-
Notifications
You must be signed in to change notification settings - Fork 0
/
CS228_HW2
1 lines (1 loc) · 207 KB
/
CS228_HW2
1
{"cells":[{"cell_type":"code","execution_count":null,"metadata":{"id":"ebtbpBCvU9SO"},"outputs":[],"source":["#imports\n","\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","import time\n","\n","from IPython.utils import iow\n","\n","from keras.datasets import mnist"]},{"cell_type":"markdown","metadata":{"id":"b6x1N4eommZi"},"source":["## Formatting Data\n","Downloading and formatting data\n","\n","\n","**Note: From the keras dataset there are 60000 training samples instead of 50000 samples, so this code will account for that number.**"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"q6rarGQ3hz-I"},"outputs":[],"source":["# loading datasets\n","(train_X, train_y), (test_X, test_y) = mnist.load_data()"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":3,"status":"ok","timestamp":1651725918224,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"BoWXIDd8WsVF","outputId":"c2f14a96-4eed-4635-c67c-52ea96e2a2f6"},"outputs":[{"name":"stdout","output_type":"stream","text":["Training data shape: (60000, 28, 28)\n","Test data shape: (10000, 28, 28)\n"]}],"source":["# 60000 training samples\n","# 10000 testing samples\n","\n","print('Training data shape: ' + str(train_X.shape))\n","print('Test data shape: ' + str(test_X.shape))\n"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"oB5QNztwWu74"},"outputs":[],"source":["# vectorize inputs\n","\n","X_train = train_X.reshape(train_X.shape[0], -1)\n","X_test = test_X.reshape(test_X.shape[0], -1)\n","\n","num_classes = len(np.unique(train_y))\n","N = X_train.shape[0]"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":2,"status":"ok","timestamp":1651725919677,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"2Wng53h1Ww4X","outputId":"0994432e-47e0-48f2-caf7-c98d4cc51db3"},"outputs":[{"name":"stdout","output_type":"stream","text":["Training data shape: (60000, 784)\n","Test data shape: (10000, 784)\n"]}],"source":["print('Training data shape: ' + str(X_train.shape))\n","print('Test data shape: ' + str(X_test.shape))"]},{"cell_type":"markdown","metadata":{"id":"fQwVFHAW4s3V"},"source":["## 1. Applying Normalization "]},{"cell_type":"code","execution_count":null,"metadata":{"id":"nZi6yygBWyJX"},"outputs":[],"source":["# z-normalizing each image vector\n","\n","X_train = np.apply_along_axis(lambda x: (x - np.mean(x))/np.std(x), 1, X_train)\n","X_test = np.apply_along_axis(lambda x: (x - np.mean(x))/np.std(x), 1, X_test)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":3,"status":"ok","timestamp":1651725924762,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"CaIPvak9XSdm","outputId":"8a86e0c9-794c-4cad-cde7-329acd94b256"},"outputs":[{"name":"stdout","output_type":"stream","text":["Training data shape: (60000, 784)\n","Test data shape: (10000, 784)\n"]}],"source":["print('Training data shape: ' + str(X_train.shape))\n","print('Test data shape: ' + str(X_test.shape))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"iwf2dLEvXULy"},"outputs":[],"source":["# Prepending a column of 1s to account for bias\n","\n","X0 = np.ones((X_train.shape[0],1))\n","X_train = np.hstack((X_train, X0))\n","\n","X0 = np.ones((X_test.shape[0],1))\n","X_test = np.hstack((X_test, X0))"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":3,"status":"ok","timestamp":1651725924968,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"Pa3MhmlVZJE1","outputId":"3d153341-d64e-4b8e-834f-83c5fd12d024"},"outputs":[{"name":"stdout","output_type":"stream","text":["Training data shape: (60000, 785)\n","Test data shape: (10000, 785)\n"]}],"source":["print('Training data shape: ' + str(X_train.shape))\n","print('Test data shape: ' + str(X_test.shape))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"9amQl6UFfWxC"},"outputs":[],"source":["def convert_label(label):\n"," if label <= 4:\n"," return 0\n"," else:\n"," return 1"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":195,"status":"ok","timestamp":1651725927454,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"DpXvPKqikeBX","outputId":"2b984f96-fd80-437d-d2ff-3c3d20540e50"},"outputs":[{"name":"stdout","output_type":"stream","text":["[5 0 4 1 9]\n","[1 0 0 0 1]\n"]}],"source":["# converting labels for binary output\n","\n","y_train = np.array([convert_label(label) for label in train_y])\n","y_test = np.array([convert_label(label) for label in test_y])\n","\n","print(train_y[:5], y_train[:5], sep='\\n')"]},{"cell_type":"markdown","metadata":{"id":"vIcjw_ee4yeY"},"source":["## 2. Training a Linear Classifier"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0wck9LBGlbiz"},"outputs":[],"source":["def calculate_loss(W, X, Y):\n"," return (1/(2 * len(X))) * np.sum((np.matmul(X,W) - Y)**2)\n","\n","\n","def calculate_gradient(X_ri, Y_ri, W, batch_size):\n"," # print((X_ri.transpose()).shape, (np.matmul(X_ri, W)).shape, Y_ri.shape, (np.matmul(X_ri, W) - Y_ri).shape)\n"," return (1/batch_size) * np.matmul(X_ri.transpose(), (np.matmul(X_ri, W) - Y_ri))\n","\n","\n","def SGD(X, Y, iters, batch_size=1, learning_rate=0.00001, num_classes=10, tol=pow(10, -5)):\n"," loss_history, weights = [], []\n"," W = np.zeros((X.shape[1], num_classes))\n","\n"," for iter in range(iters):\n","\n"," # Compiling batch values\n"," r = np.random.randint(low=0, high=X.shape[0], size=batch_size)\n","\n"," X_batch = X[r]\n"," Y_batch = Y[r]\n","\n"," # Calculating loss\n"," # loss = mean_squared_error(Y, np.matmul(X, W))\n"," loss = calculate_loss(W, X_batch, Y_batch)\n"," loss_history.append(loss)\n","\n"," if (iter + 1) % 20 == 0:\n"," print('Loss value at epoch {}: {}'.format(iter + 1, loss))\n","\n"," # Check for convergence\n"," if iter > 1:\n"," if np.absolute(loss_history[iter] - loss_history[iter-1])/loss_history[iter-1] <= tol:\n"," print(f'Convergence criteria met @ iteration {iter + 1}')\n"," break\n","\n"," # Calculating gradient\n"," grad = calculate_gradient(X_batch, Y_batch, W, batch_size)\n","\n"," # print(W.shape, grad.shape)\n","\n"," # Update weights\n"," W = W - (learning_rate * grad)\n","\n"," # For accuracy graphs later\n"," weights.append(W)\n","\n"," return W, loss_history, iter, weights"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":178,"status":"ok","timestamp":1651715471464,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"2k2IMZuy47BE","outputId":"7e320280-db36-4c27-8aa9-97a3973daafe"},"outputs":[{"name":"stdout","output_type":"stream","text":["Loss value at epoch 20: 0.13373091795345063\n","Loss value at epoch 40: 0.07930010324714888\n","Loss value at epoch 60: 0.08790160104280936\n","Loss value at epoch 80: 0.06956832554628829\n","Loss value at epoch 100: 0.08680543114737668\n"]}],"source":["W, loss, _, weights = SGD(X_train, y_train.reshape((len(y_train), 1)), iters=100, batch_size=10, learning_rate=0.001, num_classes=1)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"I1YA0XK75CRd"},"outputs":[],"source":["def predict(X,w):\n"," # your code goes here \n"," \n"," yhat = np.matmul(X, w)\n"," yhat = [1 if probs > 0.5 else 0 for probs in yhat]\n","\n"," return np.array(yhat)"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":2,"status":"ok","timestamp":1651715480475,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"WxVbUWK1WTUT","outputId":"7e0f4735-b66c-4b07-e61f-49b0dad51750"},"outputs":[{"name":"stdout","output_type":"stream","text":["Accuracy: 0.7962\n"]}],"source":["yhat = predict(X_test, W)\n","acc = np.mean(yhat == y_test)\n","\n","print(f'Accuracy: {acc}')"]},{"cell_type":"markdown","metadata":{"id":"fncaBLLmBMsN"},"source":[" ### Analysis\n"," As we can see, the accuracy for the linear classifier is not bad, but it could be improved upon. The neural network should improve on the accuracy for this task. \n","\n"," ## Neural Network Classifier\n"," This is a general test for the classifer. Answer to (3) is afterwards:"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"hT8EFJQqP8tV"},"outputs":[],"source":["def relu(x):\n"," return np.maximum(x,0)\n","\n","def predict(w,U,x):\n"," return w.dot(relu(U.dot(x)))\n","\n","def get_grad(w,U,y,x):\n"," h=relu(U.dot(x))\n"," sigmap=U.dot(x)>0+0.\n"," yh=predict(w,U,x)\n"," r=yh-y\n"," grad_w=r*h\n"," grad_U=r*np.outer(w*sigmap,x)\n"," return grad_w,grad_U\n","\n","def loss(w,U,Y,X):\n"," return np.linalg.norm(Y-predict(w,U,X))**2"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000},"executionInfo":{"elapsed":99706,"status":"ok","timestamp":1651627184018,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"xqdSot6icVoB","outputId":"713acaca-2b23-4043-e939-ac726990da23"},"outputs":[{"name":"stdout","output_type":"stream","text":["Normalized Loss: 0.9842807431607549\n","Normalized Loss: 0.35887506598581437\n","Normalized Loss: 0.301612645682402\n","Normalized Loss: 0.27373732150941166\n","Normalized Loss: 0.2580997811605021\n","Normalized Loss: 0.24582104228853394\n"]},{"data":{"text/plain":["Text(0.5, 1.0, 'Test')"]},"execution_count":17,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYAAAAEICAYAAABWJCMKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3de5yUZf3/8deHhYVll7OcDwsIiqAGtYKKpgKGFIkhaB4SS0O/+v2VWnnIsoOVlGV+y06opRapAal4IEQ8oeIaBmrgAQJZQQ6LwMrCwsDs5/fHfS8Nyx7uZWb2NO/n4zGPmXvua+a+7h34fK7ruu/7us3dERGRzNOioSsgIiINQwlARCRDKQGIiGQoJQARkQylBCAikqGUAEREMpQSgIhIhlICkJQws/vM7Efh61PN7N3D/J7fm9l3U1u75iWZv69IIiWADGJm75tZmZmVmtnmMGjnpXo77r7Y3Y+OUJ9LzeylSp+90t1vTXWdItSlpZldYWYvm9lWM9tgZo+a2RmVyvU3MzezluHygcSXxrq5mQ2qWI769z3Mbc00s3fNrNzMLq1i/bVmtsnMPjazP5pZ64R1/c3sOTPbbWbvmNm4qJ+VhqEEkHk+7+55wCeBAuA7lQtUBLdMYWa5wEJgHPANoC9wJPBbYIaZ3ZLGbTe2v/UbwFXAvyqvMLPxwI3AWCAfGAj8IKHIg8AyoAtwMzDHzLpG/Kw0BHfXI0MewPvAuITl24EnwtcOXA2sAtaG700ElgM7gFeA4xM+O4IgSOwEHgYeAn4UrjsdWJ9Qti/wd6AY+Ai4CzgG2APEgVJgR1j2vorvCZe/CqwGtgHzgF4J6xy4MqzzDuA3gIXrBgEvACXAVuDhGv4ufwR+WM261sBi4NPhcv9wuy2B6cA+IBbuw+NhmV7A3HB/1wJfS/i+7wNzgL8AHwOXAyOBJeE+bAz/Ptlh+RfD7e0Kt3F+FX/fY4Dnw8+vAM5OWHdf+Hd5MvytCoEjI/xbeQm4tNJ7fwV+krA8FtgUvj4K2Au0S1i/GLiyts/q0XAP9QAylJn1BT5L0GKrcA4wChhqZiMIAuMVBC26PwDzzKy1mWUDjwJ/BjoDs4Fzq9lOFvAEsI4gePYGHnL3twmC9xJ3z3P3jlV8dgxwG3Ae0DP8jocqFZsInAAcH5YbH75/K/A00AnoA/y6mvoNIAjA3zezjmb2SDgE9HczexzoQdBy/Vrlz7r7TGAW8LNwHz5vZi2Axwla0r0JAt01YQu4wiSCJNAx/HwcuBY4Ajgp/MxV4TY+HX7mE+E2Hq5U/1bh9p4GugH/D5hlZolDRF8kaG13IkimP67qbxHBsHC/KrwBdDezLuG6Ne6+s9L6YRE+Kw1ECSDzPGpmOwhaeC8AP0lYd5u7b3P3MoLW7R/cvdDd4+5+P0EL78Tw0Qq40933ufsc4J/VbG8kQYv4W+6+y933uPtL1ZSt7CLgj+7+L3ffC9wEnGRm/RPKzHD3He5eBDwHDA/f30cw1NCrlm2OBea6e3n4/R8TBO4fA2MAI+gFDYlY5xOAru7+Q3ePufsa4G6CIFxhibs/6u7l7l7m7q+7+6vuvt/d3ydItqdF3N6JQB7B3yHm7s8SJNwLEso84u6vuft+goQzvIrviSKPoEdVoeJ1uyrWVaxvF+Gz0kCUADLPOe7e0d3z3f2qMNhX+CDhdT7wDTPbUfEgGMrpFT42uHviVLLrqtleX2BdGHzqqlfi97p7KcEQUu+EMpsSXu8mCDQA1xME79fMbIWZfaWabXQDNoSvjyMYKtrr7q8TDKdU7MOGqj5chXygV6W/27eB7gllEv/OmNlRZvZExQFSgqR8RMTt9QI+CBNYhXVE+xvVVSnQPmG54vXOKtZVrK/oEdT0WWkgSgCSKDGgfwD8OEwWFY+27v4gwTh1bzOzhPL9qvnOD4B+1RzsrG0u8g8JAipw4GBtFyIEY3ff5O5fdfdeBMNYv008kybBVoLhJYC3gPPCYa5PEgxb9CQYPvpDdZuqtPwBwTGUxL9bO3f/bA2f+R3wDjDY3dsTJAwjmg+BvuHQU4V+RE9YdbEC+ETC8ieAze7+UbhuoJm1q7R+RYTPSgNRApDq3A1caWajLJBrZp8L/4MvAfYDXzOzVmY2mWCopyqvESSMGeF3tDGz0eG6zUCf8JhCVR4Evmxmw8NTBn8CFIbDJDUys6lm1idc3E4QdMurKPoc8IUwmd0GdACKgFuABcCdwN3u/vdqNrWZ4IyWxP3daWY3mFmOmWWZ2bFmdkIN1W1HMPRUamZDgP+pZRuJCgla9deHv8XpwOc59FhJJGaWbWZtCBJQq/D3qogTDwCXmdlQM+tIcAbZfQDu/h7BUNn3ws98geC4zNzaPisNRwlAquTuSwnOwLmLIICuBi4N18WAyeHyNoIzU6oMkO4eJwhIgwgC6/qwPMCzBC3DTWa2tYrPPgN8lyCIbCQ4NfOLlctV4wSg0MxKCc4e+no4Hl95G6uAlcBN4bGEL7h7d3c/x90nA6Pd/W81bOdegoPmO8zs0XB/JxKMs68l6GHcQ5BYqvNN4EKC4ZC7Cc6qSvR94P5wG+dVqn+M4O87IdzWb4FL3P2dGrZXk6eBMuBkYGb4+tPhtv4B/IwgaRYRDDV9L+GzXyQ4tXg7MAOY4u7FET8rDaDilDmRjGVm7YF/AG8DvwyfOxMEtC8BJ1YaYxdpFtQDkIzn7h8DZxD0Ru4naEm/DhwLTFXwl+ZKPQARkQylHoCISIZqbPOQHHDEEUd4//79G7oaIiJNyuuvv77V3btGKdtoE0D//v1ZunRpQ1dDRKRJMbPqLso8RFJDQGbW2cwWmtmq8LlTFWWGm9mS8GrMN83s/Kq+S0RE6leyxwBuBBa5+2BgUbhc2W6C85KHAWcBd4YXgoiISANKNgFMIjhtjvD5nMoF3P298GIb3P1DYAsQaXxKRETSJ9kE0N3dN4avN3HwhFeHMLORQDbwn2rWTzezpWa2tLi4OMmqiYhITWo9CGxmzxDMiV7ZzYkL7u5mVu1FBWbWk2D++GnVXVgTzq8+E6CgoEAXKIiIpFGtCcDdx1W3zoL7yvZ0941hgN9STbn2BHckutndXz3s2oqINGPxOMyfD8uWwYgRMGECZGWlb3vJngY6D5hGMPHTNOCxygXCmR4fAR4IbxwiIiKVxOMwfjwUFsKuXZCbC6NGwYIF6UsCyR4DmAGcaWarCG6oPQPAzArM7J6wzHkEswleambLw8fh3pFIRKRZicfhiSdg2jR4+WUoLQX34LmwMOgRpEtSPYDwZg5jq3h/KcHNrnH3vxDcAFtERELxOMyZA5ddBrt3B0G/sl27YPlymDgxPXVotFcCi4g0V2VlMGQIFBXVXC43F4ancbxEk8GJiNSTWAy++U1o27b24J+XFxwDmDAhffVRD0BEpB6UlkKXLkESqIkZXHQRnH9++s8CUg9ARCSNYjG4/npo16724A/QrRvcd18w7p/O4A/qAYiIpE1ZGRxxRHCQN4oWLWD16vQH/gPbq5/NiIhkjtJSGD06GOuPGvynTAk+l5eX3rolUg9ARCRF4nG491644oq6fe6jj6Bz5/TUqSZKACIiKVBSAt27w9690T9z0knw9NP12+pPpCEgEZEkxOMwaxZ07Bg9+LdsCTt3wiuvNFzwB/UAREQOW2kp9OsH27dH/0x+Prz9NuTkpK9eUakHICJyGFavDk7tjBr8zYKpH/7zn8YR/EE9ABGROtmwAfr3h/37o38mOzs40NuQwz1VUQ9ARCSCkpJguKdPn7oF/6uvDsb7G1vwB/UARERqFI/Dnb+I89wN85nGMpYxgvlMoJyar9bKzQ16Cx061FNFD4MSgIhINTZtgt494yxgPNMppC272E0uhYxiPAuqTQIPPAAXXlh/V/QeLiUAEZFKYjH40oVxds2dz308xGheJoc9ALSjlFEUMoH5PMnBE/W3bQsffti4W/2JdAxARCRBURHktI7z1bnjeZALuIhZtAmDf4W27GI4yw9676674OOPm07wB/UAREQA2LYNBg+GHdvi3MIPOJXFtKbq6Tt3k8ty/nunli1boGvX+qpp6qgHICIZb+1a6Nolzuhtj/EeR/FtbiO7UvB3oBzYSR6FjGI+E/jtb4Mzgppi8Af1AEQkg5WVwaRJsGhhcKD35HCs36oqSxvmMoWHOZ+PTphA6QtZjeaCrsOlBCAiGWn1ahg2uIw/8WXu53m6sJVs4oeUcyBGNq8wmku5j4dnZzFlSv3XNx2UAEQko5SWxLl2yHx6bypkF7eRVUXQTxQjmxncwA/5HmvXZdGvXz1VtB4oAYhIxnh3ZZwPho3nDgrJpRSDKod7IGj576ENLzOaL6/5Ht8b0MhP6j8MOggsIs1e0eoYP7ab6DasC2ewiHaU0oJDg3/Fgd7dtGENA7m250OcuGMB/Zph8AclABFp5ubMKqPT4M58mxl0pKTWoPcWx3Ies9m97D1+/+Ek8jo0z+APGgISkWZqwwY4qm8Z670neeyqcainwn5acsng13j5XzmNcvK2VFMPQESanb/dXcK2PkPZ6W3pSEmVwd+BOLCZ7qxhAA9yPite+Zg33suM4A/qAYhIM7J6NYwYvI2P6XLgvepa/gCLOZWxPMcXzs3ir38N5u3PJOoBiEiTF4vBFz9bQtngYw4E/9rO8IkD41nA6jVZzJmTecEfkuwBmFln4GGgP/A+cJ67b69UJh94hCDZtAJ+7e6/T2a7IiIVNmyA4X2K2EL+gfdqG+/fzBFcULCWHS/mNPmreZORbA/gRmCRuw8GFoXLlW0ETnL34cAo4EYz65XkdkUkw5WVxLi/23V07pN9IPhX1+p3/ntF72TmULxsE8/9My+jgz8kfwxgEnB6+Pp+4HnghsQC7p44o1JrNOwkIkla8uQ2CiYewSUJ5/DU1ur/Kd9g+zU/Yc7Psxv9jVrqS7IJoLu7bwxfbwK6V1XIzPoCTwKDgG+5+4fVlJsOTAfo15yutxaRlCjdFmNWn28xvexXQM0HeKHiat7WdONDlq3qzKBBaa9ik1Jra9zMnjGzf1fxmJRYzt0relmHcPcP3P14ggQwzcyqTBTuPtPdC9y9oGtTnV9VRNLi2VkbyOnSOlLwrwhGbzKMB371MTtdwb8qtfYA3H1cdevMbLOZ9XT3jWbWE9hSy3d9aGb/Bk4F5tS5tiKScVYvL6V4xKc5g2VAtFY/wEX8ke+8eQlXHKfxnuokOx4/D5gWvp4GPFa5gJn1MbOc8HUn4BTg3SS3KyIZ4E83r+bIEe04sZbg7wmPOPDcQ1v4q3+ZoQr+NUo2AcwAzjSzVcC4cBkzKzCze8IyxwCFZvYG8ALwc3d/K8ntikgzVrQ6xq/tUi79yWCg5nP6K+zH+FWra9m1ZS9jztcQchQWDN03PgUFBb506dKGroaI1LPZP13NuTcOPhDwaxvrB9hOLu8+v42TTsvAq7kqMbPX3b0gSlmdkikijcKG5cVstTZMCYN/bVfyVgT/OX2vJm+ngv/h0FxAItKgSopjzOv2FS5m1oH3orT632Yg2Uv/xdRPdUhr/Zoz9QBEpMEseXAted1aHwj+UVv9t174Dkfv/w+DFPyToh6AiNS7spIYj/e7mqkfB+eKRD21cyV96bbqLW4ZpMCfCuoBiEi9euuFbbTs2DpS8E9s9T90TSHDvIiuCv4pox6AiNSLsg3bKOkzkGMpAaK3+j+mFRsWFXHBmB5prV8mUg9ARNLuhR/MoU2fLnSPEPwPOsPnukV08BhDFfzTQj0AEUmb0pVFtByWz6fD5ait/lX0YP8r7zD1JA33pJN6ACKSFq9/90/kDsundbgcudU/YxlH+UaGKvinnXoAIpJSK/9RxMAJ+XwyXI7a6v8DF3Lu+j8xtbcu6Kov6gGISMrMPv83HDOh7q3+p+5YypU+i64K/vVKPQARSdqGf7xFjwnHMyVcjtrqf5rj+eS6V/lcvwy/N2MDUQ9ARJIy+/Rr6TXh+APBJGqr/9/3LGa8v0FXBf8Gox6AiByWDbOepcfFY+vc6v8Io82azRw3QFM2NzT1AESkTmIlZbxmA+l18dg6t/qfunMZR3g5eQr+jYISgIhEtvLuZ2nVsS0nsBaIPnnbSow9W3byua8Pr4daSlRKACJSq9iGYkrMOGb6WKD2O3RVBP5y4I07n2CYl5PTNS/NtZS6UgIQkRr946u/oVWfbrQPl6MO93x38J3E9zrDv/659FZQDpsOAotIlTYsKaLLyfmMD5ejHuTdC6x7eh0/OrNf+ionKaEegIgcYs6XfkOvkw9jGocTL6eNO0cr+DcJ6gGIyAGbnl1J17HDODdcjtrqLwc2PbSYqeefkr7KScqpByAiACwc92W6jx1W51M750z+GVnu9Fbwb3LUAxDJcKsffI0BF45iXLgctdUfB7YvfoeppxydvspJWqkHIJLBZh99DkdeOKrurf6xX6OlO10V/Js0JQCRDPTa7fOImzHlvceAup3X/5/HVjD1mf9Lcw2lPmgISCSDxLeV8FGXjpyQ8F6UwA/w8rnf5pQ5P2ZQmuom9U89AJEMUfTLP9OiS0cqZuGJ2urfD+xZsYZT5vw4rfWT+qcEINLMlW0q4UMz+l53CRAt8FcE/39e+XNauZMzdECaaykNQQlApBl78uybaNOzIz3D5ahn+OwC9qzZyMjffSN9lZMGl1QCMLPOZrbQzFaFz51qKNvezNab2V3JbFNEardtybvsN+Ozj88A6tbq//dP/kKeOzkDeqS5ltLQku0B3AgscvfBwKJwuTq3Ai8muT0RqcXssTfR6eQhZIXLUQP/RrIp/2gHx910UXorKI1GsglgEnB/+Pp+4JyqCpnZp4DuwNNJbk9EqlH0yOvBqZ3PRm/1Q3Bq53u/n08v30tW5w5prqU0JskmgO7uvjF8vYkgyB/EzFoAvwC+meS2RKQas8dcS9/JBXW/oOuo8WS5c/QVZ6W3gtIo1XodgJk9A1Q1GHhz4oK7u5l5FeWuAp5y9/VmNR+CMrPpwHSAfv00m6BIbbY98gIdJp9e5/vylgNr7/grU6+9IH2Vk0av1gTg7uOqW2dmm82sp7tvNLOewJYqip0EnGpmVwF5QLaZlbr7IccL3H0mMBOgoKCgqmQiIqHZfccyZf2zB5ajXtA197M3MuXJ23RBlyR9JfA8YBowI3x+rHIBdz9wRMnMLgUKqgr+IhLN6llLGHDxyYfV6t80/02mnHVc+ionTUqyxwBmAGea2SpgXLiMmRWY2T3JVk5EDjb7mHM58uKT6zzWP/e0rwRTNiv4SwJzb5wjLQUFBb506dKGroZIo/DabXP41LenRgr8cHCrf9vidzRrZwYxs9fdvSBKWU0GJ9KIxUvLeKddO04gfuC9qGP9c86awdT5NxyY+0ekMk0FIdJIPXv172jRri1Dw+Bfl/P63/7LUqbOvyHNNZSmTj0AkUam5K0iWh+fzxnhctThHoDnPn8dY+b9gqFpqps0L+oBiDQi8ybfSvvj82kdLkcN/kXksH3dTsbM+0UaayfNjRKASCNQ9Oxq9pvx+UduAeo2edtTl/6KfN9N5355aa6lNDcaAhJpYLPH3cqURbccWI56kLeIbPrs+IjPdVDgl8OjHoBIA1k9b2Uwedui6K1+CCdv+9lfyPe9ZCn4SxKUAEQawOzRX+fIScPqPnnb8K8Fk7d9S1M2S/I0BCRSj9be/ST9pk88vGkcnl7B1DN1fo+kjnoAIvVkdt+z6D99Yt1b/YPODqZxUPCXFFMCEEmzl+4Pbs84Zf0CoG5j/e//ZTFTVx0yx6JISigBiKTR7KOuZvSldb8945xx3yHLnQEXnZLeCkpGUwIQSYOFN8wKzvBZ9Vsgeqt/L/DB4nVMXXhrmmsoooPAIikVLy1jSbsujKPswHuRJ2/7zAymLrgB3QtP6ot6ACIpsvBbf6ZFu7aMDoN/XVr9H7+5jqkLNHmb1C8lAJEklWwoZYXlMu7nlwB1m8ZhzoRbaONOh+PU7pf6pwQgkoQ5F/wf7fu0Yyi7gejn9e8Adq3ZwtSnfpDO6onUSAlA5DCUbihhjRnnPnQNULdW/4vXzKSTO3kDdKsWaVhKACJ1NPuie8nt05EB4XLUwP9y79Ow/fs57ZdfTW8FRSLSWUAiERXNW07vSSMObxqHx5ZyytmfSl/lRA6DegAiEcw+93f0nTSi7tM4nHxVMI2Dgr80QuoBiNSg6NnV9Bw7+LBa/Rvmr2DqWZq/Rxov9QBEqjH7hKvpO3bwgVZS5Fb/6deT5U4/BX9p5NQDEKnk2Xvf5dOXD6lzq38/8NHiVUw9ZVD6KieSQuoBiCSYPe52zri87pO3zf3KTFq500PBX5oQ9QBEgNcffJfhF9a91V8MbH1+C1NO0zn90vSoByAZrawMrrUf88kLh9T5DJ/Hr59NN3eGKvhLE6UegGSst+59iaGXn8od4XLUVv9K+tBn/duc3Vs3ZJemTQlAMk5ZUTF78rtxbMJ7Uadsfu7OVxjz9ZPSVDOR+pXUEJCZdTazhWa2KnzuVE25uJktDx/zktmmSDKe/MYs2uR3o2O4XNMcPonDPc+3Gkf57r0K/tKsJHsM4EZgkbsPBhaFy1Upc/fh4ePsJLcpUmdlm0p437L57B0XA3W7L+/bv3+aM2ILycrJTnMtRepXsglgEnB/+Pp+4Jwkv08k5d66+wXa9OxIPvuAOlzQdebPyXJn6BVnpruKIg0i2WMA3d19Y/h6E9C9mnJtzGwpwbUyM9z90SS3K1KrktXF7BvcnWPDkF6XC7reeWwNU88eUFNxkSav1h6AmT1jZv+u4jEpsZy7JzaeKst39wLgQuBOMzuymm1NN7OlZra0uLi4rvsicsDsG/5B+8Hd6BIh+B/U6j/757Ry5zgFf8kAtfYA3H1cdevMbLOZ9XT3jWbWE9hSzXdsCJ/XmNnzwAjgP1WUmwnMBCgoKKgumYhUa+Uj73LU5Lpf0LUPKClcw9SRCvySOZI9BjAPmBa+ngY8VrmAmXUys9bh6yOA0cDKJLcrcojZ31jIMZPrPo3DnOmzyXanq4K/ZJhkjwHMAP5mZpcB64DzAMysALjS3S8HjgH+YGblBAlnhrsrAUjKrH5hAz1O71PnVn8J8HHhRqaO7JG+yok0YkklAHf/CBhbxftLgcvD168AxyWzHZHqzP76PKb86r+Ho6Je0PX4NX/h7F9edOB6AJFMpCuBpUla/eS79J9Y97H+bUD5ii2cPVTz94hoMjhpUuJx+NPEWRw5sW5j/Q48N3MFXdzpquAvAqgHIE3IyoUb6PeZPlwaLkeevK3d8Qz58FXG5OWkr3IiTZB6ANLolZXEmJs9lWM+04fc8L2orf4Pnn6HYR+/QZaCv8ghlACkUVs753XadGzN5H1zgOiTt73aayK+ey/9zjy6Hmop0jRpCEgapdLiMt7oMYaTy18Fog/37AXWL1rHSWP6pbN6Is2CegDS6Cz/83Jyu7WNFPwPuqDr4pm0cWeQgr9IJOoBSKNRUgIXd1/IvL2fAaK3+suBWOGbTB2py01E6kI9AGkUls8rIrujRQr+Fa3+cuCpu1aQ5U6Ogr9InSkBSIMqK4kxt+NX+MSkfNqE70W5mvfPTKR43V4+d/XQNNdQpPlSApAG89a8tbTu2JrJJX8Cop/h88bMxVzij9Ojn+7QJZIMHQOQerfp3RK2DxnOsbwPRB/rX8RoPrl+IcN765x+kVRQD0Dq1ZJZq+k+pCNDIgT/xLH+9x57h3H+Ep0V/EVSRglA6kVZcSn/zh7OiRcPBqLflP2B4bcT372fo8/WBV0iqaYhIEm7ooXv0vczQxgWLkcJ/OXA2qfXMO1M3aRFJF3UA5C02ba2hHdsIH0/MwSI3up/oveXie/cyyAFf5G0UgKQlIvH4iye8ks6DezI0awFoo/1b35lDZ9f/0ey83SGj0i6KQFISm1YXkysdUtOmXsdEP3UzldGXQW799LjJLX6ReqLEoCkRjxO0U/+TK8R3WhD9MD/Gsezfd1ORr/6G7Jy1OoXqU86CCxJK1m7jZYD+9CXMiDaOP8eWrB2/lpGnaWJ20QainoActhiJWUUdv887Qd2oS1lkQ/yntF1BbEdcYYq+Is0KPUA5LAUv7uNzkO6MDJcjhL448D2FVt4XvfkFWkU1AOQOomXxfj3+Os4YkgXWhD91M5dky+i5d69uiG7SCOiHoBEFtu0jRY9uzGMOBD9gq7iZRvpMbxHuqsnInWkHoDUKlYWZ/b4P9CqZxeyiEdq9Tvwz75fIL5jt4K/SCOlHoDUqLRoG+R3Zwr7gWit/mI6Ur7qA0YOykt7/UTk8KkHIFWKx+K8ePVD5OZ3IZf9kcf6V11/D932b6WHgr9Io6cegBwsHqfkvjm0uPwyTmUXEC3wl5HDvjXrOWpA57RXUURSQwlADijbVkZJ10F0L/8QiHajlnJgzx/+Qu5lX4SsrHRXUURSSAlAAChdWUTOsHy6E/0OXdtze5G3YTW5HXSTFpGmKKljAGbW2cwWmtmq8LlTNeX6mdnTZva2ma00s/7JbFdSJx6L8+rlM8kdln/gvP6qOAfP4bPnl7+jc0kR2Qr+Ik1WsgeBbwQWuftgYFG4XJUHgNvd/RhgJLAlye1KkspKYsw9+ib2tm7LqHuvAGoP/uXAxg5Hs2/LDnKuuVJDPiJNXLJDQJOA08PX9wPPAzckFjCzoUBLd18I4O6lSW5TklS6tpg2A3swmXKg9oO85UAeOynakkcvXcgr0mwk2wPo7u4bw9ebgO5VlDkK2GFmfzezZWZ2u5lV2XQ0s+lmttTMlhYXFydZNaksHovz0pX3kzuwG1mURz618+ZpGynZm0dXBX+RZqXWHoCZPQNUdSnnzYkL7u5m5lWUawmcCowAioCHgUuBeysXdPeZwEyAgoKCqr5LDlNpcRkfdTuK0awHogX+3eTQYv16ZvTWqZ0izVGtPQB3H+fux1bxeAzYbGY9AcLnqsb21wPL3X2Nu+8HHgU+mcqdkOrFS8tYN2oybbu1pR/rI9+opfB//kCbvTvJUfAXabaSPQYwD5gGzAifH6uizD+BjmbW1d2LgTHA0iS3KxGUri0mZ2A3KmbdjzJ/zxI7mZmziigAAAwYSURBVBO2LuDEzrqSV6S5S/YYwAzgTDNbBYwLlzGzAjO7B8Dd48A3gUVm9hZBHLo7ye1KDeKlZawrmETuwG6Rp2zeTCdu/N/dnLDnZbIV/EUygrk3zqH2goICX7pUHYW6KisqJju/24HMHmWsfyVHkf/RW+R11j15RZo6M3vd3QuilNVkcM1FLMa+/72GNvm1t/orhnvKaM3iq//KkL0rFfxFMpCmgmjq4nHijzyGX3ABLffHgGhj/d/o9RA/XT2FT+foYi6RTKUE0ITFt5UQ75tPq90lQLThni10YvEDRfz8wjxdyCuS4TQE1BTF48RnPUiLLh1ptbsk8h26XrryAY7YW8yULyn4i4h6AE1PPE58zJnw4nNAtFb/nrwuZK9/n1M76OweEfkv9QCainicvX+dzZa8AbR48TmyiBb8Y/c8QM6OzWQp+ItIJeoBNAGxsjjrjhzDoI0vUtt0PBXDPftz2pO1vojWnTvUQw1FpClSD6Axi8XYd+N32NB2IIM2vnhgrL+qln9F4F/foh/xOY+SvXMbWQr+IlID9QAaqXhZjP1de5C9azv9aynrQIyWLLv2AU6YcR5Z2TrCKyK1UwJobEpL2f+ZCcSXFJLNvghn9xhvcRxH7fgnJ3bQxVwiEp2GgBqT0lK8XTuylrxENvtqLFox5PPzE2dz1M5/kaPgLyJ1pB5AIxEvi7FnwFDaEvHsHlqxb30x1/fWOL+IHB71ABpaPE58zt/Zn9uBtls/qLGoA6Xk8vbkm2m5u5Q8BX8RSYJ6AA0lFoPvfx9+9Sts1y6yqXnytnKMFRzL4B1LGarhHhFJAfUA6lssRvymb1PeJge/7TZ8164Ds3cm8oTHGvL58xceYcjuZRrrF5GUUQ+gHsXLYsS79qDVru1AzWP9ADtoz3V5M/n1+ilc2kGndopIaikB1JN4aRnruhcwYPf2SAd5S6wTLz68iXsmZ2viNhFJCw0BpVs8DnPnYu3zGLB7ZY1FHYi1ymXVeTfTbtcmJk1V8BeR9FEPIJ1KS2HAANi6NdKUzZafT+v33uOobI3zi0j6qQeQBrEY/PD6UuLt2uFbtwI1H+SN0wKOPQ7eew8U/EWknigBpFA8Do88Ap3ax5l++5FVnt2TaB19efbU78Ojj2HLlyn4i0i90hBQisRLy3h+0Jf5xObXeJI+dKW42lk7AfbTkv857V2eWJSjcX4RaRBKAKlQWoq178gYjwMwgLU1Fi9p34eX7nmPJyYr+ItIw1ECSFY8DoMGYR4/qMXvlYo54Vz+WVl03PQeE3Ny6q+OIiJV0DGAwxQvi/HeF29hc+9PUr55c5XDPeUJD1q0gMmTYedOUPAXkUZAPYDDECuNUdaxB4Pj22sst6TFqZSd+hlO+/pwWp09AY33iEhjogRQR/E4/HHQj7giXv0VvQ64ZXFiyQKy8tTaF5HGSQkggngc5s+HZctg3z44fcvLh5SpGPM3M6xbN2z1alDwF5FGTAmgFvE4jB8PhYWwaxe0agVZPpozePaQsluPPZ2ut30DJmi4R0Qav6QOAptZZzNbaGarwudOVZQ5w8yWJzz2mNk5yWy33sTjvP6DJzht8a2cVvoE5nFiMfgR32E7nQ66mvfjrE50fm0BTJyo4C8iTUKyPYAbgUXuPsPMbgyXb0gs4O7PAcMhSBjAauDpJLebfmHT/xOLC/lUbBe7yaWQUYxnAfvJpk/WJm6I/4hT7BVWdTuZr6z+Dlk5upJXRJqOZBPAJOD08PX9wPNUSgCVTAHmu/vuJLebeokD/SNGBMuFhbSOlQLQjlJGUcgE5vN87kSuuy6brOwfUjYcvqoRHxFpgpJNAN3dfWP4ehPQvZbyXwTuqG6lmU0HpgP069cvyarVQSwGI0fC228HR3lzc6Fbt2A2zwRt2cXI7OXsOXEi3/uegr6ING21JgAzewboUcWqmxMX3N3NrPIFsInf0xM4DlhQXRl3nwnMBCgoKKj2u1IqHg+C/xtv/Pe90lLYvx/atIE9ew68vT87l7NuGM7NCv4i0gzUmgDcfVx168xss5n1dPeNYYDfUsNXnQc84u77DqOe6TN/ftDyr2zv3mAu/y1bgtN/cnNpPWoUI783ART8RaQZSHYIaB4wDZgRPj9WQ9kLgJuS3F7KVAz55/1yGafFYode1NWqFdxxR9DUX74chg/X6Z0i0qwkmwBmAH8zs8uAdQStfMysALjS3S8Pl/sDfYEXktxeSiSe23966QgKyCWPXQcXOuaY/57SOXFiw1RURCSNkkoA7v4RMLaK95cClycsvw/0TmZbqTR/fhD8S0vhKSbwKidyIq+Syy4sOzsI/q+9pta+iDRrGTkb6LJlwbA+QDlZjGcBF/AQL4y9FebOhddf1925RKTZy8ipIEaMCM70rDjLs5wsns+byBXXTASN9ohIhmiePYB4HJ54Am69NXiOxw9aPWECjBoFeXlgFjyPGhW8LyKSKZpdDyAei7Nt5Hjav11I9r7g9E0bNQoWLDgwpp+VFSzOn68TfEQkczWrHkA8DreMnE/OG8EUDuaOlZbirxYG0T5Bxck93/mO5m8TkczUrBLA/PnQ5u1l5FQ+pXP3rqCpLyIiBzSrBLBsGbwWG8Fucg96P9YqNxjnERGRA5pVAhgxAl7MnUAho9hJHnGMUvL4+Bgd4RURqaxZHQSeMAFOODGLc19dwKd3zeeE7OXsPWY4P3xNR3hFRCprVgngv2f3ZLF8+USGD5+os3tERKrRrBIA/PfsHk3fIyJSs2Z1DEBERKJTAhARyVBKACIiGUoJQEQkQykBiIhkKHOvn3uv15WZFRPcZayhHQFsbehK1BPta/OTKfsJ2tcK+e7eNcqXNNoE0FiY2VJ3L2joetQH7Wvzkyn7CdrXw6EhIBGRDKUEICKSoZQAajezoStQj7SvzU+m7CdoX+tMxwBERDKUegAiIhlKCUBEJEMpAVRiZp3NbKGZrQqfO1VR5gwzW57w2GNm5zREfZMRZV/Dcv3M7Gkze9vMVppZ//qtafLqsK/xhN91Xn3XM1lR9zMs297M1pvZXfVZx1SJ+H8138z+Ff6eK8zsyoaoa7Ii7utwM1sS7uebZnZ+bd+rBHCoG4FF7j4YWBQuH8Tdn3P34e4+HBgD7Aaert9qpkSt+xp6ALjd3Y8BRgJb6ql+qRR1X8sqflt3P7v+qpcyUfcT4FbgxXqpVXpE2deNwEnh/9VRwI1m1qse65gqUfZ1N3CJuw8DzgLuNLOONX6ru+uR8ADeBXqGr3sC79ZSfjowq6Hrna59BYYCLzV0XevrdwVKG7qu9bSfnwIeAi4F7mroeqdzXxPKdwGKgF4NXfd072tY7g1gcE1l1AM4VHd33xi+3gR0r6X8F4EH01ultImyr0cBO8zs72a2zMxuN7OmeI+1qL9rGzNbamavNsVhPSLsp5m1AH4BfLM+K5YGkX5TM+trZm8CHwA/dfcP66uCKVSnuGRmI4Fs4D81lWt2dwSLwsyeAXpUsermxAV3dzOr9jxZM+sJHAcsSG0NUycF+9oSOBUYQdB6epig1XhvamuavBT9rvnuvsHMBgLPmtlb7l7jf6L6loL9vAp4yt3Xm1k6qpgyqfhN3f0D4Phw6OdRM5vj7ptTX9vkpDgu/RmY5u7lNW0zIxOAu4+rbp2ZbTaznu6+MfxD1jTefR7wiLvvS3klUyQF+7oeWO7ua8LPPAqcSCNMAKn4Xd19Q/i8xsyeJ0h8jSoBpGA/TwJONbOrgDwg28xK3b2m4wUNIoX/V3H3D83s3wQNmjkprmrSUrGvZtYeeBK42d1frW2bGgI61DxgWvh6GvBYDWUvoOkO/0C0ff0n0NHMKmYXHAOsrIe6pVqt+2pmncysdfj6CGA0TW9fa91Pd7/I3fu5e3+CYaAHGmPwjyDKb9rHzHLC152AUwjG05uaKPuaDTxC8HtGS3ANfXCjsT0IDhQtAlYBzwCdw/cLgHsSyvUHNgAtGrrO9bCvZwJvAm8B9wHZDV33dOwrcHK4j2+Ez5c1dL3T9ZsmlL+UpnsQOMpvWvFv943weXpD1zuN+3oxsA9YnvAYXtP3aioIEZEMpSEgEZEMpQQgIpKhlABERDKUEoCISIZSAhARyVBKACIiGUoJQEQkQ/1/SkbdMfGIkOEAAAAASUVORK5CYII=\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYAAAAEICAYAAABWJCMKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deXxU9b3/8deHQEJI2A37LriAC2gEFa0bFmmpqCVSlxb91dLe3t5qW6v2em+tt72K11a9rde2Lq1aLSJUhNamqCjuRoPgAlaJoMi+SSAhMDB8fn+cExxClhMmk23ez8djHjNn5jtzvmcCn8/3+z3f8x1zd0REJP20aeoKiIhI01ACEBFJU0oAIiJpSglARCRNKQGIiKQpJQARkTSlBCAikqaUAKRBmNmDZvaL8PHpZvbBIX7O78zsPxu2dq1LMt+vSCIlgDRiZh+bWYWZlZnZhjBo5zb0ftz9JXc/MkJ9rjCzl6u89zvu/vOGrlOEurQ1s2+b2StmttnM1pjZk2Z2VpVyg8zMzaxtuL0/8aWwbm5mQyu3o36/h7Cfw8Lj32Jm28zsNTMbW6XMD8xsvZltN7M/mFlWwmuDzOx5M9tpZv80s3FR3ytNQwkg/XzF3XOBE4B84D+qFqgMbunCzHKAZ4BxwI+A/sDhwD3AdDP7aQr33Zy+6zLg/wF5QFfgNuCvCcluPHADcA4wEBgC3Jzw/hnAYqA7cCMw28zyIr5XmoK765YmN+BjYFzC9u3A38LHDvwrsBxYGT43EVgCbANeBY5LeO8o4C1gBzATeAz4RfjamcDqhLL9gSeATcAW4G7gaGAXECcIPNvCsg9Wfk64/S2gBNgKzAP6JLzmwHfCOm8D/g+w8LWhwAtAKbAZmFnL9/IH4L9qeC0LeAn4Qrg9KNxvW2AasAeIhcfw17BMH+Av4fGuBL6f8Hk/A2YDjwDbgauA0cBr4TGsC7+fzLD8i+H+ysN9TKnm+z0aWBi+fylwfsJrD4bfy1Ph36oIODzCv5U2wFfCffcIn/szcEtCmXOA9eHjI4DdQMeE118CvlPXe3VrwpjQ1BXQrRH/2AkJIAzKS4Gfh9tO0AruBmQTBPiNwBggA5gavj8LyAQ+AX4AtAMmh4HwoAQQvvdt4E4gB2gPnBa+dgXwcpU6PpjwOWcTBO8Twv3+BngxoawDfwO6AAPCgHte+NoMglZom8R9VvOdDAbeC8t1AeaE+3wC+CtBa3UsMDssPyjcb9uq9Q232wCLgJ+G39MQYAUwPnz9Z+F3dUFYNhs4ETiZIKkMAt4HrqlynEMTthO/33YECfLfw/2dTRDoj0yo3xaCJNMWeBR4rI5/J+8QJDUH7kt4/m1gSsL2YWGZ7sCFwPtVPudu4Dd1vbep/1+k801DQOnnSTPbBrxM0EK+JeG1W919q7tXELRuf+/uRe4ed/eHCFp4J4e3dsBd7r7H3WcDb9awv9EELeIfu3u5u+9y95drKFvVZcAf3P0td98N/AQ4xcwGJZSZ7u7b3H0V8DwwMnx+D0Hw7lPHPs8B/uLu+8LP3w70Bf6bIJgaQS/oqIh1PgnIc/f/cveYu68A7gO+llDmNXd/0t33uXuFuy9y99fdfa+7fwz8Hjgj4v5OBnIJvoeYuz9HkBQvSSgzx93fcPe9BAlgZDWfs5+7Hwd0Ai4l+HdSKZegR1Wp8nHHal6rfL1jhPdKE2lO44/SOC5w92dreO3ThMcDgalm9m8Jz2USBHMH1rh74lKyn9Twmf2BT8LgU199CIaZAHD3MjPbQhCgPw6fXp9QfidBoAG4Dvg58IaZfQb8yt3/UM0+egBrwsfHAneHyWaRmS1NOIY11by3OgOBPmGSrZRBMBxSKfF7xsyOAO4gOCfTgeD/5aKI++sDfBomsEqfEHxHlWr6jmrk7ruAGWb2vpktcfe3CYagOiUUq3y8o5rXKl/fET6u7b3SRNQDkESJAf1T4L/dvUvCrYO7zyAYp+5rZpZQfkANn/kpMKCGk511rUW+liCgAvtP1nYnQjB29/Xu/i137wN8G7gncSZNgs1A7/Dxu8DFZpZlZicAI8LXfkPQKq92V1W2PyU4h5L4vXV09y/V8p7fAv8Ehrl7J4LhHCOatUB/M0v8vzyA6AmrLu0IhrEgGDI8PuG144EN7r4lfG2ImXWs8vrSCO+VJqIEIDW5D/iOmY2xQI6ZfTn8D/4asBf4vpm1M7OLCIZ6qvMGQcKYHn5G+4SphRuAfmaWWcN7ZwBXmtnIcMrgLUBROExSKzMrMLN+4eZnBEF3XzVFnwcuDJPZrUBnYBXBGP584C6CcfAnatjVBj4PkJXHu8PMrjezbDPLMLNjzOykWqrbkWDoqczMjgL+pY59JCoiaNVfF/4tziQ4eftYLfurlpmdbGanmVlmWPfrgZ7hPgAeBr5pZsPNrAvBDLIHAdz9Q4KhspvCv/GFwHEEJ8Nrfa80HSUAqZa7FxPMwLmbIICWEJy0xd1jwEXh9laCmSnVBkh3jxMEpKEEgXV1WB7gOYKW4Xoz21zNe58F/pMgiKwjmJr5tarlanASUGRmZQSzh64Ox+Or7mM5sAz4SXgu4UJ37+nuF7j7RcBYd3+8lv08AAwP580/GR7vRIJx9pUEPYz7CRJLTa4lGG/fQZB4Z1Z5/WfAQ+E+Lq5S/xjB9zsh3Nc9wDfc/Z+17K8mWQQzhrYQ9CC+BHzZ3deG+/oH8D8ESXMVwVDTTQnv/xrBMNZnwHRgsrtvivheaQKVU+ZE0paZdQL+QTD75s7wvhtBQPs6cHKVMXaRVkE9AEl77r4dOIugN/IQQUt6EXAMUKDgL62VegAiImlKPQARkTTVbK8DOOyww3zQoEFNXQ0RkRZl0aJFm909L0rZZpsABg0aRHFxcVNXQ0SkRTGzmi7KPEhSQ0Bm1s3MnjGz5eF912rKjAyXlV1qZu+Y2ZTqPktERBpXsucAbgAWuPswYEG4XdVOgnnJI4DzgLvCC0FERKQJJZsAJhFMmyO8v6BqAXf/MLzYhvCCko0E642LiEgTSjYB9HT3deHj9QSXjdfIzEYTLCj2UQ2vTzOzYjMr3rRpU5JVExGR2tR5EtjMngV6VfPSjYkb7u5mVuNFBWbWG/gTMLWmC2vc/V7gXoD8/HxdoCAikkJ1JgB3H1fTaxb8rmxvd18XBviNNZTrRPCLRDe6++uHXFsRkVYsHofCQli8GEaNggkTICMjdftLdhroPIJfipoe3s+tWiBc6XEO8HD4wyEiIlJFPA7jx0NREZSXQ04OjBkD8+enLgkkew5gOnCumS0n+EHt6QBmlm9m94dlLga+AFxhZkvCW62/SCQiki7icfjb32DqVHjlFSgrA/fgvqgo6BGkSlI9gPDHHM6p5vligh+7xt0fIfgBbBERCcXjMHs2fPObsHNnEPSrKi+HJUtg4sTU1KHZXgksItJaVVTAUUfBqlW1l8vJgZEpHC/RYnAiIo0kFoNrr4UOHeoO/rm5wTmACRNSVx/1AEREGkFZGXTvHiSB2pjBZZfBlCmpnwWkHoCISArFYnDdddCxY93BH6BHD3jwwWDcP5XBH9QDEBFJmYoKOOyw4CRvFG3aQElJ6gP//v01zm5ERNJHWRmMHRuM9UcN/pMnB+/LzU1t3RKpByAi0kDicXjwgThzvl3I2SymK6MoZAL7qL1Jv2ULdOvWSJVMoAQgItIASkuhT884c3ePZwZFdKCcneRQxBjGM7/aJHDKKfD0043b6k+kISARkSTE4/Doo9ClC5y1u5AxFNGRMjJwOlLGGIqYwIGX87ZtCzt2wKuvNl3wByUAEZFDVlYGeXlw+eXB9igW04HyA8p0oJyRLNm/PXAgbN/etIG/khKAiMghKCkJpnZ+9tnnzy1mFDvJOaDcTnJYwkjMgqUfPvoIsrMbubI10DkAEZF6WLMGBg2CvXsPfq2QCRQxhjFVzgEsaDeB7VubR6s/kRKAiEgEpaVw7LHw6ac1l9lHBuOZzwQKGckSljCSId+dQOmdGWRmNl5do1ICEBGpRTwOd/0qzvPXFzKVxSyuY2rnPjJ4iokszJnImjXQuXMjV7gelABERGqwfj307R1nPuOZFnFqJ8DDD8OllzbeFb2HSglARKSKWAy+fmmc8r8U8iCPMZZXyGYXwAFTO5/iwIX6O3SAtWubd6s/kWYBiYgkWLUKsrPifOsv45nBJVzGo7QPg3+lqlM7Ae6+O5je2VKCP6gHICICwNatMGwYbNsa56fczOm8RBbVL99ZObWz0saNwfUALY16ACKS9lauhLzuccZuncuHHMG/cyuZVYK/A/uAHeRSxBgKmcA99wTTQVti8Af1AEQkjVVUwKRJsOCZ4ETvqeFYv1VXlvb8hcnMZApbTppA2QsZzeaCrkOlBCAiaamkBEYMq+CPXMlDLKQ7m8kkflA5B2Jk8ipjuYIHmTkrg8mTG7++qaAEICJppaw0zg+OKqTv+iLKuZWMaoJ+ohiZTOd6/oubWPlJBgMGNFJFG4ESgIikjZJlMcpGjOZu3qcdMQyqHe6BoOW/i/a8wliuXHETNw1u5pP6D4FOAotIq7eqJMZ/2w0MHNGB43mbLGK04eDgX3midyftWcEQftD7MU7eNp8BrTD4gxKAiLRycx4tI29YJ/6d22hLvMYWf6V3OYaLmcXOxR/yu7WTyO3cOoM/aAhIRFqp9WvifL//E/zZp5CB1zrUU2kvbfnGsDd45a3sZrdyZyqoByAirc6s+zbRuV8OM/3iOoN/BVmsYDAzmMLSV7fz9ofpEfxBPQARaUVKSuCkYevZSm+g5hO8lRy4hBm0++qF/PnPNMslm1NJPQARafFiMfjal0qpGHZUpODv4W0hZ/CbFecze3b6BX9IsgdgZt2AmcAg4GPgYnf/rEqZgcAcgmTTDviNu/8umf2KiFRaswaO6fd5qx9qn9oJUEY29+T/kR+8OJnM7NZ7krcuyfYAbgAWuPswYEG4XdU64BR3HwmMAW4wsz5J7ldE0lxFaYxHelxDj35tDmj1Vxf8K1v8e8jgqzzOx4t3cP2bU9I6+EPy5wAmAWeGjx8CFgLXJxZw98QVlbLQsJOIJOmNpzZxwsQeXJbwXF2t/tu5hi3X3MasX2Y2+x9qaSzJJoCe7r4ufLwe6FldITPrDzwFDAV+7O5rayg3DZgGMKA1XW8tIg2ibGuMGX1/xFW77gaineTdh3EYa3lzeS+GDk15FVuUOlvjZvasmb1XzW1SYjl3r+xlHcTdP3X34wgSwFQzqzZRuPu97p7v7vl5LXV9VRFJiWceXU9296xIwb8yGK1kAH/8dTmfuYJ/dersAbj7uJpeM7MNZtbb3deZWW9gYx2ftdbM3gNOB2bXu7YiknZKlpSxadQZjOMtIFqrH+ASHuan71zKVcdqvKcmyY7HzwOmho+nAnOrFjCzfmaWHT7uCpwGfJDkfkUkDdx/40oOH9WRkyME/8pW/24ymP/YNh7zrzNcwb9WySaA6cC5ZrYcGBduY2b5ZnZ/WOZooMjM3gZeAH7p7u8muV8RacXWl5Txmo3im7cMAWqe3VOpchG3e9p9n90bd3LelBb0w7xNyIKh++YnPz/fi4uLm7oaItLIZt22jMk3jNi/XVfgByijLe8v3M7oM1r4T3Q1ADNb5O75UcpqSqaINAurlmxltXXdH/zrWqu/MvjP7v+vZO0oV/A/BFoLSESaVOmmGPN6XMnl/Hn/c1Fa/e9zOJnFiyg4UcM9h0o9ABFpMq/NWEluj6z9wT9qq/+WS5dy5N4Shir4J0U9ABFpdBWlMeYO+B5Ttt8HRJ/a+SndyV3+ITcO7ZbS+qUL9QBEpFG9+8JW2nZpHyn4J7b6779mKQN8M90U/BuMegAi0ijK1pSyvt/RHEOwekzUVv9y+rJjwVK+dbaGexqaegAiknIv3zyTnH5dODxC8D9ghs8PCznCV3Oign9KqAcgIikTW1ZCmxHDGBtuR231l9CDPa9+SMEpCvyppB6AiKTEkv98gHYjhlG5GEPUVv9fp7/KMN/AcAX/lFMPQEQa1Af/WMngCUM4PtyO2ur/B2cyZvXfOb+vLuhqLOoBiEiDmTXlfzliwhDahdtRW/1/v6OYCf483RT8G5V6ACKStFX/WEbfCSOYHG5HbfU/zfGc8MlrfHmAAn9TUA9ARJIy68x/o/+EEfuDSdRW/1v3FzHel5Cn4N9k1AMQkUOy6tEX6Hv5mfVu9f+TPHquWM6Jg3WSt6mpByAi9RIrreANG0r/y8+sd6v/L3f9k6N9I90U/JsFJQARiWzJfS/TrksHTuIjIPribauAPRu3MfnqI1NfSYlMCUBE6hRbs4lSM46fdjoQ7Re6IPiVrtfvWsBAdzLz1OpvbpQARKRWs771EO369aBTuB11uOfGYb8mvts55eqzU1tBOWQ6CSwi1Vrz2iq6nzqw3id59wCrnl7BLecOTl3lpEGoByAiB5n19d/S59SBZIXbkRdvO/l7ZLozVMG/RVAPQET2W/PcB/Q856h6t/r3ASWPLaZgysjUVU4anHoAIgLArHFX0+eco+q9eNvsi+4hw50jFfxbHPUARNLcBzMWMfTS/Hq3+mPA5pdWUHCahntaKvUARNLYrCOncsSl+fW/oOuc75LlTl8F/xZNCUAkDb17+0ziZkz+8GGgfvP6P527mMnP/l+KayiNQUNAImkkvrWULd27cEzCc1ECP8CzX/0Z586+iQEpqps0PvUARNLEqjv/RJvuXcgLt6O2+uPAnqXLOXf2TSmtnzQ+JQCRVq5ifSlrrC39f/gNIFrgrwz+L37n17R1J3P40BTXUpqCEoBIKzbv/Btp37sLfYgD0Wf4bAPKV2zkjN/+WyqrJ00sqQRgZt3M7BkzWx7ed62lbCczW21mdyezTxGp29bXPmCvGV/56y1A/Vr9793yCF3dyR2cV8s7pDVItgdwA7DA3YcBC8LtmvwceDHJ/YlIHWadczNdT63/BV3ryGLflm0c+5PLUltBaTaSTQCTgIfCxw8BF1RXyMxOBHoCTye5PxGpwco5S4Kpnc/9DKjf1M6Pfvc3+vguMrppyeZ0kmwC6Onu68LH6wmC/AHMrA3wK+DaJPclIjWYdfb1DLpoVL0v6Jp9xPlkuDP0219ObQWlWarzOgAzexboVc1LNyZuuLubmVdT7rvA3919tVntp6DMbBowDWDAAM02FqnLpjkv0+2i0w9p8bYP7phFwQ8m11ZcWrk6E4C7j6vpNTPbYGa93X2dmfUGNlZT7BTgdDP7LpALZJpZmbsfdL7A3e8F7gXIz8+vLpmISGhW/4lMXv3U/u2oF3Q9+aXruPCp2xiesppJS5HslcDzgKnA9PB+btUC7r7/jJKZXQHkVxf8RSSakkdfY/Dlpx5Sq3994TtceN6xqauctCjJngOYDpxrZsuBceE2ZpZvZvcnWzkROdCsows4/PJT6z/Wf8Z3yXCnr4K/JDD35jnSkp+f78XFxU1dDZFmYdmtf+LIf/9GpMAPnwf+vcCWl5bT6zRdyZsuzGyRu+dHKavF4ESasXhZBf/smMtw9u1/LupY/+zzbqGg8CfVzuAQAS0FIdJsPfevv6VNxw77g3995vV/+EgRBYU/SXENpaVTD0CkmSl9dxVZxw3krHA76nAPwLNfuZZz593OkSmqm7Qu6gGINCOzLrqNTscNJCvcjhr8NwHln2zh3Hm3p65y0uooAYg0AyufW8keMybPCWZI12fxttlXPEgPd3IHdEtxLaW10RCQSBObNe7nTF7w0/3bUU/ybgJ6bNtGQWet3yOHRj0AkSbywbxgyebK4F+fk7xv/s9ceriDgr8kQQlApAnMGvtjjphU/yWbZ4+8jgx3Rv/4/NRWUNKChoBEGtHK+55iwLSJh7aMw9NLKThXK/hIw1EPQKSRzOo/iUHTJtZ/GYehFwXLOCj4SwNTAhBJseceCmf4rJ4HHMIFXcv/kuIaSrpSAhBJoYeP+AFnXTFk/1hr5Fb/uJ+R4c6Rl41Oaf0kvSkBiKTAU9fPJG7G15ffBURv9e8B1r60goJnbkpxDUV0ElikQcXLKnitY0++xI79z0VevO2Ld1Ew/2r6pqx2IgdSD0CkgTz14xm06diBsWHwj9rq3w5sfmcdBfOvTnENRQ6kBCCSpK1rKnjZ+vOlX14K1HMZhwn/Q2d38o7Vos3S+JQARJIw65L76NqvA2NZDdRv8bbtK7ZQ8Pcfp7J6IrVSAhA5BOvXxPmDjWPyY9OA+rX6/37Nw/Rwp/NgLd4mTUsJQKSeZl02gx792nIlC4Dogf+Vvl/A9u7ly3d+PdVVFIlEs4BEIvpg3gccPumoQ1vGYW4xp51/YuoqJ3II1AMQiWDWV397aIu3nXpDsIyDgr80Q+oBiNSi5LlV9DtnYL1b/XuBFYUrKDhvcOoqJ5Ik9QBEajDrpP/k8HOi/TzjAa3+M39BO3eOVPCXZk49AJEq/vHASs66aki9W/27gY0vfULBaQNSVzmRBqQegEiCWeN+w/irhpAZbkdu9f+/R2jvzgAFf2lB1AMQAd6YUcIJlw6rd6t/E7B54UYKzshLXeVEUkQ9AElrFRVwtd3GSZcOq/cMnyeve4Ie7gxX8JcWSj0ASVsvP/Aup1x1HHeF29Fb/dl0XL2aC/vqSl5p2dQDkLRTtmorGyyXsVcdV6+fZ9wH/P2uxfTwnWQr+EsrkFQCMLNuZvaMmS0P77vWUC5uZkvC27xk9imSjNk/mk3OwO70oByofQ2fxOGeR+0y4jv38uWrRzZCLUUaR7I9gBuABe4+DFgQblenwt1Hhrfzk9ynSL2VrS/jLTuMr95RANTvd3nf/t1CLt/3CJnZGbW8Q6TlSTYBTAIeCh8/BFyQ5OeJNLgX7nuXnN4dGcUWoB5TO8/9JRnujPz2GamuokiTSPYkcE93Xxc+Xg/0rKFcezMrJrhCfrq7P5nkfkXqtLVkK2XD+vEFKoDoJ3njwEdz/0nB+UemsnoiTa7OHoCZPWtm71Vzm5RYzt0TG09VDXT3fOBS4C4zO7yGfU0zs2IzK960aVN9j0Vkv1nXv0bXYd3pHyH4H9DqP/8O2rpzpIK/pIE6ewDuPq6m18xsg5n1dvd1ZtYb2FjDZ6wJ71eY2UJgFPBRNeXuBe4FyM/PrymZiNTojTlrGHFRv0NaxmFb0ScUjNaVvJI+kj0HMA+YGj6eCsytWsDMuppZVvj4MGAssCzJ/YocZNaPXuOki/rRIdyO3OqfNpf27vRS8Jc0k+w5gOnA42b2TeAT4GIAM8sHvuPuVwFHA783s30ECWe6uysBSIMpeWENvc6sf6t/E1BetJGC0bqSV9JTUgnA3bcA51TzfDFwVfj4VeDYZPYjUpNZV/+Dyb+esH87ytROgNnXPEHBnRemrF4iLYGWgpAWadlTKxk6sf5LNm8H4kvXUTC8V+oqJ9JCaCkIaVHicfjVxKc4euIQ2oXPRR3rf/7epXR2p5uCvwigHoC0IEue2UTfLw7gh+wCorf63+uUz/A1L3J2bnZK6yfS0qgHIM1eRWmMx9t/neO/2IPDIgT/xMXbPnp6BceWvkmGgr/IQZQApFlbNnsZWV2yKNj9CBB98bZX+pwPO3cz9Fz9Lq9ITTQEJM1S2aYKlvQ+j7HxF4Howz07gdULVnPa2X1TWT2RVkE9AGl2XvvTB+T06BAp+B9wQdflj5DjzpEK/iKRqAcgzUZpKUzq/QbPV4wBorf6Y8D2ohUUjNZwj0h9qAcgzcKieWvI6NIuUvBPPMn75N3LyXInT8FfpN6UAKRJVZTGeKzzNE6Y1I8c9gLRruZ9gAvZ9MluLvzXoSmvo0hrpQQgTWbJvFVkdcliyvb7gOgzfF6/t5ir/Al6DchshFqKtF46ByCNbv0HpWw96kSOD1cEjzrWfz+Xc8HqBzilrwK/SENQD0Aa1WuPltDzqC4cHSH4J7b6P5z7T77lfyJPwV+kwSgBSKOo2FTGu1mjOPnyYUD0H2V/86Rp7Nu5W7/QJZICGgKSlFv5TAmDvjiMY8LtKIF/H1Dy9CeMPlc/0iKSKuoBSMpsWlnG63YCg75Yv1b/X/teRXzHbo5U8BdJKSUAaXDxWJwFk/+Pw4Z0ZAyLgejz+je8uoLzV99HZq7G+kVSTQlAGtSqJVupyGrH2X/5HhB9audLY74PO3fT6xRd0CXSWJQApGHE43x8y6P0H9WdHDxy4C9iJJ99soMvvP6/ZGSr1S/SmHQSWJK2dWUpbYb0ZyA7gGjj/OW0Y2XhSk4+Twu3iTQV9QDkkFWUxpjV67t0HdKFzuyIfJJ3bN5y4ttiHKvgL9Kk1AOQQ7LmgzK6HtUx0o+yVwb+PcDWpVt4dXi31FZORCJRD0DqJVYR5/fnzKTXUR3JJvrUzm0XXUHm7t30UvAXaTbUA5DIKtaXsqv3AKaxHYh+Qdf6xRvpOzIv1dUTkXpSD0DqFKuI8/h599G+dxe6sD1Sq9+BN/tfSHzbTgV/kWZKPQCp1aZVFewYOJgCNgDRWv2b6MK+5Z8yemhuyusnIodOPQCpVjwW57nvzabLwBwGsyFyq3/ZdQ/SY+9mein4izR76gHIAeJxmPGHCk6dNpyz+BiI2urPw1asYMRgBX6RlkI9ANmvbGuMOzOv5ZJpHRjMx5Fa/RVksu33j9Nj7zryFPxFWhT1AASA0mVryB3Rjx+F21Fa/Z92OJK8te/QtbOWcBBpiZLqAZhZNzN7xsyWh/ddayg3wMyeNrP3zWyZmQ1KZr/ScGIxuOmqNXQa0Y82RF+8rezO+xmwfSnZCv4iLVayQ0A3AAvcfRiwINyuzsPA7e5+NDAa2JjkfiVJZaVxrj1iLrOzLuGmB/oBdQf+OMayLqeya+MOOl7zTcjIaKzqikgKJDsENAk4M3z8ELAQuD6xgJkNB9q6+zMA7l6W5D4lSVtXlmJDBnI7pfufqy3478MoYCb3b7yIEXkK+iKtRbI9gJ7uvi58vB7oWU2ZI4BtZvaEmS02s9vNrNooYmbTzKzYzIo3bdqUZNWkqngszkv/8ihdh3ShC6X7h3tqD/7woys+47HdBXRT8BdpVersAZjZs0Cval66MXHD3d3MvJpybYHTgVHAKmAmcAXwQNWC7n4vcC9AflXz37wAAAzmSURBVH5+dZ8lh6hsUwVbehzFaawCop3k3Ux3Mld/zF19NbtHpDWqswfg7uPc/ZhqbnOBDWbWGyC8r25sfzWwxN1XuPte4EnghIY8CKlZrCzGM6NvILtHDgNYFekkrwOv/MuDdNu9gc4K/iKtVrJDQPOAqeHjqcDcasq8CXQxs8oFYc4GliW5X4lg68pS9nXMYdybt9Em/JWumjhQRg63trmRnVt2c9o9U8nI1JCPSGuWbAKYDpxrZsuBceE2ZpZvZvcDuHscuBZYYGbvEjRA70tyv1KLirI4v8wPxvqz2Bvpgq6V9ONn39vKtRW/ILebpnaKpANzb55D7fn5+V5cXNzU1Whxtq4qIzZwMD3ZDNQ+3FNpKUcxaMvbCvwirYCZLXL3/ChltRREaxGLUf5v19F1YEd6sjnSWP+7DGfh9x7n6N3vKfiLpCEtBdHSxePE58zFL72MDnt2AXUP92wgj9P6fMK7Jdkcl90otRSRZkgJoAWLbS1jd//Dydm5cf8yDjWpHPJ5h+F8+MhiPvhapi7kFUlzGgJqieJx9jw6k7bdO5IbMfjvA176l0c4Zvc7FFym4C8i6gG0PPE48bPPpc2Lz0f+QfZduYeRuXolX+isOf0i8jn1AFqKeJyKGU9Qkns8bV58ngyirNWfxfb7Z5K9bT0ZCv4iUoV6AC1ArCLOx0PHMWztQg6vo2zlcM+K7GPpvbqYzprdIyI1UA+gOYvF2HPDf7Cmw+EMW7uw1sXbKqd2rm4zkH2zn2TYjsWa2ikitVIPoJmKV8TYm9eLzPLPGFRHWQd2kcXiHzzEmOmTtYSDiESiHkAzEyuL8ewp/8HmDv3JLP+szlZ/HOMdjoNt2zn1jikK/iISmXoAzUisLEZZx16cw2d1lnUgRjvuOnkm33/mfLJzFfhFpH6UAJqJWEWcFwZ/g3F8FmFOv/EJA+myehnX99WlvCJyaDQE1MTicXhiVpyXc8Zz1ubZ1ZapPMG7D1jBYB65aA79dpbQTcFfRJKgHkBTicXYe/MvWPTrV9hdlsdJFNGWeLVFg4XbjuFmbubhbZOY2lnDPSKSPCWARhaPxXnzp3MZdftlZO7bxWhgdDXlPOH+ec7idxc+w6OPZpCtRr+INBAlgEYUq4jzVt54RpW/SCZ7Dhjrr/qrDPtow3sM51cdb+aeTydxjlr9ItLAlAAaSawsxj96foMv7VxY41DPXjIw9rGTHN60MWybOZ8/XpShhdtEJCWUAFItHif+5Dz2FVzKV3xXrUUfZzIl7Y5h8IUjmfLgBDKzFflFJHWUAFIoVhZj8+CT6Ln5XbJq+FH2yqGfz+jKzwY+zHsfZpKpFRxEpBFoGmgKxGLwk+viLOt4Er03v0NGNcG/8irerXTlF9zIucesV/AXkUalBNCA4nGYMwc6d4Z3by9kBMtqvahrJhcz+fRNHPfkL3hjiYK/iDQuDQE1kHhZBQuHXsnxG97gAUbzIUeQwd6DyiUO+Tx4xsM8u0AneUWkaSgBNIB4WQV06sTZHgT8wawkTht2kUUHdh9UvrDTxey5/08UXqSfZhSRpqMEkKR4HBYOvZKzfe8Bwz0Z7KOUTmSyhQz2AcHc/pczzmDc+j9rho+INDklgENUUQFXXgkLF8KrG96otsxOcrmI+yhgNm3awN4LJnPJIxMV/EWkWVACOARlZdClS9D6B3id0Qxm5UHl3soYzfbTJpF79STOPx8N94hIs2LuVRchaB7y8/O9uLi4qatxkHgc+vaFDRs+fy6TCsroRNuEk777rC1s305GrhbvEZHGY2aL3D0/Sln1ACKIx6GwEBYvhj17YOPGA1+PkU0u2/kjV3KyvcnKHidxZskfFfxFpFlTAqhDPA7jx0NREZSXQ7t2UF2nKUY2tx7zGLfeChMmaLhHRJq/pBKAmXUDZgKDgI+Bi939syplzgLuTHjqKOBr7v5kMvtuFPE4i24u5IyXFtM+NopCJhCLVR/ZMzLgjTfQcs0i0mIk2wO4AVjg7tPN7IZw+/rEAu7+PDAS9ieMEuDpJPebemHT//iXijgxVs5OcihiDOOZzz6Ci7ficTCDHj2gpETBX0RalmQTwCTgzPDxQ8BCqiSAKiYDhe6+M8n9NrzEgf5Ro4LtoiKyYmUAdKSMMRQxgUIW5kzkhz+EzEwYOVJDPiLSMiWbAHq6+7rw8XqgZx3lvwbcUdOLZjYNmAYwYMCAJKsWXTwWZ+vo8XR6v4jMPeWQk4P16BHM90zQgXJGZy5h18kTuekmBX0RadnqXAzOzJ41s/equU1KLOfBfNIa55SaWW/gWGB+TWXc/V53z3f3/Ly8vHocxqGLx+GnowvJfjto7Zs7VlaGr10L7dsfUHZvZg7nXT+S+fMV/EWk5auzB+Du42p6zcw2mFlvd18XBviNNZUFLgbmuPueQ6hnyhQWQvv3F5NN+YEv7N4NgwcHcz7Lg15B1pgxjL5pAij4i0grkOwQ0DxgKjA9vJ9bS9lLgJ8kub8GUznkf+edkB0bxU5y6MjnQz6xdjlk3XFH0NRfskSD/SLS6iSbAKYDj5vZN4FPCFr5mFk+8B13vyrcHgT0B15Icn8NourcfmMCRYxhDEV0oJwKcqg4egx5EycGAX/ixKausohIg0sqAbj7FuCcap4vBq5K2P4Y6JvMvhpSYWEQ/CvP8ToZjGc+EyhkdOYSdh89kv96Q619EWnd0vJK4MWLg5Z/IrcMdp09kROumaiRHhFJC2n5k5CjRkFOzoHP5eTANdcEoz0K/iKSDlplAojH4W9/g5//PLivXLa50oQJMGYM5OYGV/Lm5gbbEyY0TX1FRJpCqxsCisVg9Gh4//3gcU4OnHwyB8zdz8gItgsLNcFHRNJXq0oA8XgQ/N9++/Pnysvh9deDYJ84madyco8m+IhIumpVQ0CFhUHLv6ry8qClLyIin2tVCaDyB1uqqly0TUREPteqEkB1s3sAjj5aJ3hFRKpqVQmgcnZPTk4wuyczE44/PvihFp3gFRE5UKs6CazZPSIi0bWqBACa3SMiElWrGgISEZHolABERNKUEoCISJpSAhARSVNKACIiacqC33JvfsxsE8GvjDW1w4DNTV2JRqJjbX3S5ThBx1ppoLvnRfmQZpsAmgszK3b3/KauR2PQsbY+6XKcoGM9FBoCEhFJU0oAIiJpSgmgbvc2dQUakY619UmX4wQda73pHICISJpSD0BEJE0pAYiIpCklgCrMrJuZPWNmy8P7rtWUOcvMliTcdpnZBU1R32REOdaw3AAze9rM3jezZWY2qHFrmrx6HGs84e86r7HrmayoxxmW7WRmq83s7sasY0OJ+H91oJm9Ff49l5rZd5qirsmKeKwjzey18DjfMbMpdX2uEsDBbgAWuPswYEG4fQB3f97dR7r7SOBsYCfwdONWs0HUeayhh4Hb3f1oYDSwsZHq15CiHmtF5d/W3c9vvOo1mKjHCfBz4MVGqVVqRDnWdcAp4f/VMcANZtanEevYUKIc607gG+4+AjgPuMvMutT6qe6uW8IN+ADoHT7uDXxQR/lpwKNNXe9UHSswHHi5qevaWH9XoKyp69pIx3ki8BhwBXB3U9c7lceaUL47sAro09R1T/WxhuXeBobVVkY9gIP1dPd14eP1QM86yn8NmJHaKqVMlGM9AthmZk+Y2WIzu93MWuJvrEX9u7Y3s2Ize70lDusR4TjNrA3wK+DaxqxYCkT6m5pZfzN7B/gUuM3d1zZWBRtQveKSmY0GMoGPaivX6n4RLAozexboVc1LNyZuuLubWY3zZM2sN3AsML9ha9hwGuBY2wKnA6MIWk8zCVqNDzRsTZPXQH/Xge6+xsyGAM+Z2bvuXut/osbWAMf5XeDv7r7azFJRxQbTEH9Td/8UOC4c+nnSzGa7+4aGr21yGjgu/QmY6u77attnWiYAdx9X02tmtsHMerv7uvCLrG28+2JgjrvvafBKNpAGONbVwBJ3XxG+50ngZJphAmiIv6u7rwnvV5jZQoLE16wSQAMc5ynA6Wb2XSAXyDSzMnev7XxBk2jA/6u4+1oze4+gQTO7gauatIY4VjPrBDwF3Ojur9e1Tw0BHWweMDV8PBWYW0vZS2i5wz8Q7VjfBLqYWeXqgmcDyxqhbg2tzmM1s65mlhU+PgwYS8s71jqP090vc/cB7j6IYBjo4eYY/COI8jftZ2bZ4eOuwGkE4+ktTZRjzQTmEPw9oyW4pj650dxuBCeKFgDLgWeBbuHz+cD9CeUGAWuANk1d50Y41nOBd4B3gQeBzKaueyqOFTg1PMa3w/tvNnW9U/U3TSh/BS33JHCUv2nlv923w/tpTV3vFB7r5cAeYEnCbWRtn6ulIERE0pSGgERE0pQSgIhImlICEBFJU0oAIiJpSglARCRNKQGIiKQpJQARkTT1/wHC4TDca5DItgAAAABJRU5ErkJggg==\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# My neural network\n","k=50 # Number of hidden units\n","d=X_train.shape[1] # Input dimension. The third dimension is for bias\n","U=np.random.randn(k,d)*0.01 # Input layer\n","w=np.random.randn(k)*0.01 # Output layer\n","\n","eta=0.001 # learning rate\n","\n","ITNUM=5001\n","for it in range(ITNUM):\n"," grad_w=0\n"," grad_U=0\n"," for i in np.argsort(np.random.randn(N))[:10]:\n"," # print(X_train.shape)\n"," gw,gU=get_grad(w,U,y_train[i],X_train[i])\n"," grad_w+=gw\n"," grad_U+=gU\n"," w-=eta*grad_w/10\n"," U-=eta*grad_U/10\n"," \n"," if it%int(ITNUM/5)==0:\n"," print('Normalized Loss:',loss(w,U, y_train,X_train.T)/np.linalg.norm(y_train)**2)\n"," Yh=predict(w,U,X_test.T)>0.5+0.\n"," ix0=Yh==0\n"," ix1=Yh==1\n"," plt.figure()\n"," plt.plot(X_test[ix0,0],X_test[ix0,1],'b.',MarkerSize=10)\n"," plt.plot(X_test[ix1,0],X_test[ix1,1],'r.',MarkerSize=10)\n"," plt.title('Predictions @Iteration '+str(it))\n","\n","plt.figure()\n","ix0=y_train==0\n","ix1=y_train==1\n","plt.plot(X_train[ix0,0],X_train[ix0,1],'b.',MarkerSize=20)\n","plt.plot(X_train[ix1,0],X_train[ix1,1],'r.',MarkerSize=20)\n","plt.title('Training')\n","\n","ix0=y_test==0\n","ix1=y_test==1\n","plt.figure()\n","plt.plot(X_test[ix0,0],X_test[ix0,1],'b.',MarkerSize=10)\n","plt.plot(X_test[ix1,0],X_test[ix1,1],'r.',MarkerSize=10)\n","plt.title('Test')"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"elapsed":5,"status":"ok","timestamp":1651627184018,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"5JqLFhA5coRS","outputId":"7045ba5a-e6e4-4557-a742-e870f2d8f2c7"},"outputs":[{"name":"stdout","output_type":"stream","text":["Test accuracy = 0.848300\n"]}],"source":["yhat = predict(w,U,X_test.T)>0.5+0.\n","yhat = yhat.astype(int)\n","\n","acc = np.mean(yhat == y_test)\n","print(\"Test accuracy = %f\" % acc)"]},{"cell_type":"markdown","metadata":{"id":"2bNaWUo5e7Ch"},"source":["### Just as a baseline, the neurel network improves on the linear classifier. We shall test for different k's below:\n","\n","## 3. Neural Network Classifier w/ Quadratic Loss"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000},"executionInfo":{"elapsed":12078574,"status":"ok","timestamp":1651654678680,"user":{"displayName":"Zubair Qazi","userId":"17200828963209408500"},"user_tz":420},"id":"QKg01kQNeTIp","outputId":"682c5b95-fa28-4814-f23a-93b8bfd79ac9"},"outputs":[{"name":"stdout","output_type":"stream","text":["5 hidden units:\n","\tNormalized Loss: 0.984922652250338\n","\tNormalized Loss: 0.23423681849605146\n","\tNormalized Loss: 0.1747603002169233\n","\tNormalized Loss: 0.15308649253923193\n","\tNormalized Loss: 0.1398537535726779\n","\tNormalized Loss: 0.13514203097553948\n","Test accuracy with 5 hidden layers = 0.9336\n"]},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stdout","output_type":"stream","text":["\n","40 hidden units:\n","\tNormalized Loss: 1.0108370018105248\n","\tNormalized Loss: 0.20680743752027833\n","\tNormalized Loss: 0.13213054854640735\n","\tNormalized Loss: 0.10352970724027817\n","\tNormalized Loss: 0.0915293881939989\n","\tNormalized Loss: 0.08292932123023732\n","Test accuracy with 40 hidden layers = 0.9635\n"]},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAZwAAAEGCAYAAABRvCMcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deXhU5d3/8fc3Cfu+uoAaFgURFwRxqQgVtUhRWqvWpaWKRdHa7bG/FrV9eNpaaO3TPrXVS4vV+virooK1P1HE7RK3KoILCOISEDWIgoAIAUKS+f7+OCdhZjJJJiFnZjL5vK5rrpxznzP3+d65JvPNOec+923ujoiISNQKsh2AiIi0Dko4IiKSEUo4IiKSEUo4IiKSEUo4IiKSEUXZDiBX9e7d24uLi5v03rKyMjp16tS8AeU4tbl1aG1tbm3thX1v86uvvvqZu/dJtU0Jpw7FxcUsW7asSe9dvHgx48aNa96Acpza3Dq0tja3tvbCvrfZzD6oa5suqYmISEYo4YiISEYo4YiISEYo4YiISEYo4YiISEYo4YiISEYo4YiISEboORwRkX30yvtbKO7VkU07yhl2QFfMrGZbWXklHdoUYgYxh8KCvdt2V1TRvk0hAO6e8D53xx0K4vaPV72/u1O6dRcfbN7JlDuX8Ndvj2Lo/l1o36aQE2c/TWWs9hQ0JwzsyZQTizl1aF9++9jbPP/eJtZsKgPAgHfHxGhT2PznI0o4ItJiPfP2Rjq3L+K44p41ZWs27eDRFRs4b1R/DGNF6edc88BytpdX8rMJQykrr+TmZ0ro0bENuyti7Kqoqv8gix6NuBXNa9rdDT+w/vLaLby8dkvKbQ5s311Jz05tmzkyJRwRiVBVzNldUUWndkWs2bSD8X94lhu/cRTnjepP6dZdjLnxGU47fD/KK6t4/r3PGHlID179YGuzHPuPT75bq+x3i96uWd66s6JZjpOPokg2oIQjIg2oijkVVTE+3LKTT8tiLF23hR/d9wY3XXAMW8r2cPn/fbVR9f30wRX89MEVNetPrf60Zrm5kk2m3fatkUz/x97fw/dPHcygPp2544X3WfD9kykrr6R06y7eXL+N6x96k/LKWM2+T18zlvF/eJb+PTpwzRmHsX13JUP378qR/bqxpzJGl/ZF/M9T77KidBuD+3ZmV0UV85eV8uWhffjzhSNYuX4bhx/QlY5ti3B3Nm4vZ7+u7ZvclsWLF+/Lr6JeSjgiee61D7dS3KsTW3fuYfwfnq0pb1tUwJ64L760Pf8SAOfe9lJzhZiWWV8/kuseepNxQ/qwcv0XzJkykoN7dqSowDjmV09yzoh+XDluEF07tKHAjE7tCmlfVJhwD2R3RRVm0K6oMK1jNmZcsXW//Wqtsq+N6AdAp3ZFDNm/C0P278K5I/un9V6ADm2DOK85Y0hC+ayvH1mzPPKQvZcTzWyfkk3UlHBEWoiqmCfccK628YvdjJ71dKPra1KyaaKj+ndj/vSTaFsU3Iie+f9WUlhQwH+eNaxR9Vx0/MEpy+v6wk5WfYNeskMJRyTHvPHR56zZuINr5i3Pdig1zh3Zn/NHHcSy115n9MgRDOjdiZ17qnhz/TbOGLYfRY3s0fTLycMjilRymRKOSAbsqYyxaUc5L6/ZzKyFq9lcticjx71y3CAuHzOQuUs/ZPopgygoMJau20Kfzu0o7t34OU92flDIqLBHWC/goJ4dmzliyWdKOCJpisWcdZvLmPnwKi4/ZSCXLCrj/M+W86vJwxn6i0WRH3/o/l14+5PtAPTo2IatOyu4//IT6Ni2iCP7d6v3vVeNG1yzHN+FWCSTlHBEkrg7b234ggO7dWDEr59Muc/z730GwAPLSnlgWWmzHfvi4w/mF5OG6V6D5CUlHGm1imdk5oG+AoNff204Ywb34cDu7Skwq/PpcZF8poQjrYq7M+DahU16700XHMPEIw+g0IyB1y1kcPcCvjP2cIYd2I1jD+6eMCyJiNSmhCN5pXr8qY+27mTs7xc3qY6zjz6Q04ftxyfbdvPdMQNSJpLVv5rAv194jvEnFu9bwCKtiBKO5IUlazfzzTkvN/p9D155Egf16MCTqz/l4uMPSft9HdoWpnwmRkTqpoQjLVIs5qz/PBiLq7F+MWkYl508IKGsMclGRJpGCUdaBHfnuodWMveVD9N+z7zpJ7J/1/Z6VkQkRyjhSM6qqIpx6PWPpb3/mlkTdZlLJIcp4UhOGv2bp9i4vbzefZb9/DR6d26XoYhEZF8p4UhOaejZmBdnnMoBXdvrORaRFkgJR3LCxu27Gf2b2iMez/n2SHp1bkuPjm0Z2KdzFiITkebSqhKOmQ0Erge6ufu52Y5HAqnOau797vGcNLh3FqIRkahEmnDM7IfANMCA2939T02s505gErDR3YcnbZsA3AQUAn9z99/WVY+7rwUuM7P5TYlDmk9dT/wvuPrkBgeiFJGWKbKEY2bDCZLNaGAPsMjMHnH3krh9+gK73H17XNng+H1CdwE3A3cnHaMQuAU4HSgFlprZwwTJZ3ZSHVPdfWNztE2a5s9Pv5dynvlqS64bn9OzFYrIvonyDOdwYIm77wQws2eBc4Ab4/YZC0w3s4nuXm5m08J9zoyvyN2fM7PiFMcYDZSEZy6Y2X3AZHefTXBG1GhmdhZw1uDBgxvcVxq2bWcFT63+tN7JxFI9iCki+SfKhLMS+I2Z9QJ2AROBZfE7uPs8MxsA3G9m84CpBGcr6eoHfBS3XgocX9fOYSy/AUaY2bVhYkrg7guABaNGjZrWiDgkhd0VVRz9qyfq3SfdqYFFpOWLLOG4+2oz+x3wBFAGvAFUpdjvxvDM5FZgkLvviDCmzcD0qOoX2LyjnJE3PJVymxmU/EYPZ4q0VpF2GnD3O4A7AMxsFsEZSAIzGwMMBx4CZgJXN+IQ64GD4tb7h2WSBZf+/RWeeWdTrfJ/XnUSxx7cIwsRiUguKYiy8rBTAGZ2MMG9mXuTto8A5gCTgUuBXmZ2QyMOsRQ41MwGmFlb4ALg4eaIXdK3pWwPlywqS5lsnvjxKUo2IgJE/xzOg+F9kwrge+7+edL2jsD57r4GwMymAJckV2Jmc4FxQG8zKwVmuvsd7l5pZlcDjxP0TLvT3VdF1hpJUBVzPk4xYvPFxx/MtDED6dOlHZ3atapHvUSkHlFfUhvTwPYXk9YrgNtT7HdhPXUsBJo2haM0yQvvfca37liSctvaWRM17IyIpKR/P6VR6hrr7NDuBTw548yU20REQAlHGqGuZPPw1V9iS8kbGY5GRFoaJRxp0KyFq5nz3Npa5at++ZWaezSLk8eGEBFJooQjKdU3TcD0sYN4ZMXH6hAgIo2ibwypsWtPFQuWf8xPH1xR5z7VIwPMOHNopsISkTyhhCMNTuU8fewgfnLGYRQVRvrYlojkOSWcVu6ZdzZy6d+Xptz22A/HcEC39nTv2DbDUYlIPlLCaYX+XfIZF/0t9XM01V6+djz7d9NUASLSfJRwWplYzOtMNg9eeSL7dW1P28IC+mpeGhFpZko4rURD92lmn3MkIw/pmcGIRKS1UcLJY0vXbeG8215Kue3sow/kki8V84O5r3PjN47ipMG9MxydiLQ2Sjh5aNeeKg7/z0V1bv/uyQP4+aRhALzws1MzFZaItHJKOHnkk227OWH20/Xuoxk2RSRblHDywE1Pvcf/PPVuym1rZk1k3eYynnzrU84b2T/DkYmI7KWE00Jt2l7OObe+yEdbdqXcvuznp9G7czsABvXpzKCxnTMZnohILUo4LVDJxh2c9sdn69yuOWlEJBcp4bQw73yyna/86bla5Q9ccSJvfbyNKScWK9mISE5Swmkh5r9ayk/mLa9V/v7siZgFCWb0AD1HIyK5Swknx8VizsDrUs+grR5nItKSaPjfHLb8o8+VbEQkb+gMJ0edd9u/Wbpua81653ZFrPzlV7IYkYjIvlHCyUG79lQlJJt7v3u8hp4RkRZPCSfHVFTFEoaleeeGCbQrKsxiRCIizUP3cHJM/IjOT/z4FCUbEckbSjg5ZP6rpQnrh+3XJUuRiIg0PyWcHBGLecJzNiv+64wsRiMi0vyUcHJEfPfn135xOl3bt8liNCIiza9VJRwzG2hmd5jZ/GzHEq94xqM1y5ecVEzPTm2zGI2ISDQiTThm9mMzW2VmK81srpm1b2I9d5rZRjNbmWLbBDN7x8xKzGxGffW4+1p3v6wpMURlS9mehPX/OvuILEUiIhKtyBKOmfUDfgCMcvfhQCFwQdI+fc2sS1LZ4BTV3QVMSHGMQuAW4ExgGHChmQ0zsyPN7JGkV99maVgzO/bXT9Ysv/3rWk0UEckbUV9SKwI6mFkR0BH4OGn7WOBfZtYOwMymAX9JrsTdnwO2pKh/NFASnrnsAe4DJrv7m+4+Kem1MZ2AzewsM5uzbdu2tBvZVGXllTXLy2eeQfs26gItIvkrsoTj7uuB/wY+BDYA29z9iaR95gGPA/eb2cXAVOC8RhymH/BR3HppWJaSmfUys9uAEWZ2bR1xL3D3y7t169aIMJrmiJmP1yx366BOAiKS36K8pNYDmAwMAA4EOpnZt5L3c/cbgd3ArcDZ7r4jqpjcfbO7T3f3Qe4+O6rjpGP1hi9qlq+feHgWIxERyYwoL6mdBrzv7pvcvQL4J3BS8k5mNgYYDjwEzGzkMdYDB8Wt9w/Lct6ZNz1fszztlIFZjEREJDOiTDgfAieYWUcLZggbD6yO38HMRgBzCM6ELgV6mdkNjTjGUuBQMxtgZm0JOiU83CzRR6i8sqpmedbXj8xiJCIimRPlPZwlwHzgNeDN8FhzknbrCJzv7mvcPQZMAT5IrsvM5gIvAUPMrNTMLguPUQlcTXAfaDXwgLuviqhJzWbIz/cOznnR8QdnMRIRkcyJdLRod59JPZfJ3P3FpPUK4PYU+11YTx0LgdSzlOW4K8cNynYIIiIZ06pGGsgF7l6z/LMJQ7MYiYhIZinhZNiV/3gt2yGIiGSFEk6GLVr1CQDHFffIciQiIpmlhJNB8ZfT5k2v1UNcRCSvKeFk0EW3L8l2CCIiWaOEk0Evrd2c7RBERLJGCSdD9lTGapbfnz0xi5GIiGSHEk6G3PDoWwD079GBYOAFEZHWRQknQ+5+KRhA4c5LjstyJCIi2dFgwjGzL5lZp3D5W2b2RzM7JPrQ8tNh+3VpeCcRkTyUzhnOrcBOMzsauAZYA9wdaVR5ZteeqoZ3EhHJc+kknEoPHiCZDNzs7rcA+je9EVZ+HP3soSIiuS6dwTu3h7NjfhsYY2YFgKanbISr7gmGs7ns5AFZjkREJHvSOcP5JlAOTHX3TwgmOft9pFHlmU3bywGNDi0irVuDCSdMMg8C7cKizwhm55RG6t25XcM7iYjkqXR6qU0jmEjtr2FRP+BfUQYlIiL5J51Lat8DvgR8AeDu7wF9owwqn8Ri3vBOIiKtQDoJp9zd91SvmFkRoG/RNK3/fBcAs75+ZJYjERHJrnQSzrNmdh3QwcxOB+YBC6INK3+s2bQDgMF9O2c5EhGR7Eon4cwANgFvAlcAC4GfRxlUPinZqIQjIgJpPIfj7jHg9vAljTT7sbcB6NmpbZYjERHJrjoTjpk94O7nm9mbpLhn4+5HRRpZnqhSpwEREaD+M5wfhj8nZSKQfBQ/pbSISGtXZ8Jx9w3hYgGwwd13A5hZB2C/DMTW4pWHk64d1b9bliMREcm+dDoNzANicetVYZk0YN3mMgAKCzThmohIOgmnKP45nHBZd8DT8N+PvwtAeUWsgT1FRPJfOglnk5mdXb1iZpMJxlOTBjy1+lMAxg3pk+VIRESyL53pCaYD95jZzYABHwFTIo0qz0w+pl+2QxARybp0Rote4+4nAMOAw939JHcviT60lu+i4w8GYMj+mq9ORCSdMxzM7KvAEUB7s+AGuLv/KsK48kJ5RYx+3TtkOwwRkZyQzvQEtxFMwvZ9gktq5wGHRBxXXigrr6RTu8JshyEikhPS6TRwkrtPAba6+y+BE4HDog0rP2z4YjdFBen8ikVE8l86l9R2hz93mtmBwGbggOhCio6ZDQSuB7q5+7lRH2/5R59HfQgRkRYjnX+/F5hZd+D3wGvAOuDeht5kZkPM7I241xdm9qOmBGlmd5rZRjNbmWLbBDN7x8xKzGxGffW4+1p3v6wpMTSWJl4TEUlU7xmOmRUAT7v758CDZvYI0N7dtzVUsbu/AxwT1lMIrAceSqq/L7DL3bfHlQ1O0QvuLuBm4O6k9xcCtwCnA6XAUjN7GCgEZifVMdXdNzYUd3PZXl4JwBVjB2bqkCIiOa3eM5xwaoJb4tbL00k2KYwH1rj7B0nlY4F/mVk7ADObBvwlRRzPAVtS1DsaKAnPXPYA9wGT3f1Nd5+U9Eor2ZjZWWY2Z9u2pjRzry92VQAwqI/mwRERgfQuqT1tZt+w6v7QTXMBMDe50N3nAY8D95vZxcBUgl5w6epH8CBqtdKwLCUz6xX2uhthZtem2sfdF7j75d267duAm9vChNO9Q5t9qkdEJF+k02ngCuA/gEoz203QNdrdvWs6BzCztsDZQF1f8Dea2X3ArcAgd9+RVuRN4O6bCUZOiNxbG74AQLdyREQC6Yw00MXdC9y9rbt3DdfTSjahM4HX3P3TVBvNbAwwnOD+zsxG1AvBfaGD4tb7h2U5o2/XdtkOQUQkJzR4hmNmp6QqD++rpONCUlxOC+seAcwhmOTtfYIx225w95+nWfdS4FAzG0CQaC4ALkrzvZHq1Db41XZul9ZgDiIieS+db8P/E7fcnuBG/avAqQ290cw6EfQgu6KOXToC57v7mnD/KcAlKeqZC4wDeptZKTDT3e9w90ozu5rgPlAhcKe7r0qjTZGrjAVTEmguHBGRQIMJx93Pil83s4OAP6VTubuXAb3q2f5i0noFcHuK/S6sp46FwMJ04smkiqrg5k0bjTQgIgKk10stWSlweHMHkm+qwjOcokKd4YiIQHr3cP4CVPe1KiB4mPO1KIPKB9VnOEW6pCYiAqR3D2dZ3HIlMDf5UpjUVhX2hy4q1CU1ERFIL+HMB3a7exUEw8mYWUd33xltaC1bRZU6DYiIxEtrpAEgfhaxDsBT0YSTPyrDM5w2uocjIgKkl3Daxz/9Hy53jC6k/FBzSU291EREgPQSTpmZHVu9YmYjgV3RhZQfqi+pqdOAiEggnXs4PwLmmdnHBOOo7U8w5bTUoyrmFBgUKOGIiADpPfi51MyGAkPConfCBzSlHhVVrstpIiJxGvxGNLPvAZ3cfaW7rwQ6m9lV0YfWslVWxfTQp4hInHT+BZ8WzvgJgLtvBaZFF1J+qIy57t+IiMRJJ+EUxk++Fk7r3Da6kPJDVcz1DI6ISJx0Og0sIpiR86/h+hXAY9GFlB+qXAlHRCReOgnnZ8Dl7J0pcwVBTzWpx71LPsx2CCIiOSWdGT9jwBJgHcFcOKcCq6MNS0RE8k2dZzhmdhjBbJ0XAp8B9wO4+5czE5qIiOST+i6pvQ08D0xy9xIAM/txRqISEZG8U98ltXOADcAzZna7mY0nGGlARESk0epMOO7+L3e/ABgKPEMwxE1fM7vVzM7IVIAiIpIf0uk0UObu97r7WUB/4HWCnmtSj+MH9GT0gJ7ZDkNEJGc0arAvd9/q7nPcfXxUAeULB/QYjojIXhpdMiLujumWl4hIDSWciLiDBosWEdlLX4kRiekMR0QkgRJORBww5RsRkRpKOBFxB1PGERGpoYQTkaDTgIiIVFPCiYi6RYuIJFLCiUjMXZfURETiKOFExF1nOCIi8ZRwIhJz0FinIiJ7KeFExN3VLVpEJI4SToR0SU1EZC8lnIhopAERkURKOBHRWGoiIon0lRgRneGIiCRSwomIOqmJiCRSwonI2k1lPLpiQ7bDEBHJGa0q4ZjZQDO7w8zmZ+J4h/TqmInDiIi0CJEmHDPrbmbzzextM1ttZic2sZ47zWyjma1MsW2Cmb1jZiVmNqO+etx9rbtf1pQYGqtf9w6MOqRnJg4lItIiFEVc/03AInc/18zaAgn/8ptZX2CXu2+PKxvs7iVJ9dwF3AzcnfT+QuAW4HSgFFhqZg8DhcDspDqmuvvGfW9Setxdz+GIiMSJLOGYWTfgFOASAHffA+xJ2m0sMN3MJrp7uZlNA84Bzozfyd2fM7PiFIcZDZS4+9rwmPcBk919NjCpiXGfBZw1ePDgpry9Rsw1AZuISLwoL6kNADYBfzez183sb2bWKX4Hd58HPA7cb2YXA1OB8xpxjH7AR3HrpWFZSmbWy8xuA0aY2bWp9nH3Be5+ebdu3RoRRop6ULdoEZF4USacIuBY4FZ3HwGUAbXusbj7jcBu4FbgbHffEVVA7r7Z3ae7+6DwLCgyevBTRCRRlF+JpUCpuy8J1+cTJKAEZjYGGA48BMxs5DHWAwfFrfcPy7JOo0WLiCSKLOG4+yfAR2Y2JCwaD7wVv4+ZjQDmAJOBS4FeZnZDIw6zFDjUzAaEnRIuAB7e5+CbhUaLFhGJF/VFn+8D95jZCuAYYFbS9o7A+e6+xt1jwBTgg+RKzGwu8BIwxMxKzewyAHevBK4muA+0GnjA3VdF1ppG0ARsIiKJIu0W7e5vAKPq2f5i0noFcHuK/S6sp46FwMJ9CDMSGktNRCSRbmtHxFG3aBGReEo4EXFXlwERkXhKOBEJpphWyhERqaaEExHXSAMiIgmUcCLioE4DIiJxlHAiosE7RUQSKeFERIN3iogkUsKJiKNOAyIi8ZRwIqJOAyIiiZRwIhI8h6OMIyJSTQknIq7BO0VEEijhRESDd4qIJFLCiYgG7xQRSaSEExEN3ikikkgJJyJBLzVlHBGRako4EXB3QKNFi4jEU8KJgIc/dYIjIrKXEk6ECpRxRERqKOFEIBae4ijdiIjspYQTIZ3giIjspYQTgb33cJRxRESqKeFEwKsvqSnfiIjUUMKJQM0Zju7iiIjUUMKJgs5wRERqUcKJQPUZjgbvFBHZSwknArqkJiJSmxJOBNRpQESkNiWcCKhbtIhIbUo4EXCNNCAiUosSToR0giMispcSTgT2dhoQEZFqSjgRqL6kVqh+0SIiNZRwIhALz3HUaUBEZC8lnAhUn+FoPhwRkb2UcCIQq0k42Y1DRCSXKOFEoGZoG2UcEZEaSjgR0CU1EZHalHAioME7RURqU8KJQExnOCIitSjhRKA64VRUxbIbiIhIDlHCicCOiiDjrNtcluVIRERyR1G2A8g3V/7jVZaUlANw7ME9shyNiEjuUMJpZgf37MjWHgUMHXAQxw3ome1wRERyhhJOM7t24uEsXvwp48Ydke1QRERyiu7hiIhIRijhiIhIRijhiIhIRrSqhGNmA83sDjObn+1YRERam0gTjpmtM7M3zewNM1u2D/XcaWYbzWxlim0TzOwdMysxsxn11ePua939sqbGISIiTZeJXmpfdvfPUm0ws77ALnffHlc22N1Lkna9C7gZuDvp/YXALcDpQCmw1MweBgqB2Ul1THX3jfvSEBERabpsd4seC0w3s4nuXm5m04BzgDPjd3L358ysOMX7RwMl7r4WwMzuAya7+2xgUqSRi4hIo0R9D8eBJ8zsVTO7vNZG93nA48D9ZnYxMBU4rxH19wM+ilsvDctSMrNeZnYbMMLMrq1jn7PMbM62bdsaEYaIiDQk6jOck919fXjp7Ekze9vdn4vfwd1vDM9MbgUGufuOqIJx983A9Ab2WQAsMLOvm9kHTTxUbyDlZcQ8pja3Dq2tza2tvbDvbT6krg2RJhx3Xx/+3GhmDxFcAktIOGY2BhgOPATMBK5uxCHWAwfFrfcPy/aZu/dp6nvNbJm7j2qOOFoKtbl1aG1tbm3thWjbHNklNTPrZGZdqpeBM4CVSfuMAOYAk4FLgV5mdkMjDrMUONTMBphZW+AC4OHmiF9ERJpXlPdw9gNeMLPlwCvAo+6+KGmfjsD57r7G3WPAFKDWZSwzmwu8BAwxs1IzuwzA3SsJzogeB1YDD7j7qshaJCIiTRbZJbWw59jRDezzYtJ6BXB7iv0urKeOhcDCJoYZlTnZDiAL1ObWobW1ubW1FyJss7l7VHWLiIjUaFVD24iISPYo4YiISEYo4TSjxozrlotSjVlnZj3N7Ekzey/82SMsNzP7c9jWFWZ2bNx7vhPu/56ZfSeufGQ4tl5J+F7LbAtrM7ODzOwZM3vLzFaZ2Q/D8rxtt5m1N7NXzGx52OZfhuUDzGxJGOf9Yc9PzKxduF4Sbi+Oq+vasPwdM/tKXHnO/S2YWaGZvW5mj4Tr+d7eWmNZZv1z7e56NcOLYPy2NcBAoC2wHBiW7bga2YZTgGOBlXFlNwIzwuUZwO/C5YnAY4ABJwBLwvKewNrwZ49wuUe47ZVwXwvfe2YOtPkA4NhwuQvwLjAsn9sdxtE5XG4DLAnjewC4ICy/DbgyXL4KuC1cvgC4P1weFn7O2wEDws9/Ya7+LQD/AdwLPBKu53t71wG9k8qy+rnWGU7zqRnXzd33APcRPF/UYngwCsSWpOLJwP+Gy/8LfC2u/G4PvAx0N7MDgK8AT7r7FnffCjwJTAi3dXX3lz34tN4dV1fWuPsGd38tXN5O0L2+H3nc7jD26hE92oQvB04FqqfuSG5z9e9iPjA+/G92MnCfu5e7+/tACcHfQc79LZhZf+CrwN/CdSOP21uPrH6ulXCaT6PGdWtB9nP3DeHyJwTPV0Hd7a2vvDRFec4IL52MIPiPP6/bHV5eegPYSPAlsgb43INn2yAxzpq2hdu3Ab1o/O8im/4E/BSIheu9yO/2QuqxLLP6uc72aNHSgri7m1le9qM3s87Ag8CP3P2L+MvR+dhud68CjjGz7gTDSg3NckiRMbNJwEZ3f9XMxmU7ngyqNZZl/MZsfK51htN8IhvXLcs+DU+fCX9WzylUV3vrK++fojzrzKwNQbK5x93/GRbnfbsB3P1z4BngRILLKNX/hMbHWdO2cHs3YDON/11ky5eAs81sHcHlrlOBm8jf9gKJY1kS/FMxmmx/rrN9YytfXgRni2sJbiZW3zg8IttxNaEdxSR2Gvg9iTcZbwyXv0riTcZXwvKewPsENxh7hMs9w23JNxkn5iiwHCoAAAL0SURBVEB7jeD685+SyvO23UAfoHu43AF4nmD+qHkk3kS/Klz+Hok30R8Il48g8Sb6WoIb6Dn7twCMY2+ngbxtL9AJ6BK3/G9gQrY/11n/AOTTi6Cnx7sE18Ovz3Y8TYh/LrABqCC4JnsZwbXrp4H3gKfiPmxGMNvqGuBNYFRcPVMJbqiWAJfGlY8iGMB1DcEMrpYDbT6Z4Fr3CuCN8DUxn9sNHAW8HrZ5JfCfYfnA8EukJPwybheWtw/XS8LtA+Pquj5s1zvE9VLK1b8FEhNO3rY3bNvy8LWqOqZsf641tI2IiGSE7uGIiEhGKOGIiEhGKOGIiEhGKOGIiEhGKOGIiEhGKOGIRMzMdoQ/i83somau+7qk9X83Z/0izUkJRyRzioFGJZy4J+HrkpBw3P2kRsYkkjFKOCKZ81tgTDg/yY/DATR/b2ZLwzlIrgAws3Fm9ryZPQy8FZb9KxyEcVX1QIxm9lugQ1jfPWFZ9dmUhXWvDOcs+WZc3YvNbL6ZvW1m96Q1j4lIM9DgnSKZMwP4ibtPAggTxzZ3P87M2gEvmtkT4b7HAsM9GAYfYKq7bzGzDsBSM3vQ3WeY2dXufkyKY50DHAMcDfQO3/NcuG0EwTAtHwMvEow19kLzN1ckkc5wRLLnDGBKOE3AEoJhRw4Nt70Sl2wAfmBmy4GXCQZTPJT6nQzMdfcqd/8UeBY4Lq7uUnePEQzlU9wsrRFpgM5wRLLHgO+7++MJhcEQ+mVJ66cBJ7r7TjNbTDDeV1OVxy1Xoe8ByRCd4YhkznaCaayrPQ5cGU6PgJkdZmadUryvG7A1TDZDCUborVZR/f4kzwPfDO8T9SGYPvyVZmmFSBPpPxuRzFkBVIWXxu4imJOlGHgtvHG/idTT9C4CppvZaoJRil+O2zYHWGFmr7n7xXHlDxHMcbOcYDTsn7r7J2HCEskKjRYtIiIZoUtqIiKSEUo4IiKSEUo4IiKSEUo4IiKSEUo4IiKSEUo4IiKSEUo4IiKSEf8fTqbpM3uvjGgAAAAASUVORK5CYII=\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stdout","output_type":"stream","text":["\n","200 hidden units:\n","\tNormalized Loss: 1.0286826288032394\n","\tNormalized Loss: 0.1516436824068353\n","\tNormalized Loss: 0.1039415003242974\n","\tNormalized Loss: 0.08651406690365601\n","\tNormalized Loss: 0.07636802126386459\n","\tNormalized Loss: 0.07059589957438792\n","Test accuracy with 200 hidden layers = 0.9708\n"]},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stdout","output_type":"stream","text":["\n"]}],"source":["for k in [5, 40, 200]:\n"," # My neural network\n"," d=X_train.shape[1] # Input dimension. The third dimension is for bias\n"," U=np.random.randn(k,d)*0.01 # Input layer\n"," w=np.random.randn(k)*0.01 # Output layer\n","\n"," eta=0.001 # learning rate\n","\n"," accuracies, loss_history = [], []\n","\n"," print(f'{k} hidden units:')\n","\n"," ITNUM=50001\n"," for it in range(ITNUM):\n"," grad_w=0\n"," grad_U=0\n"," for i in np.argsort(np.random.randn(N))[:10]:\n"," # print(X_train.shape)\n"," gw,gU=get_grad(w,U,y_train[i],X_train[i])\n"," grad_w+=gw\n"," grad_U+=gU\n","\n"," w-=eta*grad_w/10\n"," U-=eta*grad_U/10\n","\n"," if it%int(ITNUM/5)==0:\n"," print('\\tNormalized Loss:',loss(w,U, y_train,X_train.T)/np.linalg.norm(y_train)**2)\n","\n"," # loss_history.append(loss(w,U, y_train[i],X_train[i].T)/np.linalg.norm(y_train[i])**2) \n"," Yh=predict(w,U,X_test.T)>0.5+0.\n"," Yh = Yh.astype(int)\n","\n"," acc = np.mean(Yh == y_test)\n"," accuracies.append(acc)\n","\n"," yhat = predict(w,U,X_test.T)>0.5+0.\n"," yhat = yhat.astype(int)\n","\n"," acc = np.mean(yhat == y_test)\n"," print(f\"Test accuracy with {k} hidden layers = {acc}\")\n","\n"," # plt.figure()\n"," # plt.semilogy(loss_history) \n"," # plt.grid()\n"," # plt.xlabel('Iteration')\n"," # plt.ylabel('Training loss') \n"," # plt.show()\n","\n"," plt.figure()\n"," plt.semilogy(accuracies) \n"," plt.grid()\n"," plt.xlabel('Iteration')\n"," plt.ylabel('Accuracies') \n"," plt.show()\n","\n"," print()"]},{"cell_type":"markdown","metadata":{"id":"u3GnJAzjGIcj"},"source":["### As we can see, the neural network with quadratic loss improves on the linear classifier by a a very good margin. It seems that increasing the number of hidden units has a positive effect on accuracy, however the tradeoff is that it takes longer to train the model at times. There may be ways to deal with this but in this case, k=200 was marginally better than k = 40 and took much longer, so this is most likely another hyper-paramater that should be optimized."]},{"cell_type":"markdown","metadata":{"id":"7q8hFG7F8olm"},"source":["## 4. Neural Network Classifier w/ Logistic Loss"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"9x36r-kBdhVp"},"outputs":[],"source":["def sigmoid(x):\n"," return 1 / (1 + np.exp(-x))\n","\n","def relu(x):\n"," return np.maximum(x,0)\n","\n","def predict(w,U,x):\n"," return sigmoid(w.dot(relu(U.dot(x))))\n","\n","def get_grad(w,U,y,x):\n"," h=sigmoid(U.dot(x))\n"," sigmap=sigmoid(U.dot(x)) * (1-sigmoid(U.dot(x)))\n"," yh=predict(w,U,x)\n"," r=yh-y\n"," grad_w=r*h\n"," grad_U=r*np.outer(w*sigmap,x)\n"," return grad_w,grad_U\n","\n","def loss(w,U,Y,X):\n"," return np.linalg.norm(Y-predict(w,U,X))**2"]},{"cell_type":"code","execution_count":null,"metadata":{"colab":{"background_save":true,"base_uri":"https://localhost:8080/","height":945},"id":"9CXczm_f_a6g","outputId":"3c3418a8-bfa4-462f-d1d5-82c96c2fd0a1"},"outputs":[{"name":"stdout","output_type":"stream","text":["5 hidden units:\n","\tNormalized Loss: 0.5099981880369611\n","\tNormalized Loss: 0.40739703768151747\n","\tNormalized Loss: 0.2811552249899347\n","\tNormalized Loss: 0.24763002827492905\n","\tNormalized Loss: 0.23199062881203122\n","\tNormalized Loss: 0.23222702589676608\n","Test accuracy with 5 hidden layers = 0.8518\n"]},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stdout","output_type":"stream","text":["\n","40 hidden units:\n","\tNormalized Loss: 0.5102299874938626\n","\tNormalized Loss: 0.3280817199279439\n","\tNormalized Loss: 0.256908137884206\n","\tNormalized Loss: 0.23934570171735445\n","\tNormalized Loss: 0.22542369764060036\n","\tNormalized Loss: 0.2109676771017391\n","Test accuracy with 40 hidden layers = 0.8693\n"]},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stdout","output_type":"stream","text":["\n","200 hidden units:\n","\tNormalized Loss: 0.5088571598651025\n","\tNormalized Loss: 0.297538153732224\n","\tNormalized Loss: 0.25279955458881326\n","\tNormalized Loss: 0.24096850826265565\n","\tNormalized Loss: 0.23254231984421062\n","\tNormalized Loss: 0.22674772306204224\n","Test accuracy with 200 hidden layers = 0.8592\n"]},{"data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{},"output_type":"display_data"},{"name":"stdout","output_type":"stream","text":["\n"]}],"source":["for k in [5, 40, 200]:\n"," # My neural network\n"," d=X_train.shape[1] # Input dimension. The third dimension is for bias\n"," U=np.random.randn(k,d)*0.01 # Input layer\n"," w=np.random.randn(k)*0.01 # Output layer\n","\n"," eta=0.001 # learning rate\n","\n"," accuracies, loss_history = [], []\n","\n"," print(f'{k} hidden units:')\n","\n"," ITNUM=50001\n"," for it in range(ITNUM):\n"," grad_w=0\n"," grad_U=0\n"," for i in np.argsort(np.random.randn(N))[:10]:\n"," # print(X_train.shape)\n"," gw,gU=get_grad(w,U,y_train[i],X_train[i])\n"," grad_w+=gw\n"," grad_U+=gU\n","\n"," w-=eta*grad_w/10\n"," U-=eta*grad_U/10\n","\n"," if it%int(ITNUM/5)==0:\n"," print('\\tNormalized Loss:',loss(w,U, y_train,X_train.T)/np.linalg.norm(y_train)**2)\n","\n"," # loss_history.append(loss(w,U, y_train[i],X_train[i].T)/np.linalg.norm(y_train[i])**2) \n"," Yh=predict(w,U,X_test.T)>0.5+0.\n"," Yh = Yh.astype(int)\n","\n"," acc = np.mean(Yh == y_test)\n"," accuracies.append(acc)\n","\n"," yhat = predict(w,U,X_test.T)>0.5+0.\n"," yhat = yhat.astype(int)\n","\n"," acc = np.mean(yhat == y_test)\n"," print(f\"Test accuracy with {k} hidden layers = {acc}\")\n","\n"," # plt.figure()\n"," # plt.semilogy(loss_history) \n"," # plt.grid()\n"," # plt.xlabel('Iteration')\n"," # plt.ylabel('Training loss') \n"," # plt.show()\n","\n"," plt.figure()\n"," plt.semilogy(accuracies) \n"," plt.grid()\n"," plt.xlabel('Iteration')\n"," plt.ylabel('Accuracies') \n"," plt.show()\n","\n"," print()"]},{"cell_type":"markdown","source":["## 5. Comments"],"metadata":{"id":"wEtEexCAyxpL"}},{"cell_type":"markdown","source":["The neural networks in both cases seem to outperform the linear model. The linear model had an average accuracy of around 80% (variable, but I ran it a few times and it never exceeded 83% accuracy). Both neural networks outperformed the linear model, as they both had accuracies of 85% or higher. \n","\n","The neural network with quadratic loss outperformed the network with logistic loss by a decent margin. The NN with quadratic loss had an average accuracy of over 95%, but the NN with logistic loss had a lower average accuracy of around 85%. The NN with quadratic loss outperforms, so it may be better suited to this binary classification task with this data. \n","\n","Increasing the number of hidden units seemed to have a positive effect on the accuracy of the NN with quadratic loss. Howevever, this did not seem to be the case with the NN with logistic loss. In both cases though, the accuracy of the model increased over the iterations, so it can be said that both models are suitable for the task, altough the NN with quadratic loss may be better suited. "],"metadata":{"id":"dO7XO-_A1tQA"}}],"metadata":{"colab":{"collapsed_sections":[],"name":"CS228_HW2","provenance":[],"authorship_tag":"ABX9TyNGIMeP5/gA2acdNhxlQaPv"},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python"}},"nbformat":4,"nbformat_minor":0}