44Zp//nb35\nE5J0KIQYmAQGQuy0oNLPkssW9ecY9PVFX9vYRSzeu5IQiydYXd+RUWAAgFI0z/0yHVNPp/zNGyl7\n97eUvnc7gYpj6C5bSLhgJtriwIh242xbh6d+Ge6md0kYdprnfYUdB11Jwp7hYw48DQol6VA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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import BayesianRidge\n", "\n", "reg = BayesianRidge(fit_intercept=False)\n", "\n", "# prepare the design matrix\n", "mus = np.reshape(np.linspace(-3, 3, 16), (16, 1))\n", "params = {'s':s, 'mus':mus}\n", "\n", "# perform the fitting (optimization with respect to alpha and beta is also performed)\n", "Phi = gen_desmat_gaussian(X, params = {'s':s, 'mus':mus})\n", "reg.fit(Phi, t)\n", "\n", "Phi_test = gen_desmat_gaussian(Xtest, params)\n", "pred_mean,pred_std = reg.predict(Phi_test, return_std=True)\n", "\n", "print(f's={s}\\nalpha={reg.lambda_} \\nbeta={reg.alpha_}')\n", "plot_result(pred_mean, pred_std)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }