{ "cells": [ { "cell_type": "markdown", "id": "6909afe7", "metadata": {}, "source": [ "## Demonstration of Univariate Linear Regression using Gradient Descent\n", "\n", "This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Data-Driven Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de)." ] }, { "cell_type": "markdown", "id": "1905ee9e", "metadata": {}, "source": [ "This notebook demonstrates the application of gradient descent to a univariate linear regression in order to iteratively estimate the parameters of a one-dimensional predictor model from a set of examples." ] }, { "cell_type": "code", "execution_count": 1, "id": "e36bd395", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "id": "29769ed1", "metadata": {}, "source": [ "### Generate Dataset\n", "\n", "In the following, a synthetic dataset with $N$ examples is generated by implementing a simple linear relationship and additive noise." ] }, { "cell_type": "code", "execution_count": 2, "id": "7fceda9a", "metadata": {}, "outputs": [], "source": [ "N = 500 # total number of examples\n", "theta = [1.2, .1] # true intercept/slope\n", "\n", "x = np.random.uniform(low=-10, high=10, size=N)\n", "X = np.concatenate((np.ones((len(x),1)), x[:,np.newaxis]), axis=1)\n", "Y = X @ theta + .2 * np.random.normal(size=N)" ] }, { "cell_type": "markdown", "id": "597681f2", "metadata": {}, "source": [ "The data points are plotted in order to illustrate the structure of the dataset" ] }, { "cell_type": "code", "execution_count": 3, "id": "78574fc0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_data(X, Y, ylabel=r'$y$', alpha=1):\n", "\n", " plt.scatter(X, Y, s=15, label=r'examples $(x_n, y_n)$', alpha=alpha)\n", " plt.xlabel(r'$x$')\n", " plt.ylabel(ylabel)\n", " plt.grid()\n", "\n", "\n", "plot_data(x, Y, alpha=.5)" ] }, { "cell_type": "markdown", "id": "2727bf9c", "metadata": {}, "source": [ "### Estimate Parameters of Linear Regression using Gradient Descent\n", "\n", "The parameters of the linear model are estimated by gradient descent. First a function is defined which implements the mini-batch gradient descent algorithm" ] }, { "cell_type": "code", "execution_count": 4, "id": "0f5f0901", "metadata": {}, "outputs": [], "source": [ "def split_array(a, size):\n", " return np.split(a, np.arange(size, len(a), size))\n", "\n", "\n", "def mini_batch_gradient_descent(X, Y, theta_0, gradient, lr=0.01, mu=1e-10, max_iter=100, batch=32):\n", "\n", " N = X.shape[0]\n", " theta_min = theta_0.copy()\n", " n_batch = int(np.ceil(N/batch))\n", " n_epoch = int(np.ceil(max_iter/n_batch))\n", " indices = np.arange(N)\n", "\n", " history = list()\n", " history.append(theta_0.copy())\n", "\n", " for epoch in range(n_epoch):\n", " Xb = split_array(X[indices, :], batch)\n", " Yb = split_array(Y[indices], batch)\n", " np.random.shuffle(indices)\n", "\n", " for b in range(n_batch):\n", " theta_min -= lr/batch * gradient(theta_min, Xb[b], Yb[b], mu)\n", " history.append(theta_min.copy())\n", "\n", " return np.array(history)\n", "\n", "\n", "def gradient(theta, X, Y, mu):\n", " return - 2*(X.T @ Y) + 2*(X.T @ X) @ theta + mu * theta\n", "\n", "\n", "def predict(X, theta):\n", " return np.dot(X, theta)" ] }, { "cell_type": "markdown", "id": "718bf42c", "metadata": {}, "source": [ "Now the parameters of the linear regression are estimated" ] }, { "cell_type": "code", "execution_count": 5, "id": "19dfe9aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated/true intercept: 1.197 / 1.200\n", "Estimated/true slope: 0.105 / 0.100\n" ] } ], "source": [ "theta_0 = np.random.normal(size=2)\n", "lr = 5e-3\n", "max_iter = 500\n", "batch = 32\n", "\n", "history = mini_batch_gradient_descent(X, Y, theta_0, gradient, lr=lr, max_iter=max_iter, batch=batch)\n", "\n", "print('Estimated/true intercept: {0:.3f} / {1:.3f}'.format(history[-1,0], theta[0]))\n", "print('Estimated/true slope: {0:.3f} / {1:.3f}'.format(history[-1,1], theta[1]))" ] }, { "cell_type": "markdown", "id": "63320836", "metadata": {}, "source": [ "The estimated regression line after convergence is plotted in the following. Only a slight deviation between the true and the estimated regression line can be observed." ] }, { "cell_type": "code", "execution_count": 6, "id": "c4d3edbc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot data points\n", "plot_data(x, Y, alpha=.5)\n", "# plot regression lines\n", "xl = np.linspace(-10, 10)\n", "xl = np.concatenate((np.ones((len(xl),1)), xl[:,np.newaxis]), axis=1)\n", "\n", "plt.plot(xl[:,1], predict(xl, theta), color='C1', linestyle='--',\n", " linewidth=2, label='data generation model')\n", "plt.plot(xl[:,1], predict(xl, history[-1,:]), color='C2', linestyle='-',\n", " linewidth=2, label='estimated regression')\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "d80c6959", "metadata": {}, "source": [ "### Evaluation\n", "\n", "In order to illustrate the convergence of the gradient descent algorithm, the mean-squared error (MSE) between the predicted and the true output is plotted for the parameters estimated at a particular iteration. The convergence of the algorithm is clearly observable." ] }, { "cell_type": "code", "execution_count": 7, "id": "bfa2900e", "metadata": {}, "outputs": [ { "data": { "image/png": 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oL10b++tY7K9jsb+O5Qz9vZVju3QYevjhh21/7tWrF3r37o1OnTphx44dGDVq1G3tc9myZViyZEmL5d999x28vb1vu9brycjIuO3vNVsBmSBHdb0ZH2/YhCC1HQtzE23pL90Y++tY7K9jsb+OJWV/6+pufi6tS4ehn+vYsSNCQkKQm5uLUaNGISIiAqWlpc22MZvNqKysvOY8o4ULF2LBggW2zzqdDjExMRgzZgy0Wq1d6zWZTMjIyMDo0aOhVCpvez/vn9+D0yV6RCQNQFq3sBt/g4ewV3+pdeyvY7G/jsX+OpYz9Lfpys7NcKswdOnSJVRUVCAyMhIAkJqaiqqqKhw6dAj9+/cHAGzbtg1WqxUpKSmt7kOtVkOtbjm8olQqHfYDbeu+e3QIwOkSPXJKazG+N/+j/jlH/uyI/XU09tex2F/HkrK/t3Jcp55ArdfrkZ2djezsbABAfn4+srOzUVBQAL1ejxdeeAF79+7F+fPnsXXrVtx7773o3Lkzxo4dCwDo1q0bxo0bhyeeeAL79+/H999/j7lz5+Lhhx92izvJmnSP4iRqIiKi2+XUYejgwYNITk5GcnIyAGDBggVITk7GokWLIJfLcfToUdxzzz3o2rUrZs6cif79+2PXrl3NRnY+/vhjJCUlYdSoUZgwYQKGDh2K9957T6pTcogeTWGoiGGIiIjoVjn1ZbIRI0ZAFK/9zq1vv/32hvsICgrC2rVr7VmW0+l29fb6S1fqUV1ngr83h3yJiIhullOPDNHN8fdSIibICwCQfalK2mKIiIhcDMOQmxjSKQQAsO1UicSVEBERuRaGITeR1i0cALDlVOl1Ly0SERFRcwxDbmJolxCoFDJcrqpHQSVf2kpERHSzGIbchEYpR0KwDwDgPN9gT0REdNMYhtxITFDj60I4MkRERHTzGIbcSFzw1TBUUStxJURERK6DYciNxHJkiIiI6JYxDLmRpjB0gXOGiIiIbhrDkBuJDf5xZIi31xMREd0chiE3EhPoDZVChjqjBfnlnDdERER0MxiG3IhKIUOfaH8AwKELVySuhoiIyDUwDLmZfnGBABiGiIiIbhbDkJsZEBcEADjIMERERHRTGIbcTN+YAABAXpketQaztMUQERG5AIYhNxPqp0a4Vg1RBE4V6aQuh4iIyOkxDLmhnlGNk6iPX66WuBIiIiLnxzDkhnp0uBqGCjkyREREdCMMQ26oZ5QWAEeGiIiIbgbDkBvqeXVk6GypHg0mi8TVEBEROTeGITcU6a9BkI8KFquInOIaqcshIiJyagxDbkgQBPRoulRWyEtlRERE18Mw5KaaLpVx3hAREdH1MQy5qaZ3lB2+UCVtIURERE6OYchN9b/6Wo4zpTWorjdJXA0REZHzYhhyU6F+asQHe0MUgcMFfE8ZERHRtTAMubGm0aHDfGkrERHRNTEMubG+sQEAgKOXOImaiIjoWhiG3Fjvq3eUHbtcDVEUJa6GiIjIOTEMubHECD8oZAIqa40orG6QuhwiIiKnxDDkxjRKORIj/AAARy9WSVsMERGRk2IYcnN9YwIAAAfOcxI1ERFRaxiG3NzgjsEAgKxzFRJXQkRE5JwYhtxcUxg6VaTDlVqjxNUQERE5H4YhNxfqp0bnMF8AwL58jg4RERH9HMOQB0i9Ojq091ylxJUQERE5H6cOQzt37sSkSZMQFRUFQRCwYcMG2zqTyYQXX3wRvXr1go+PD6KiovDoo4+isLCw2T7i4+MhCEKzr+XLl7fzmUgrtdPVeUN5HBkiIiL6OacOQ7W1tejTpw9WrlzZYl1dXR0OHz6MV155BYcPH8b69euRk5ODe+65p8W2S5cuRVFRke3r6aefbo/ynUZKQuNrOXJKalCuN0hcDRERkXNRSF3A9YwfPx7jx49vdZ2/vz8yMjKaLXv77bcxaNAgFBQUIDY21rbcz88PERERDq3VmQX7qpEU4YfTxTXIyqvApD5RUpdERETkNJw6DN2q6upqCIKAgICAZsuXL1+O1157DbGxsZg6dSrmz58PhaL1UzcYDDAYfhw90el0ABovy5lMJrvW27Q/e++3NYMTAnG6uAa7z5ZiXPdQhx/PGbRnfz0R++tY7K9jsb+O5Qz9vZVjC6KLvLRKEAR8/vnnuO+++1pd39DQgCFDhiApKQkff/yxbfkbb7yBfv36ISgoCHv27MHChQsxY8YMvPHGG63uZ/HixViyZEmL5WvXroW3t7ddzkUKJ64IeO+0HMFqEYv6WaQuh4iIyKHq6uowdepUVFdXQ6vVXndbtwhDJpMJkydPxqVLl7Bjx47rnvSqVavw5JNPQq/XQ61Wt1jf2shQTEwMysvLb9jMW2UymZCRkYHRo0dDqVTadd8/pzeYMfBP22G2iti2YChiAl032N2s9uyvJ2J/HYv9dSz217Gcob86nQ4hISE3FYZc/jKZyWTCgw8+iAsXLmDbtm03POGUlBSYzWacP38eiYmJLdar1epWQ5JSqXTYD9SR+24SqFSib0wADl64gv3nq9ExzN+hx3Mm7dFfT8b+Ohb761jsr2NJ2d9bOa5T3012I01B6OzZs9iyZQuCg4Nv+D3Z2dmQyWQICwtrhwqdyx2dQwAA3/MWeyIiIhunHhnS6/XIzc21fc7Pz0d2djaCgoIQGRmJBx54AIcPH8ZXX30Fi8WC4uJiAEBQUBBUKhWysrKwb98+jBw5En5+fsjKysL8+fPxyCOPIDAwUKrTkszQziFYsfUsduSUokJvQLBvyxEwIiIiT+PUI0MHDx5EcnIykpOTAQALFixAcnIyFi1ahMuXL+OLL77ApUuX0LdvX0RGRtq+9uzZA6Dxkld6ejqGDx+OHj164I9//CPmz5+P9957T8rTkkz/uEAkRfihpsGM1zfnSF0OERGRU3DqkaERI0bgevO7bzT3u1+/fti7d6+9y3JZcpmA30/shl99sB87zpRKXQ4REZFTcOqRIbK/PjEBAIASnQG6Bj5fg4iIyK5hyGQy4eLFi8jJyUFlJV8K6oy0GiXC/BrnCuWV6iWuhoiISHptDkM1NTV45513MHz4cGi1WsTHx6Nbt24IDQ1FXFwcnnjiCRw4cMAetZKddA7zBQDkldVKXAkREZH02hSG3njjDcTHx2P16tVIS0vDhg0bkJ2djTNnziArKwuvvvoqzGYzxowZg3HjxuHs2bP2qpvaoCkM5XJkiIiIqG0TqA8cOICdO3eiR48era4fNGgQHn/8cbz77rtYvXo1du3ahS5durTlkGQHTWEop1gncSVERETSa1MYWrdu3U1tp1ar8dRTT7XlUGRHfa9Ooj504QosVhFymSBtQURERBKy+631VVVVSE9Px7lz5xAUFIQ+ffpg5MiR0Gg09j4U3abukVr4qOTQNZiRU1yD7lH2fecaERGRK7H7rfUTJ05EYWEhkpKSsGLFCrz11lvo2LEjli9ffsPnAlH7UMhl6B8fBADYl89XcxARkWezexiqqqrC0qVL8fjjjyM8PBzffPMNTp8+jYqKCsybN8/eh6PblJLQGIb25/MRCERE5NnsHoaGDBmCjz76CAAgCI1zUbRaLf7yl79g8+bN9j4c3aafhiGO2BERkSez+5yhlStXYsmSJRg2bBhKSkrw8ccfQ61WY9++fdBqOTfFWfSODoBaIUNFrRF5ZXp0DvOTuiQiIiJJ2D0MKZVK/OEPf4BOp8OWLVvwww8/oKqqCp07d+bIkBNRKWToFxuIrHMVWLvvIhZN6i51SURERJJw2ItatVot7r//ftx///24dOkS6uvrERwc7KjD0W2YNjgWWecqsOr7fIzuHo7UTvz5EBGR57FLGHrsscdw5coVREdHo0OHDoiOjm72pdFo8PzzzyM9Pd0ehyM7ubt3FL47UYIvfijE7twyhiEiIvJIdglDK1aswC9/+Uukp6dDEATbS1qbJlADwJ133mmPQ5GdpXYKxhc/FOLwhSqpSyEiIpKEXcKQVqvFpk2b8PLLL2Po0KEYOXIkLl26ZPsqLCzEpEmT7HEosrPk2AAAwA+Xqvg0aiIi8kh2mzMkk8nwpz/9Cf/617/wwQcfYO7cuXwPmQvoEuYHX7UCeoMZZ0pq0C2Sd/wREZFnsftzhp588kkkJibixRdfhMVisffuyc7kMgHdIhtvqz9TUiNxNURERO3P7mEIAEaPHo0ZM2Zg9uzZqKqqcsQhyI6anjF0tkQvcSVERETtzyFhCACSkpKwfPlyPP3008jNzXXUYcgOuob7AuDIEBEReSaHhCGz2YxNmzbhqaeeQnp6Ou644w5cvnzZEYciO+hydWQot5QjQ0RE5HnsNoE6NzcX27dvR0ZGBrZs2YKqqipERkbipZdewqxZs9ChQwd7HYrsrMvVkaHzFbVoMFmgUcolroiIiKj92CUMzZkzB+vXr0dJSQk0Gg1mz56NKVOmoH///s2eNUTOKcxPjUBvJa7UmZBTXIM+MQFSl0RERNRu7HKZbOXKlSgqKsKFCxewatUqGI1GvPnmm/jDH/6Aixcv2uMQ5ECCINgCUPbFKklrISIiam92fTdZTEwMHn74YTz88MMAgFOnTuGDDz6ATqfDq6++Cn9/f3sejuyob0wAduSUIftiFaZLXQwREVE7ctjdZADQrVs3LF68GGlpabjnnnsceShqo75XR4aOFFyRthAiIqJ25tAw1OTll19GTk5OexyKblNyTCAUMgHnK+oQ/9LXWP19vtQlERERtYt2CUNvvvkmtmzZ0h6Hotvk763EiMRQ2+clX56UsBoiIqL2Y9c5Q9cybNiw9jgMtdH9/aKx5VSp1GUQERG1qzaNDBUUFNzS9nzwonMb1yMCM4bEAwAEATCardIWRERE1A7aFIYGDhyIJ598EgcOHLjmNtXV1Xj//ffRs2dP/O9//2vL4cjBZDIBr0zsDpVcBlEESmsapC6JiIjI4dp0mezkyZP44x//iNGjR0Oj0aB///6IioqCRqPBlStXcPLkSZw4cQL9+vXD66+/jgkTJtirbnIQmUxAmFaNS1fqUVzdgOhAb6lLIiIicqg2jQwFBwfjjTfeQFFREd5++2106dIF5eXlOHv2LABg2rRpOHToELKyshiEXEikvwYAUKzjyBAREbk/u0yg9vLywgMPPIAHHnjAHrsjiYVrr4ahaoYhIiJyfw6/tb6wsNDRhyA7axoZKmIYIiIiD+DwMJSZmXndCdbXs3PnTkyaNAlRUVEQBAEbNmxotl4URSxatAiRkZHw8vJCWlqa7RJdk8rKSkybNg1arRYBAQGYOXMm9Hr97Z6OR4gNapwndLpYJ3ElREREjnfLYWjdunUtlu3duxdJSUno3bs3vv7662brHnroISxcuPC2iqutrUWfPn2wcuXKVte//vrrWLFiBd59913s27cPPj4+GDt2LBoafhzRmDZtGk6cOIGMjAx89dVX2LlzJ2bNmnVb9XiK1E7BAIAD56+gwWSRuBoiIiLHuukwVFxcjPvvvx8ZGRkt1i1btgwdO3bEyJEj8eijj+LkyR+fXrxjx47bHhkaP348/vCHP+AXv/hFi3WiKOLNN9/Eyy+/jHvvvRe9e/fGf/7zHxQWFtpGkE6dOoXNmzfj3//+N1JSUjB06FC89dZbSE9P5+W76+gU6osIrQZGsxUHzldKXQ4REZFD3fQE6vfeew8mkwmrVq1qsa6iogK7d+8GAEyePBmvv/465s+fj0cffRTHjx/HM888Y7+Kr8rPz0dxcTHS0tJsy/z9/ZGSkoKsrCw8/PDDyMrKQkBAAAYMGGDbJi0tDTKZDPv27Ws1ZBkMBhgMBttnna7xUpHJZILJZLLrOTTtz977tYc7OgVh/ZFCZOaUYnB8gNTl3BZn7q87YH8di/11LPbXsZyhv7dy7JsOQ8888wyeffZZTJ48ucXDEwMDA21/HjZsGNasWYMHHngAkZGR2Lx5M0aPHn3TBd2s4uJiAEB4eHiz5eHh4bZ1xcXFCAsLa7ZeoVAgKCjIts3PLVu2DEuWLGmx/LvvvoO3t2OeudPaaJvUfGoEAHJsPpKPXpZcqctpE2fsrzthfx2L/XUs9texpOxvXV3dTW9702EoICAAH374Ib755ptmy00mE06dOoWsrCykpqYCaAxEarUa77zzzk0X4iwWLlyIBQsW2D7rdDrExMRgzJgx0Gq1dj2WyWRCRkYGRo8eDaVSadd9t9UgvQH/9+dMXKoVkDI8DcE+KqlLumXO3F93wP46FvvrWOyvYzlDf5uu7NyMW37O0M8fniiTyXDu3DkMHToUoaGhmDhxIoYMGYJFixbd6q5vSUREBACgpKQEkZGRtuUlJSXo27evbZvS0uYvHjWbzaisrLR9/8+p1Wqo1eoWy5VKpcN+oI7c9+2KDFQiKcIPp4tr8H3eFUzuHy11SbfNGfvrTthfx2J/HYv9dSwp+3srx23zrfVyuRzR0dFIT0/Hgw8+iG3btuHXv/41OnfujHvvvRebN29u6yFalZCQgIiICGzdutW2TKfTYd++fbYRqtTUVFRVVeHQoUO2bbZt2war1YqUlBSH1OVOJvRqDJkf7bsgcSVERESOY5fnDN1555345S9/iRUrViA/Px9Hjx7F73//e5SVleHuu+/GP//5z9var16vR3Z2NrKzswE0TprOzs5GQUEBBEHAvHnz8Ic//AFffPEFjh07hkcffRRRUVG47777AADdunXDuHHj8MQTT2D//v34/vvvMXfuXDz88MOIioqyx6m7tSmDYqGSy3CkoApHL1VJXQ4REZFD2CUMzZ49G1988YXtc8+ePfG73/0Oe/bswfnz55Gfn39b+z148CCSk5ORnJwMAFiwYAGSk5Ntl+B++9vf4umnn8asWbMwcOBA6PV6bN68GRqNxraPjz/+GElJSRg1ahQmTJiAoUOH4r333mvD2XqOUD81xvdqvJz42cFLEldDRETkGHZ5N9nQoUNx+vTpVtdFR0e3enfWzRgxYgREUbzmekEQsHTpUixduvSa2wQFBWHt2rW3dXwCftk/BhuzC7Ex+zJ+P7EbNEq51CURERHZld1ex5GUlHTNdY66JZ0cL7VTMKIDvaBrMGPtvgKpyyEiIrI7h7+bjFybXCZg9ohOAIB3M/NgsV57pI6IiMgVMQzRDf2yfwx8VHKU1hhwtrRG6nKIiIjsimGIbkilkKF3dAAAILugStJaiIiI7I1hiG5K39gAAMARhiEiInIzbQ5DEyZMQHV1te3z8uXLUVVVZftcUVGB7t27t/UwJLHkmAAAwKGCK9e9w4+IiMjVtDkMffvtt83e8v6nP/0JlZWVts9msxk5OTltPQxJbGB8EFQKGXJL9ThccEXqcoiIiOymzWHo56MEHDVwT4E+KtzXt/Gp3at2n5e2GCIiIjvinCG6aY+mxgMAMk6VQG8wS1sMERGRnbQ5DAmCAEEQWiwj99MjSouEEB8YzVZsPVUidTlERER20ebXcYiiiMceewxqtRoA0NDQgKeeego+Pj4A0Gw+Ebk2QRAwsVck3t6ei6+PFuHevh2kLomIiKjN2hyGpk+f3uzzI4880mKbRx99tK2HIScx4WoY2nGmDHqDGb5qu7zejoiISDJt/pds9erV9qiDXES3SD8khPggv7wWW0+VcHSIiIhcHidQ0y0RBAETekUAAL4+WiRxNURERG3X5jCUlZWFr776qtmy//znP0hISEBYWBhmzZrFeUNuZmKvxlvsmy6VERERubI2h6GlS5fixIkTts/Hjh3DzJkzkZaWhpdeeglffvklli1b1tbDkBNpulRmNFux5STvKiMiItfW5jCUnZ2NUaNG2T6np6cjJSUF77//PhYsWIAVK1bg008/bethyIkIgoBJfRpHhz49eFHiaoiIiNqmzWHoypUrCA8Pt33OzMzE+PHjbZ8HDhyIixf5D6a7eXBANAQB2JNXgQsVtVKXQ0REdNvaHIbCw8ORn58PADAajTh8+DAGDx5sW19TUwOlUtnWw5CTiQ70xp1dQgEAnxxg2CUiItdll7fWv/TSS9i1axcWLlwIb29v3Hnnnbb1R48eRadOndp6GHJCDw+MAQB8dugSTBarxNUQERHdnjaHoddeew0KhQLDhw/H+++/j/feew8qlcq2ftWqVRgzZkxbD0NOKK1bOIJ9VCirMWD76VKpyyEiIrotbX7oYkhICHbu3Inq6mr4+vpCLpc3W//ZZ5/Bz8+vrYchJ6RSyPBA/2j8a+c5pB+4iDE9IqQuiYiI6Ja1OQw9/vjjN7XdqlWr2noockIPDozBv3aew46cUlToDQj2VUtdEhER0S1pcxhas2YN4uLikJycDFEU7VETuZBOob5IivDD6eIa7M4t5+s5iIjI5bQ5DM2ePRvr1q1Dfn4+ZsyYgUceeQRBQUH2qI1cxPDEUJwurkHmmTKGISIicjltnkC9cuVKFBUV4be//S2+/PJLxMTE4MEHH8S3337LkSIPMfzqLfY7z5TBzLvKiIjIxdjlRa1qtRpTpkxBRkYGTp48iR49euA3v/kN4uPjodfr7XEIcmID4oMQ6K1Eud6I3bnlUpdDRER0S+z+1nqZTAZBECCKIiwWi713T05IpZDZLo+t2HqWL28lIiKXYpcwZDAYsG7dOowePRpdu3bFsWPH8Pbbb6OgoAC+vr72OAQ5uSmDYqGQCThcUIVFG49LXQ4REdFNa/ME6t/85jdIT09HTEwMHn/8caxbtw4hISH2qI1cSGKEH/72YB88m56N706UwGi2QqWw+8AjERGR3bU5DL377ruIjY1Fx44dkZmZiczMzFa3W79+fVsPRU5uUu8oLP3yJCpqjThccAWDOwZLXRIREdENtTkMPfrooxAEwR61kIuTyQQM6xqKz49cRsbJEoYhIiJyCXZ56CJRk4m9IvH5kcv49MBFPJvWBVqNUuqSiIiIrouTOsiu7koKQ5cwX9QYzPjvwUtSl0NERHRDDENkVzKZgIcGxgAAMs+USVwNERHRjbl0GIqPj4cgCC2+5syZAwAYMWJEi3VPPfWUxFW7vyGdG+8m3J9fCaOZT6QmIiLn1uY5Q1I6cOBAswc7Hj9+HKNHj8Yvf/lL27InnngCS5cutX329vZu1xo9UWK4H4J9VKioNeL73HKMTAqTuiQiIqJrcumRodDQUERERNi+vvrqK3Tq1AnDhw+3bePt7d1sG61WK2HFnkEmEzCuZwQA4MX/HUVVnVHiioiIiK7NpUeGfspoNOKjjz7CggULmt3q//HHH+Ojjz5CREQEJk2ahFdeeeW6o0MGgwEGg8H2WafTAQBMJhNMJpNda27an7336wyeH90ZWXnlOFdeh//bk4+nhnds9xrcub/OgP11LPbXsdhfx3KG/t7KsQXRTV4t/+mnn2Lq1KkoKChAVFQUAOC9995DXFwcoqKicPToUbz44osYNGjQdR8AuXjxYixZsqTF8rVr1/IS2y06UCbgo1w5/JUiFvWzgA+kJiKi9lJXV4epU6eiurr6hleF3CYMjR07FiqVCl9++eU1t9m2bRtGjRqF3NxcdOrUqdVtWhsZiomJQXl5ud0vsZlMJmRkZGD06NFQKt3veTwGsxV3vbELpTUGLJqYhF8Njm3X47t7f6XG/joW++tY7K9jOUN/dTodQkJCbioMucVlsgsXLmDLli03fOVHSkoKAFw3DKnVaqjV6hbLlUqlw36gjty3lJRK4JlRXfDyhuP4Z+Y5PJKaIMn7yty1v86C/XUs9tex2F/HkrK/t3Jct7hwsXr1aoSFhWHixInX3S47OxsAEBkZ2Q5VEQA8NDAGoX5qlOuN2HWWzx0iIiLn4/JhyGq1YvXq1Zg+fToUih8HuvLy8vDaa6/h0KFDOH/+PL744gs8+uijGDZsGHr37i1hxZ5FKZfh7t6N4XNDdqHE1RAREbXk8mFoy5YtKCgowOOPP95suUqlwpYtWzBmzBgkJSXhueeew+TJk687p4gc4xfJHQAA3x4vRmlNg8TVEBERNefyc4bGjBmD1uaAx8TEIDMzU4KK6Od6RwegX2wADhdU4cM95/HC2CSpSyIiIrJx+ZEhcg2zhjU+Z+ijvQWoNZglroaIiOhHDEPULkZ3j0B8sDeq601IP3BR6nKIiIhsGIaoXchlAmYNa3ycwVvbzuJKLV/RQUREzoFhiNrNgwOikRjuh6o6E/69+5zU5RAREQFgGKJ2pJDL8MyoLgCADUcKYbW6xcPPiYjIxTEMUbsa1S0MvmoFLlfVI+NUidTlEBERMQxR+9Io5bbnDj299ghOF+skroiIiDwdwxC1u99P7IahnUNgtFjx7o48qcshIiIPxzBE7U6jlOOl8Y0PXvzyaBEuV9VLXBEREXkyhiGSRM8O/rijUzAsVhHvZXJ0iIiIpMMwRJJpeir1h1kX8KdvTklcDREReSqGIZLM8K6huP/qZOr3d51DWY1B4oqIiMgTMQyRZARBwBsP9UWPKC1EEdh+ulTqkoiIyAMxDJHkxnSPAAB8ebQQosgHMRIRUftiGCLJTewdCblMwK6z5fjih0KpyyEiIg/DMESS6xzmi6fv6gwA+MfWsxwdIiKidsUwRE7h13d2hLdKjnNltfjs4CWpyyEiIg/CMEROwVetwKTeUQCA3/7vKP749UmOEBERUbtgGCKn8bsJ3TCpT2Mgen9XPj47xBEiIiJyPIYhchr+3kq8NSUZL4xNBAC8mXEGDSaLxFUREZG7YxgipzNzaAIitBoUVjfgi2zeXUZERI7FMEROR6OU47Eh8QCAt7afRYWeT6YmIiLHYRgip/TwwBj4qhW4WFmPB/+VBbPFKnVJRETkphiGyCkFeKvwfzMHQSWXIa+sFt/nVUhdEhERuSmGIXJaybGBeHhQDADgf7yzjIiIHIRhiJzaL/s3hqFNx4twuape4mqIiMgdMQyRU+sV7Y/UjsEwWUS8vS1X6nKIiMgNMQyR05uX1gUAsG5/Ab4+WiRxNURE5G4YhsjppXQMxiODYwEAc9YexpT39qKshrfbExGRfTAMkUt45e7u+PXQBAgCkHWuAsu+OSV1SURE5CYYhsglqBVyvHx3d6z99WAAwPojl3H8crXEVRERkTtgGCKXktopGPf1bXyZ6x++PgmrlW+2JyKitmEYIpfz/NhEqBQy7D1XiZc3Hpe6HCIicnEMQ+RyogO98ZcHekMmAGv3FSDtjUx8c4x3mRER0e1hGCKXdG/fDrivbwcAQG6pHi989gPqjRaJqyIiIlfk0mFo8eLFEASh2VdSUpJtfUNDA+bMmYPg4GD4+vpi8uTJKCkpkbBisqcnh3eCTGj8c63Rgg3Zl6UtiIiIXJJLhyEA6NGjB4qKimxfu3fvtq2bP38+vvzyS3z22WfIzMxEYWEh7r//fgmrJXtKjPDDlgXDMWdkJwDAvzLz+HZ7IiK6ZQqpC2grhUKBiIiIFsurq6vxwQcfYO3atbjrrrsAAKtXr0a3bt2wd+9eDB48uL1LJQfoGOqL34zojLX7CnC+og4bswsxuX+01GUREZELcfkwdPbsWURFRUGj0SA1NRXLli1DbGwsDh06BJPJhLS0NNu2SUlJiI2NRVZW1jXDkMFggMHw49ONdTodAMBkMsFkMtm19qb92Xu/nkYlA2YOicdfM85ixdazmNAjFAq5jP11MPbXsdhfx2J/HcsZ+nsrxxZEUXTZB7Vs2rQJer0eiYmJKCoqwpIlS3D58mUcP34cX375JWbMmNEs2ADAoEGDMHLkSPz5z39udZ+LFy/GkiVLWixfu3YtvL29HXIe1HYGC7DksBy1ZgETYiwYG+2yv9ZERGQHdXV1mDp1Kqqrq6HVaq+7rUuPDI0fP9725969eyMlJQVxcXH49NNP4eXldVv7XLhwIRYsWGD7rNPpEBMTgzFjxtywmbfKZDIhIyMDo0ePhlKptOu+PZEh4hJe+eIkvrkoR2pyd0zuG87+OhB/fx2L/XUs9texnKG/TVd2boZLh6GfCwgIQNeuXZGbm4vRo0fDaDSiqqoKAQEBtm1KSkpanWPURK1WQ61Wt1iuVCod9gN15L49ya/uSECRzoB/7sjDoi9Pwt+r8deb/XUs9tex2F/HYn8dS8r+3spxXf5usp/S6/XIy8tDZGQk+vfvD6VSia1bt9rW5+TkoKCgAKmpqRJWSY70wthETE2JhSgCz/33GE5XCVKXRERETs6lw9Dzzz+PzMxMnD9/Hnv27MEvfvELyOVyTJkyBf7+/pg5cyYWLFiA7du349ChQ5gxYwZSU1N5J5kbEwQBr93bExN7R8JkEfFBjgzZF6ukLouIiJyYS18mu3TpEqZMmYKKigqEhoZi6NCh2Lt3L0JDQwEAf//73yGTyTB58mQYDAaMHTsW//znPyWumhxNLhPw9wf7orrOiN25FfjN2mxsmjcMIb4tL38SERG5dBhKT0+/7nqNRoOVK1di5cqV7VQROQuVQoaVU/pg7F+3olhvxAPv7MF7jw5A13A/qUsjIiIn49KXyYiux1ulwGNdLQj1VeF8RR0Wrj8GF36SBBEROQjDELm1SG/gsydToFbIcOjCFXy45zxMfGUHERH9BMMQub0OAV6YOTQBALD4y5NIXbYVmWfKJK6KiIicBcMQeYTnxyTiudFdodUoUK434tcfHsD58lqpyyIiIifAMEQeQSYT8PSoLtj/+zSkdgyGySLirW25UpdFREROgGGIPIpGKcdvxyUCAP53+BLe3HKGk6qJiDwcwxB5nOTYQMxP6woAeHPLWSzaeAIWKwMREZGnYhgij/RsWhcsuacHBAH4v70X8Ez6ERjMFqnLIiIiCTAMkceafkc8VjycDKVcwNdHizBxxW6cKamRuiwiImpnDEPk0Sb1icLqxwYhxFeN3FI97lv5PRauP4acYoYiIiJPwTBEHm9olxB8N38YUhKCUGe0YN3+Atzz9m4cPF8pdWlERNQOXPrdZET2EuSjwronBmNvfgXezDiL/ecr8cC7WegQ4IWeHbR4fkwiuvC9ZkREbokjQ0RXyWQC7ugUgvenD8CdXUIAAJer6vHtiRIs+fKkxNUREZGjMAwR/Yy/lxL/NzMF/5t9BzqH+QIAdueWY+KKXSiubpC4OiIisjeGIaJr6B8XiC0LhmN093AAwIlCHWasOYB6I2/BJyJyJwxDRDew/P5emJ/WFV5KOU4V6fDmljNSl0RERHbEMER0A8G+ajyb1gVvT00GALy/6xx25JRKXBUREdkLwxDRTRrVLRwPDoiGVQQeW30AD/0rC/vOVaBE1wBdg0nq8oiI6Dbx1nqiW7D03p6oM1rwzbEi7MuvxEPv7QUACAIwrkcE3niwL7xUcomrJCKiW8GRIaJboFHK8fbUfvj+pbswqU8UgMYgJIrApuPF+OeOXNQZzRJXSUREt4JhiOg2RPp7YcXDfZExfxhOLR2Hlyd2AwC8tS0X497cxUBERORCGIaIbpMgCOgS7geNUo5fpcYhLtgbAFBQWYeV23Mlro6IiG4WwxCRHagVcnwxZyh+Oy4RALByex76vZaBTw9clLgyIiK6EU6gJrITf28lnhrWCbp6M97NzENlrRELPz+GvfkVSI4NxIMDoqFWcHI1EZGz4cgQkR3JZAJeGp+EH14dg9Hdw2Gxilh/+DJe2XAck97ajYuVdVKXSEREP8ORISIH8PdS4l+P9Mf2nFL8cKkaa/cV4EyJHhP+sQu/6NcBd3QKwR2dg6HVKKUulYjI43FkiMhBZDIBo7qFY8Horvjq6aHoEaVFjcGM/2RdwFMfHcKw17fjv4cuQRRFqUslIvJoHBkiagcR/hp8OXcovs8rx/rDl3HwQiUuVtbj+c9+wL93nUO/uEDc3SsSd3QOkbpUIiKPwzBE1E5kMgF3dgnFnV1CYbZY8a+d5/DWtrM4XVyD08U1WLuvAHclhWHm0AQMYSgiImo3vExGJAGFXIY5Izvj+xfvwoopyXhwQDQAYNvpUkxftR/p+wtgMFskrpKIyDNwZIhIQsG+atzTJwr39InC1JQ4/O27HOw6W46X1h/DX7/LwdDOIegQ6IWOIb6IDfbGwPggqUsmInI7DENETqJvTAA+mD4Q7+86h//LuoBiXQM2ZBfa1ssE4IWxSQj2VWFEYijC/DQSVktE5D4YhoiciErRePls1rCO+D63HEcKqrDpeBHOlOhhFYE/bz4NAIjy12D6HfEI8Fbi7t5RUCtk+DDrAvrG+KN/HEePiIhuBcMQkRNSymUYkRiGEYlhmJfWBWariH9uz0PGqWIcv6xDYXUDlm1qDEZ/++4MKmqNsFhF+HspsXfhKHip+KRrIqKbxTBE5OQEQYBSLuDZtC54Nq0LrtQa8eaWM9iXX4lz5bUorTHYtq2uN+GVjccxsVckUjsFQ62QQRAECasnInJ+Lh2Gli1bhvXr1+P06dPw8vLCHXfcgT//+c9ITEy0bTNixAhkZmY2+74nn3wS7777bnuXS2QXgT4qLLm3JwCgwWTBllMleGdHHk4U6gAA/z10Cf89dAkA4KOSo1e0PzqG+mLGHfHoEu4nWd1ERM7KpcNQZmYm5syZg4EDB8JsNuN3v/sdxowZg5MnT8LHx8e23RNPPIGlS5faPnt7e0tRLpHdaZRy3N07Cnf3joIoiliz5zw2ZhfiTEkN6owW1Bot2HuuEnvPVeKzgxcxZVAsenXwh0wQML5XBLxVLv1XABGRXbj034SbN29u9nnNmjUICwvDoUOHMGzYMNtyb29vREREtHd5RO1KEATMGJKAGUMSUGswI7+8Fpeu1ONCRS32nqvA9pwy/Cfrgm37xV+cQLdILfw0CnQM9cHMoR0R4c871IjI87h0GPq56upqAEBQUPO7aT7++GN89NFHiIiIwKRJk/DKK69wdIjcmo9agZ4d/NGzgz8AYNawjth1thxfHS3EubJaHC+sRo3BjP3nKwEAW08D7+/KR5CPCh1DfHBv3yj0jQlEzw5azjkiIrfnNmHIarVi3rx5GDJkCHr27GlbPnXqVMTFxSEqKgpHjx7Fiy++iJycHKxfv77V/RgMBhgMP05I1eka52GYTCaYTCa71ty0P3vvlxqxv82lJgQgNSEAAKA3mHH8sg6Xq+pRUWvE9pwyHLxQhcpaIyprjTh44QoAIMhHiYRgH8QFeyMh2BsdAr1gsYq4o1MwAjWND7Bnfx2Dv7+Oxf46ljP091aOLYhu8srs2bNnY9OmTdi9ezeio6Ovud22bdswatQo5ObmolOnTi3WL168GEuWLGmxfO3atRxNIrdW3gAYLMDpKgEnqwQU6AUYrdceFQpSi4jzFeGlAOJ8RST6iwhQARxIIiJnUFdXh6lTp6K6uhparfa627pFGJo7dy42btyInTt3IiEh4brb1tbWwtfXF5s3b8bYsWNbrG9tZCgmJgbl5eU3bOatMplMyMjIwOjRo6FUKu26b2J/26reaEFeWS3OV9TifEUdzl2dg1RvsiKnpAat/c3hpZQhIcSn8Su48f88aL2UiA1qHFEaGB+IQG9VO5+Ja+Lvr2Oxv47lDP3V6XQICQm5qTDk0pfJRFHE008/jc8//xw7duy4YRACgOzsbABAZGRkq+vVajXUanWL5Uql0mE/UEfum9jf26VUKpHso0FyfHCLdboGE7IvVOC/W/cjJLojdudV4FxZLepNVpwsqsHJoppr7jc+2BvdIrXQKOUI9lHBT6NEsa4BY7qHIzk2AP5eStQYzFDJZdAo+fBI/v46FvvrWFL291aO69JhaM6cOVi7di02btwIPz8/FBcXAwD8/f3h5eWFvLw8rF27FhMmTEBwcDCOHj2K+fPnY9iwYejdu7fE1RO5Lq1GidSOwbhyWsSE8YlQKpUwWay4WFmHvLJanCvTI7+8FgBwpc6Igsp6GEwWnCtvHGU6X1HXYp/r9hcAADRKGRpMVviqFRgYH4i4YB+E+qkR4K1Epd4ImUxAv9hAFFTWwkulwLAuIQjwVqFE14AGkwVxwT4t9k1EdD0uHYbeeecdAI0PVvyp1atX47HHHoNKpcKWLVvw5ptvora2FjExMZg8eTJefvllCaolcm9KuQwdQ33RMdQXQHir21TWGnGqSIeThToYLVaU1RhQVWeE3mDGoQtXcKXOhAaTFUDjJO/tOWUAyq57XLlMQLCPCmV6A0QRCPFVo0eUFsmxAVDIBNQ0mKFSyODvpcTgjsHwUSvgpZRDo5TBW6WASiFDdb0J/zt0CVZRxKCEIHSL1MJotiK/vBY9oprfUVeqa0BOSQ02Hy/GM6O6IFzLxxEQuTqXDkM3mu4UExPT4unTRCSdIB8VhnQOwZDOIa2ubzBZkFemh69agXK9AaeLa1BQWYcrtUZU1poglwF1RgsuVNQhQqtBVb0RZ0r0zV5JUq43IPNMGTLPXD9ENfH3UkJvMMNi/fHvkwitBgazBVfqTOgRpUViuB/8vZW4UmvEhuxC23Yf7yvA3JGdkRDiAz+NAlfqjAjz0yA22Buhfmr4qRUQBAHlegNkggCTxYpQXzVksh/DldFshUwALKKIL38owukiHcb0iEBytHM8LdxssUIhl0ldxk2rM5pv+WGip4t1iA70hq/apf9JhK7BhDe+O4Pk2ADc27eD1OW4FNf+yRORW9Eo5egR1fhspLhgH/SPC7ru9qIooqi6AWU1Bnip5Kg1mFFQWYe8Uj3Ka40wW6zw0yjRYLLgbIke58prYTBZUGey2MJPdX3j7bexQY0B5kxxDYp1DbZjnCjU2V510pq3t+dec51aIYOPWoHKWqNtWaC3Ev5eSogA5IKAS1X1kAmNf641WgAA/96djzs6BUFeK8Phb07DbAUMZiuM5sZRs0h/DYJ9VVDIZJDLBJTVGKBRyhDgrYLWS4mc4sZ6B8Q39u9iZR0CvVWwiiJEETCYLVh/+DK6RWoxLSUWcpkAhUwGmQwQRSCnuAZaLyV2ninDB7vz8ZsRnfCr1DioFXLsza+Ar1qB/rGBsIgiLFYRdUYLfrhUBYPJiu6RWvhqFDBZrPjs4EV8e6IEi+/pgf5xgS36Y7WKaDBbbjq8FFbVQ+ulhK7ehMMFVxAX5INe0f62da99dRKbjhdjflpXzBgaj5lrDqCwqgGJEX64KykMjwyOA9D4e2OyNPZyY3Yhnv/fcXQI8EL6rMGICfKGyWLFjpwyXKiohdkqYkBcIAbEB8Fibfy+W53LJooiBEGAxSrC0Mr5Wqwi5LKbvw3zZKEOa/bkY2LvKHSL9EO90QKNUo7pq/bjdHEN0g/IMKJrGPy9lRBFEUaLFWqFY+ffmS1W7Dpbjr4xAQj0cb2bJNzibjJH0ul08Pf3v6nZ6LfKZDLhm2++wYQJEziBzwHYX8dy9f6aLFbUNJhRoTdA66W0Xe6qNZixPacUSrkMAV5KHDhfCYVchqo6E2oNZoxMCkWkvxdyimvw9bEiAEB1nQmXrtRB69U4d6pEZ4DeYL7lmsL81EiM8MP3ueWwutnfzNGBXhBFoNZohkImwFulQHW9CdX1JgT5NAY1fy8lvJRyXKkzQldvRpCPCvUmS2N4FEXbXDNBgO1uxgitBr4aBQoq62xhEQAUMgHmnzXxzi4hUMllOH018EZ7W3FB3zyEhGvVKKsxtOh/lzBflOgaUGMwI9xPgwBvJeKCvVFvsqKqzoiLlXWICvAC0Hip1no1cF2srEeJrgG9o/1xuaoeV+pMGJUUBm+VAoLQGFT3n69E+NURRT+1AlovJSxW0Ra+rKJoC6x1RjN2ni2HxSo260Nr7u4diROFjc8TS4rww6Ur9fBWyaGSy6BSyKDVKKH1agznXioZDCYrjl2uRoS/BuF+GtSbLDhVpENVvQndI7UQAWgUMtQaG29w8FYroJQJMFqsyC+vw6kiHaL8NRieGIoyXQPyL5diQGI0BEGG0hoDiqsb0CHQCwqZAJNFhNlqhclihckionOYL/70i16398t1Dbfy7zfD0A0wDLku9tex2N/rqzdaUFZjQJ3JjAitxjaakFNcA7PVenUbKwJ9lNAo5ai6eklOo5TjRGE1duaU4sjx0+jYqRM0V+c2qRVyWK0iCqvrUV1ngskqwmyxIthXBZNZRGWdEVV1RihkMogQUVXXOOoV6a9BrdECpVyAAAF1RjN0DWbUGsyovzpKZrWKMFsbR46CfFSoNZghAvBSyWEwWaBraAx3MgGtBrUOAV5QK2Qoqm5AvckCuUyAt0qOmoZbD4U3o0uYL/LLa5sFngFxgYgP8bG9qNhPo8CUQbHYd64CP1yqvu6+VApZsxHAAO/GmwTqTRbsPFPmEuG0S5gvxveMwIpt1x6tdFZ9ov2xce5Qu+7zVv795mUyIiIH8FLJERvc8kGtfWICbvi9PaL80TXUG9/oTmLC6C5OETaNZivqTRb4qhsvgdUZLZALAmQy2IJaE4tVhExofF+e1Soit0wPvcEMuSDASyWH2SKi3mSGWiFHkI8KFXoj1EoZdPUm1JssCPBSwUslR2WtEVovBarrTKg1mpEYoUVVnRGhvmqEaTW4dKUOuaV6AECEvwaJ4X4QBAG/GdEJ1fUm2yMcRFHE7txyFFU1QIQIb5UC0f5qbNj6PcYPH4xBHUNhEUUcKaiCRilDhFaDYF+17dJVUXU99p2rREKID2SCgPyKWlitInQNJvioFPBRKxDqp0JZTePcsKp6E5RyATJBQKS/F3zVChwvrIZGKYeXUo5zZXo0ZSuFTMDgjsEwmC0orGqArsGEOoMFMpkAuQAoFTLIBQEWUbzaNwt6dfDHHZ2CcfyyDrHB3iioqENuWQ0m9oqCQiZcvdQnos5ohr+XEn4aJcr1BnSL1ELXYIJaLoNFFG0jc7p6MxpMjZdoY4K8G8NyvQkapRzhWk3j5eOSGihkMhjMjSN1ZquIOoMZZqt49ecvQ68OAdiXXwF9gxkqOZB35hQi47tCIZcj2FeNYF8ViqsbIAiNN1woZELj/8oFBEl8aY1hiIiIbkilaLy0AgBymfy682Z+Ov9FJhPQNfz6k8GbLi/djA4/2TY60BvRgS0DZ+MdjT8SBAF3dglttsxkMqEgRET/uEDIZAJkEDAoofU5apH+Xrgv+ccJyU3zlG5F96ifjky0frdl/7hb22dTHb2i/ZvV9MsBMbda3g0N7tjyeWOtaTpPk8mEb6pPYsLITk4R5m/EdW4RICIiInIAhiEiIiLyaAxDRERE5NEYhoiIiMijMQwRERGRR2MYIiIiIo/GMEREREQejWGIiIiIPBrDEBEREXk0hiEiIiLyaAxDRERE5NEYhoiIiMijMQwRERGRR2MYIiIiIo/GMEREREQejWGIiIiIPBrDEBEREXk0hiEiIiLyaAxDRERE5NEYhoiIiMijMQwRERGRR2MYIiIiIo/GMEREREQejWGIiIiIPBrDEBEREXk0hiEiIiLyaAxDRERE5NEYhoiIiMijMQwRERGRR2MYIiIiIo/GMEREREQezWPC0MqVKxEfHw+NRoOUlBTs379f6pKIiIjICXhEGPrkk0+wYMECvPrqqzh8+DD69OmDsWPHorS0VOrSiIiISGIeEYbeeOMNPPHEE5gxYwa6d++Od999F97e3li1apXUpREREZHEFFIX4GhGoxGHDh3CwoULbctkMhnS0tKQlZXVYnuDwQCDwWD7XF1dDQCorKyEyWSya20mkwl1dXWoqKiAUqm0676J/XU09tex2F/HYn8dyxn6W1NTAwAQRfGG27p9GCovL4fFYkF4eHiz5eHh4Th9+nSL7ZctW4YlS5a0WJ6QkOCwGomIiMgxampq4O/vf91t3D4M3aqFCxdiwYIFts9WqxWVlZUIDg6GIAh2PZZOp0NMTAwuXrwIrVZr130T++to7K9jsb+Oxf46ljP0VxRF1NTUICoq6obbun0YCgkJgVwuR0lJSbPlJSUliIiIaLG9Wq2GWq1utiwgIMCRJUKr1fI/Rgdifx2L/XUs9tex2F/Hkrq/NxoRauL2E6hVKhX69++PrVu32pZZrVZs3boVqampElZGREREzsDtR4YAYMGCBZg+fToGDBiAQYMG4c0330RtbS1mzJghdWlEREQkMY8IQw899BDKysqwaNEiFBcXo2/fvti8eXOLSdXtTa1W49VXX21xWY7sg/11LPbXsdhfx2J/HcvV+iuIN3PPGREREZGbcvs5Q0RERETXwzBEREREHo1hiIiIiDwawxARERF5NIYhiaxcuRLx8fHQaDRISUnB/v37pS7JJezcuROTJk1CVFQUBEHAhg0bmq0XRRGLFi1CZGQkvLy8kJaWhrNnzzbbprKyEtOmTYNWq0VAQABmzpwJvV7fjmfhvJYtW4aBAwfCz88PYWFhuO+++5CTk9Nsm4aGBsyZMwfBwcHw9fXF5MmTWzzUtKCgABMnToS3tzfCwsLwwgsvwGw2t+epOKV33nkHvXv3tj2ILjU1FZs2bbKtZ2/ta/ny5RAEAfPmzbMtY49v3+LFiyEIQrOvpKQk23qX7q1I7S49PV1UqVTiqlWrxBMnTohPPPGEGBAQIJaUlEhdmtP75ptvxN///vfi+vXrRQDi559/3mz98uXLRX9/f3HDhg3iDz/8IN5zzz1iQkKCWF9fb9tm3LhxYp8+fcS9e/eKu3btEjt37ixOmTKlnc/EOY0dO1ZcvXq1ePz4cTE7O1ucMGGCGBsbK+r1ets2Tz31lBgTEyNu3bpVPHjwoDh48GDxjjvusK03m81iz549xbS0NPHIkSPiN998I4aEhIgLFy6U4pScyhdffCF+/fXX4pkzZ8ScnBzxd7/7nahUKsXjx4+Losje2tP+/fvF+Ph4sXfv3uKzzz5rW84e375XX31V7NGjh1hUVGT7Kisrs6135d4yDElg0KBB4pw5c2yfLRaLGBUVJS5btkzCqlzPz8OQ1WoVIyIixL/85S+2ZVVVVaJarRbXrVsniqIonjx5UgQgHjhwwLbNpk2bREEQxMuXL7db7a6itLRUBCBmZmaKotjYT6VSKX722We2bU6dOiUCELOyskRRbAysMplMLC4utm3zzjvviFqtVjQYDO17Ai4gMDBQ/Pe//83e2lFNTY3YpUsXMSMjQxw+fLgtDLHHbfPqq6+Kffr0aXWdq/eWl8namdFoxKFDh5CWlmZbJpPJkJaWhqysLAkrc335+fkoLi5u1lt/f3+kpKTYepuVlYWAgAAMGDDAtk1aWhpkMhn27dvX7jU7u+rqagBAUFAQAODQoUMwmUzNepyUlITY2NhmPe7Vq1ezh5qOHTsWOp0OJ06caMfqnZvFYkF6ejpqa2uRmprK3trRnDlzMHHixGa9BPj7aw9nz55FVFQUOnbsiGnTpqGgoACA6/fWI55A7UzKy8thsVhaPP06PDwcp0+flqgq91BcXAwArfa2aV1xcTHCwsKarVcoFAgKCrJtQ42sVivmzZuHIUOGoGfPngAa+6dSqVq8vPjnPW7tZ9C0ztMdO3YMqampaGhogK+vLz7//HN0794d2dnZ7K0dpKen4/Dhwzhw4ECLdfz9bZuUlBSsWbMGiYmJKCoqwpIlS3DnnXfi+PHjLt9bhiEiatWcOXNw/Phx7N69W+pS3EpiYiKys7NRXV2N//73v5g+fToyMzOlLsstXLx4Ec8++ywyMjKg0WikLsftjB8/3vbn3r17IyUlBXFxcfj000/h5eUlYWVtx8tk7SwkJARyubzFDPuSkhJERERIVJV7aOrf9XobERGB0tLSZuvNZjMqKyvZ/5+YO3cuvvrqK2zfvh3R0dG25RERETAajaiqqmq2/c973NrPoGmdp1OpVOjcuTP69++PZcuWoU+fPvjHP/7B3trBoUOHUFpain79+kGhUEChUCAzMxMrVqyAQqFAeHg4e2xHAQEB6Nq1K3Jzc13+95dhqJ2pVCr0798fW7dutS2zWq3YunUrUlNTJazM9SUkJCAiIqJZb3U6Hfbt22frbWpqKqqqqnDo0CHbNtu2bYPVakVKSkq71+xsRFHE3Llz8fnnn2Pbtm1ISEhotr5///5QKpXNepyTk4OCgoJmPT527Fiz0JmRkQGtVovu3bu3z4m4EKvVCoPBwN7awahRo3Ds2DFkZ2fbvgYMGIBp06bZ/swe249er0deXh4iIyNd//dX0unbHio9PV1Uq9XimjVrxJMnT4qzZs0SAwICms2wp9bV1NSIR44cEY8cOSICEN944w3xyJEj4oULF0RRbLy1PiAgQNy4caN49OhR8d5772311vrk5GRx37594u7du8UuXbrw1vqrZs+eLfr7+4s7duxodvtsXV2dbZunnnpKjI2NFbdt2yYePHhQTE1NFVNTU23rm26fHTNmjJidnS1u3rxZDA0NdYrbZ6X20ksviZmZmWJ+fr549OhR8aWXXhIFQRC/++47URTZW0f46d1kosget8Vzzz0n7tixQ8zPzxe///57MS0tTQwJCRFLS0tFUXTt3jIMSeStt94SY2NjRZVKJQ4aNEjcu3ev1CW5hO3bt4sAWnxNnz5dFMXG2+tfeeUVMTw8XFSr1eKoUaPEnJycZvuoqKgQp0yZIvr6+oparVacMWOGWFNTI8HZOJ/WegtAXL16tW2b+vp68Te/+Y0YGBgoent7i7/4xS/EoqKiZvs5f/68OH78eNHLy0sMCQkRn3vuOdFkMrXz2Tifxx9/XIyLixNVKpUYGhoqjho1yhaERJG9dYSfhyH2+PY99NBDYmRkpKhSqcQOHTqIDz30kJibm2tb78q9FURRFKUZkyIiIiKSHucMERERkUdjGCIiIiKPxjBEREREHo1hiIiIiDwawxARERF5NIYhIiIi8mgMQ0REROTRGIaIyKmMGDEC8+bNk7qMZgRBwIYNG6Qug4gchA9dJCKnUllZCaVSCT8/P8THx2PevHntFo4WL16MDRs2IDs7u9ny4uJiBAYGQq1Wt0sdRNS+FFIXQET0U0FBQXbfp9FohEqluu3vl/qN2kTkWLxMRkROpeky2YgRI3DhwgXMnz8fgiBAEATbNrt378add94JLy8vxMTE4JlnnkFtba1tfXx8PF577TU8+uij0Gq1mDVrFgDgxRdfRNeuXeHt7Y2OHTvilVdegclkAgCsWbMGS5YswQ8//GA73po1awC0vEx27Ngx3HXXXfDy8kJwcDBmzZoFvV5vW//YY4/hvvvuw1//+ldERkYiODgYc+bMsR2LiJwLwxAROaX169cjOjoaS5cuRVFREYqKigAAeXl5GDduHCZPnoyjR4/ik08+we7duzF37txm3//Xv/4Vffr0wZEjR/DKK68AAPz8/LBmzRqcPHkS//jHP/D+++/j73//OwDgoYcewnPPPYcePXrYjvfQQw+1qKu2thZjx45FYGAgDhw4gM8++wxbtmxpcfzt27cjLy8P27dvx4cffog1a9bYwhURORdeJiMipxQUFAS5XA4/P79ml6mWLVuGadOm2eYRdenSBStWrMDw4cPxzjvvQKPRAADuuusuPPfcc832+fLLL9v+HB8fj+effx7p6en47W9/Cy8vL/j6+kKhUFz3stjatWvR0NCA//znP/Dx8QEAvP3225g0aRL+/Oc/Izw8HAAQGBiIt99+G3K5HElJSZg4cSK2bt2KJ554wi79ISL7YRgiIpfyww8/4OjRo/j4449ty0RRhNVqRX5+Prp16wYAGDBgQIvv/eSTT7BixQrk5eVBr9fDbDZDq9Xe0vFPnTqFPn362IIQAAwZMgRWqxU5OTm2MNSjRw/I5XLbNpGRkTh27NgtHYuI2gfDEBG5FL1ejyeffBLPPPNMi3WxsbG2P/80rABAVlYWpk2bhiVLlmDs2LHw9/dHeno6/va3vzmkTqVS2eyzIAiwWq0OORYRtQ3DEBE5LZVKBYvF0mxZv379cPLkSXTu3PmW9rVnzx7ExcXh97//vW3ZhQsXbni8n+vWrRvWrFmD2tpaW+D6/vvvIZPJkJiYeEs1EZFz4ARqInJa8fHx2LlzJy5fvozy8nIAjXeE7dmzB3PnzkV2djbOnj2LjRs3tpjA/HNdunRBQUEB0tPTkZeXhxUrVuDzzz9vcbz8/HxkZ2ejvLwcBoOhxX6mTZsGjUaD6dOn4/jx49i+fTuefvpp/OpXv7JdIiMi18IwREROa+nSpTh//jw6deqE0NBQAEDv3r2RmZmJM2fO4M4770RycjIWLVqEqKio6+7rnnvuwfz58zF37lz07dsXe/bssd1l1mTy5MkYN24cRo4cidDQUKxbt67Ffry9vfHtt9+isrISAwcOxAMPPIBRo0bh7bfftt+JE1G74hOoiYiIyKNxZIiIiIg8GsMQEREReTSGISIiIvJoDENERETk0RiGiIiIyKMxDBEREZFHYxgiIiIij8YwRERERB6NYYiIiIg8GsMQEREReTSGISIiIvJoDENERETk0f4f3uiVTht3M/cAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "MSE = [np.linalg.norm(Y - predict(X,histn))**2 for histn in history]\n", "\n", "plt.plot(MSE)\n", "plt.xlabel('iteration')\n", "plt.ylabel(r'MSE $\\hat{\\mathcal{R}}(\\mathcal{M}_\\theta)$')\n", "plt.ylim([0, 200])\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "6e39ba46", "metadata": {}, "source": [ "We furthermore plot the development of the two parameters $\\theta_0$ (intercept) and $\\theta_1$ (slope) over the iterations. The convergence towards the true parameters is clearly observable." ] }, { "cell_type": "code", "execution_count": 8, "id": "4da24e93", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(history[:,0], history[:,1], label=r'estimated $(\\hat{\\theta}_0[k], \\hat{\\theta}_1[k])$')\n", "plt.scatter(theta[0], theta[1], alpha=1, zorder=10, s=100, color='C1', label=r'true $(\\theta_0, \\theta_1)$')\n", "\n", "plt.xlabel(r'$\\theta_0$')\n", "plt.ylabel(r'$\\theta_1$')\n", "plt.grid()\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "67686ef5", "metadata": {}, "source": [ "**Copyright**\n", "\n", "This notebook is provided as [Open Educational Resource](https://de.wikipedia.org/wiki/Open_Educational_Resources).\n", "The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/)\n", ", the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: Sascha Spors, Data driven audio signal processing - Lecture supplementals." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.6" } }, "nbformat": 4, "nbformat_minor": 5 }