FYS-STK4155/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb

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    "# Decision trees, overarching aims\n",
    "\n",
    "\n",
    "We start here with the most basic algorithm, the so-called decision\n",
    "tree. With this basic algorithm we can in turn build more complex\n",
    "networks, spanning from homogeneous and heterogenous forests (bagging,\n",
    "random forests and more) to one of the most popular supervised\n",
    "algorithms nowadays, the extreme gradient boosting, or just\n",
    "XGBoost. But let us start with the simplest possible ingredient.\n",
    "\n",
    "Decision trees are supervised learning algorithms used for both,\n",
    "classification and regression tasks.\n",
    "\n",
    "\n",
    "The main idea of decision trees\n",
    "is to find those descriptive features which contain the most\n",
    "**information** regarding the target feature and then split the dataset\n",
    "along the values of these features such that the target feature values\n",
    "for the resulting underlying datasets are as pure as possible.\n",
    "\n",
    "The descriptive features which reproduce best the target/output features are normally  said\n",
    "to be the most informative ones. The process of finding the **most\n",
    "informative** feature is done until we accomplish a stopping criteria\n",
    "where we then finally end up in so called **leaf nodes**. \n",
    "\n",
    "## Basics of a tree\n",
    "\n",
    "A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
    "and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
    "\n",
    "The leaf nodes\n",
    "contain the predictions we will make for new query instances presented\n",
    "to our trained model. This is possible since the model has \n",
    "learned the underlying structure of the training data and hence can,\n",
    "given some assumptions, make predictions about the target feature value\n",
    "(class) of unseen query instances.\n",
    "\n",
    "\n",
    "## General Features\n",
    "\n",
    "The overarching approach to decision trees is a top-down approach.\n",
    "\n",
    "* A leaf provides the classification of a given instance.\n",
    "\n",
    "* A node specifies a test of some attribute of the instance.\n",
    "\n",
    "* A branch corresponds to a possible values of an attribute.\n",
    "\n",
    "* An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute in the given example.\n",
    "\n",
    "This process is then repeated for the subtree rooted at the new\n",
    "node.\n",
    "\n",
    "\n",
    "\n",
    "In simplified terms, the process of training a decision tree and\n",
    "predicting the target features of query instances is as follows:\n",
    "\n",
    "1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
    "\n",
    "2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process\n",
    "\n",
    "3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the *predictions* we want to make for new query instances\n",
    "\n",
    "4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
    "\n",
    "Then we are essentially done!"
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      "2nd degree coefficients:\n",
      "zero power:  2.1974520015546233\n",
      "first power:  -0.07706200276162956\n",
      "second power:  -0.00041883582579717597\n"
     ]
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_1.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vvqhSDHPmzMH27dvx6aef4sMPP8SHH36IQ4cOoWvXrpg6dSratGmDlJQUREVFISIiQkxCpk+fji+++AJPPfUUXn31Vfj4+GDr1q3iz0RFVkZ+7rnnsH37dsyYMQOHDh1Cz549odFoEBMTg+3bt+OPP/5A586dsXjxYvz1118YNmwYmjZtisTERKxZswZNmjRBr169AACDBw+Gt7c3evbsCS8vL1y6dAlffPEFhg0bVur/Zw8PD8yfPx+LFi3CkCFD8NhjjyE2NhZr1qzBww8/bDSQmajWsNh8MqJ6TD/tV/8ll8sFb29vYdCgQcKqVavEaeBFxcXFCePHjxe8vb0Fa2troXHjxsLw4cOFH3/80ahecnKy8NJLLwmNGzcW5HK50KRJE2HChAniFOqi09nv3bsnvPjii0KrVq0EBwcHwcXFRejatauwfft2o/MWnc4uCIKQkJAgTJo0SWjUqJEgl8uFdu3aiefV01+vpOnyAISFCxdW+N6VNp3dwcGh1GO++uorITQ0VLCzsxOcnJyEdu3aCXPnzhXu3r1rVO/QoUNCeHi44OLiItja2gpBQUHCxIkThVOnTpUZk346+44dO0rc369fP8HZ2VlITU0VBEF3z1588UXBz89PsLa2Fry9vYWwsDDhq6++Mjru2rVrwrBhwwQ7OzvBw8NDmD17trBz504BgHD8+HGxXt++fUudap6XlycsW7ZMCA4OFmxsbASFQiGEhoYKixYtEtLS0gRBEIQ///xTePzxxwVfX19BLpcLvr6+wlNPPSVcvnxZPM+6deuEPn36CO7u7oKNjY0QFBQkzJkzRzyHIBSfzq73xRdfCK1atRKsra0FLy8vYebMmYJarTaqU9p7mDBhgtC0adMS3xtRTeCzuoiIapFPP/0Ur732Gm7fvo3GjRtbOhyieoeJDxGRhWRnZxsNys7JyUGnTp2g0Whw+fJlC0ZGVH9xjA8RkYWMGjUK/v7+6NixI9LS0rBlyxbExMSUOj2fiKqPiQ8RkYWEh4fjm2++wdatW6HRaNCmTRts27YNY8eOtXRoRPUWu7qIiIioweA6PkRERNRgMPEhIiKiBoNjfIrQarW4e/cunJycKrSAGBEREVmeIAi4f/8+fH19iz3XzxATnyLu3r0rPtiPiIiI6pZbt26hSZMmpe5n4lOEfmn2W7duwdnZ2cLREBERUUWkp6fDz8+v3EfpMPEpQt+95ezszMSHiIiojilvmAoHNxMREVGDwcSHiIiIGgwmPkRERNRgcIwPERHVOI1Gg/z8fEuHQXWYtbU1ZDJZtc/DxIeIiGqMIAhQqVRITU21dChUD7i6usLb27ta6+wx8SEiohqjT3o8PT1hb2/PhWGpSgRBQFZWFhITEwEAPj4+VT4XEx8iIqoRGo1GTHrc3d0tHQ7VcXZ2dgCAxMREeHp6Vrnbi4ObiYioRujH9Njb21s4Eqov9D9L1RkvxsSHiIhqFLu3yFRM8bPExIeIiIgaDCY+REREFdSvXz/MmjXL0mFQNTDxISIiqgGHDx+GRCLhVP5aholPHaBWqxEREQG1Wl2rz0lERFTbMfGp5dRqNYKDgzFo0CAEBwebJFGpiXMSEdU3mZmZGD9+PBwdHeHj44OPPvrIaP/mzZvRuXNnODk5wdvbG08//bS4zsz169fRv39/AIBCoYBEIsHEiRMBAPv27UOvXr3g6uoKd3d3DB8+HHFxcWZ9bw0ZE59aLjIyEkqlEgCgVCoRFRVVK89JRFTfzJkzB0eOHMGePXuwf/9+HD582OjzMj8/H0uWLMHZs2exe/duXL9+XUxu/Pz8sHPnTgBAbGwslEolVq1aBUCXUL3++us4deoU/vzzT0ilUowcORJardbs77Eh4gKGtVxoaCh8fHygVCrh6+uLkJCQWnlOIqKaplarERkZidDQUCgUihq9VkZGBtavX48tW7YgLCwMAPDdd9+hSZMmYp3JkyeLrwMDA/HZZ5/h4YcfRkZGBhwdHeHm5gYA8PT0hKurq1h39OjRRtfasGEDPDw8cPHiRbRt27YG3xUBbPGpte5H3Ydqkwq5v+Ti73f+RsR7ETh/+rxJ/rErFApER0cjIiICFy5cqPEPECKi6jJ3F31cXBzy8vLQtWtXsczNzQ0tW7YUtyMjI/Hoo4/C398fTk5O6Nu3LwDg5s2bZZ77ypUreOqppxAYGAhnZ2c0a9asQseRabDFpxZSH1Lj7ICzRmUyyHDv7j24rXYzyTUUCoX4VwwRUW1XUhe9JT/DMjMzER4ejvDwcGzduhUeHh64efMmwsPDkZeXV+axjz76KJo2bYqvv/4avr6+0Gq1aNu2bbnHkWnUyxaf1atXo1mzZrC1tUXXrl1x8uRJS4dUKenH00suP1ZyORFRfafvogdgli76oKAgWFtb48SJE2KZWq3G5cuXAQAxMTFITk7Ghx9+iN69e6NVq1biwGY9uVwOQPfMMr3k5GTExsbi7bffRlhYGFq3bs0JJmZW7xKfH374Aa+//joWLlyIqKgodOjQAeHh4cV+IGszQSOIr31n+kJio1uiW5vHgW9E1DCZu4ve0dERU6ZMwZw5c3Dw4EFcuHABEydOhFSq+7Xp7+8PuVyOzz//HNeuXcPPP/+MJUuWGJ2jadOmkEgk+PXXX5GUlISMjAwoFAq4u7vjq6++wtWrV3Hw4EG8/vrrNfpeyFi9S3w+/vhjTJ06FZMmTUKbNm3w5Zdfwt7eHhs2bLB0aBVnkN/canILUnvd/6bM1EzEx8cjIiKi2He1Wl1sbR79tmHdXbt2YdeuXaXWMTxPSdcwl7LWGSopZiKq//Rd9OYal7hixQr07t0bjz76KAYOHIhevXohNDQUAODh4YGNGzdix44daNOmDT788EOsXLnS6PjGjRtj0aJFmDdvHry8vPDSSy9BKpVi27ZtiIyMRNu2bfHaa69hxYoVZnk/pCMRBEEov1rdkJeXB3t7e/z4448YMWKEWD5hwgSkpqZiz549xY7Jzc1Fbm6uuJ2eng4/Pz+kpaXB2dnZHGEXc23BNdxcohvkNqfdHMy7PA/uue5Is0rD6uarIUCABBKj7zY2NpBAgpzcHNja2KJfv344fPgwcnJzxDqGSqtjeJ6i14jzjcOzbz6LZ0OfxUPuD9XY+9cPYlQqlfDx8UF0dLT4QWe4TyqVQqvVFqtDRLVDTk4O4uPjERAQAFtbW0uHQ/VAWT9T6enpcHFxKff3d70a3Hzv3j1oNBp4eXkZlXt5eSEmJqbEY5YuXYpFixaZI7wKu5J0BTawAQBoO2qRfzMfyAVcClzwVsxbFTvJWSAUodWvYyD3ai6eDH0S30Z/i+uvXodMKqvwsZVR1iBGw336NS9qw0BHIiKqG+pdV1dlzZ8/H2lpaeLXrVu3LB0SkjKSxNdaqRYxjUtO2szNpsAGzVXNcTv9NtJza26gdVmDGA336fvauRYRERFVVL1q8WnUqBFkMhkSEhKMyhMSEuDt7V3iMTY2NrCxsTFHeBVmOLh5sPdgBK8LRvqhdNy7fg/OLs5IT0sv9t3DwwMAkJSUBA8PD9jY2CA3NxdJSUlGdZPvJQPQJQsl1TE8j77M+6I37I/bAwBkWl0rT9GuM1PSD2KMiopCSEiIUReW4b7AwEBcu3atWB0iIqLS1KvERy6XIzQ0FH/++ac4xker1eLPP//ESy+9ZNngKqNw5iPCOoZhcK/BQC/LhXPj/RuIPx4PALDS6n5kamJomCAIyLmWA0EjwAY26O7XHUgCspKyjOqJ+/IBLz8vIAnIycyBbROOISAiorLVq8QHAF5//XVMmDABnTt3RpcuXfDpp58iMzMTkyZNsnRoFWbY4iOVWb43UmIlEV/rW3y0gmmn1guCgNM9T1drraLGLzdGi89amDAqIiKqb+pd4jN27FgkJSVhwYIFUKlU6NixI/bt21dswHNtZpj4yKxqZgBxZUisiyc+pu7qyrmWU+0FGhO2JDDxISKiMtW7xAcAXnrppVrVtaXN1aLgfgEAIC01DWfPnkWzZs1w/fZ1hPYpfNjevev3cCbyDArSC8RjpVYVa/ExfHgfgCo/yK+khwAatvi4ZLkAME1Xl+G15HlysVzwFeDWxw1yuRx5eXlQqVQAdM/JuX//Ptzd3cUVUQEgaXcStOlaaPNNv8CjPsagoCDExcWZ5eGIRERUc+pl4lPbJP+ejOhR0eK2FaxwG7chhRTvObyHt2+9jZszbkK9XQ0rWCEIQWLd7Jzscs9vuLaNl5cXJBIJVCpVpde3KW39HMMWn9d+ew2tb7dGypQUeDlWvRWt6LVO7Tgl7vvt7m/4vyP/h6NHj6J/9/7iYPWS1u1Rq9X47//+gz/8kZWZBbVabbLEhGsGERHVP5YfQNKASSHFwMyBiDoSBfX24qsPayQaxKfFl3sew7VtEhISxBYS/fo2FVXS+jkAYNPYeNbbkLNDcP74+QqftyLXunThkrhPAw2USiV27NhhNEOv6Lo9+vPkFege7CcRJJV6v5WJsaRrExFR3cPExwxSnVKR0ycHmT0zcUpxCsecjiFDmgEAkEOOm/KbYt0UqxQca3wMRx86ihWPrcBDvcpfIdlwbRtvb29x6n5l17cpbf0ct0fc4DXXuHWndYvWFT5vRa7VqkUrcZ8GGvj6+uKJJ54wGptV0ro9oaGh4jgoKaQmXc+HawYRUW22ceNGuLq6muVaEydONHoiQl3Gri4zuND4AkYNGKXbGKT79vk3n6Pt7baQQYZ5B+bhB/wAADj30DkserJwJekPXD4o9/xF170BUOIaOJU9j/5YqZUUrZe1xtE/j6J5ZHMAgKOdY4XPW5FrSWMLc/ARo0Zg0TeLoFAocOnSJRw5cgQA0KFDh2Lr9igUCrRp2wbZZ7JhLbM2aRcU1wwioobm+vXrCAgIwOnTp9GxY8cau87Zs2fx4Ycf4p9//sG9e/fQrFkzzJgxA6+++mqNXVOPiY+FaKSFi/VYa6xLLHeUO6K5W/MKnU//8D69qj6+oeh5jBSGCaGg+oObDa+VpkkTy/0D/I0SG8O/MgICAoqdx8r6wY9xDTy83jDGkq5NRESVFxkZCU9PT2zZsgV+fn74999/MW3aNMhkshqfnMSuLjNo59UOn4Z/avQV6BEo7n+nyzvi605NOuHT8E/x2ZDPEDktEs42lnlQakkEWWGyoy0w8To+BomURCYpo2YJ9D/FQs0srEhEDU+/fv3w8ssvY9asWVAoFPDy8sLXX38trgvn5OSE5s2bY+/evQAAjUaDKVOmICAgAHZ2dmjZsiVWrVolni8nJwfBwcGYNm2aWBYXFwcnJyds2LChQjFt3LgR/v7+sLe3x8iRI5GcnFyszp49exASEgJbW1sEBgZi0aJFKCgonCkskUiwdu1aDB06FHZ2dggMDMSPP/4o7tf/gdepUydIJBL069fP6PwrV66Ej48P3N3d8eKLLyI/P79CsRc1efJkrFq1Cn379kVgYCCeffZZTJo0CT/99FOVzlcZbPExg+ZuzfFqN+Pmu7NuZ6GGbkDzUy2fQhR0A2bbeLfBqG6jzB5jRRglPlWYOq7J1iB6dDTSjxdfr0fIN0h8rCqX+BglSgKASuZNREQl+e677zB37lycPHkSP/zwA2bOnIldu3Zh5MiReOutt/DJJ5/gueeew82bN2FtbY0mTZpgx44dcHd3F1swfHx88OSTT8LW1hZbt25F165dMWzYMAwfPhzPPvssBg0ahMmTJ5cby4kTJzBlyhQsXboUI0aMwL59+7Bw4UKjOn///TfGjx+Pzz77DL1790ZcXJyYaBnWfeedd/Dhhx9i1apV2Lx5M8aNG4fz58+jdevWOHnyJLp06YKIiAgEBwcbLR1y6NAh+Pj44NChQ7h69SrGjh2Ljh07YurUqQCAGTNmYMuWLWW+j4yMjFL3paWlwc3Nrdx7UV0SgX8iG6noY+2r69zQc0jZlwIA6PhXR5zpcwYA4D3FG62+aVXGkZazbsA6tDzUEgDgc9wHLbu2rNTxSbuSjKb1lybhlQSkPJtS4fM2ndoU9md1zxK79O8li6bzEokEAwMHVriLkqg+y8nJQXx8PAICAmBra/BImc6dgQezT83K2xs4dar8etC1+Gg0Gvz9998AdC06Li4uGDVqFDZt2gQA4rIhx44dQ7du3Yqd46WXXoJKpTJqUVmxYgWWL1+OcePGYefOnTh//jzc3d3Ljefpp59GWloafvvtN7Fs3Lhx2LdvH1JTUwEAAwcORFhYGObPny/W2bJlC+bOnYu7d+8C0H1GzZgxA2vXrhXrdOvWDSEhIVizZk2pY3wmTpyIw4cPIy4uDjKZbkLJk08+CalUim3btgEAEhMTkZ5e9kK0zZuX/Nn477//om/fvvjtt98wePDgUo8v9WcKFf/9zRYfCzFs1Tg38lyJ5bWOQceospsSNptt4DLMpcKLJd68YzB7zSEFGbbFM/9bjW7hI/lHUP9efHp/aT5N/RQd0AEA8OrvryLfqmpNr6biYO2AO6/fgYuti0XjIKq1VCrgzh1LR1Gu9u3bi69lMhnc3d3Rrl07sUw/6zQxMREAsHr1amzYsAE3b95EdnY28vLyig0Qnj17Nnbv3o0vvvgCe/furVDSAwCXLl3CyJEjjcq6d++Offv2idtnz57F0aNH8f7774tlGo0GOTk5yMrKgr29vXhc0fOcOXOm3BiCg4PFpAcAfHx8cP584dImnp6e8PT0rND7MXThwgU8/vjjWLhwYZlJj6kw8bEQrX1hV5E2ufB1gU1BSdVrhTyHPKPtI5OOYF6jeRVeLPF6ynW4Q/ePfGP/jfil8y8miUsrKbx/EsHyiWNmfiZik2PRpXEXS4dCVDs9WHKjtl/X2traaFsikRiVSSS6zxutVott27bhjTfewEcffYTu3bvDyckJK1aswIkTJ4zOkZiYiMuXL0Mmk+HKlSsYMmRIFd9McRkZGVi0aBFGjSo+XKJo60hVlHQ/9GucAVXr6rp48SLCwsIwbdo0vP3229WOsSKY+FhIUt8kXN1+VUwEAEAJJYJDgxGMYAtGVrrLgy8Dp4F2t3R/8dgX2BdbLLGs2WRajUGyd0sL3Cq53ty5cxEcXPF7YL/DXnwt3SMFZKWfJzo6GsuXLxe3n3zySWzfvt3o2gCM6ujPU/TYouffen4r9sftB8BB1kRlqmB3U11y9OhR9OjRAy+88IJYFhcXV6ze5MmT0a5dO0yZMgVTp07FwIED0bp1+euitW7dulgSdfz4caPtkJAQxMbGltqdZHjc+PHjjbY7deoEAOKYHo1GU+KxZVm8eDHeeOONCtePjo7GgAEDMGHCBKNWqprGxMdCQp8Kxfj3xhs9DsHX1xcXHr1g6dBKdb/xfbwy5RVs+mwT/FL8YCuxhbeXN1QqVYUW9jNMfAS1AO883V9fKpXK6B7MGzqvUmvlnPI4hQzo/oqYdWEW8pEPe3t7jPljDGwOG6863TG3I2wu2yArW9fs+9j5x9Dycktxe8wfYwDAqI7+PPpjU7NTEdkoslicZ1VnxcTH1E+vJ6LarUWLFti0aRP++OMPBAQEYPPmzfjvv/+MlsFYvXo1jh07hnPnzsHPzw+//fYbnnnmGRw/ftxoEHFJXnnlFfTs2RMrV67E448/jj/++MOomwsAFixYgOHDh8Pf3x9jxoyBVCrF2bNnceHCBbz33ntivR07dqBz587o1asXtm7dipMnT2L9+vUAdN1VdnZ22LdvH5o0aQJbW1u4uFSs274yXV0XLlzAgAEDEB4ejtdff138I1omk8HDw6NC56gqJj4WUhcXx9M36+rH0DhJnLDHdw8yXTPhFuIGJ5lTmccbJj7hQ8Kx5UNdk2h174HcrvADIxzhuhdZQMqmkgdID8AAsU7Gtgyjbf0xJZUZlo+zH1csTv39AZj4EDU006dPx+nTpzF27FhIJBI89dRTeOGFF8Tp7jExMZgzZw7Wr18PPz8/AMCaNWvQvn17vPPOO1i2bFmZ5+/WrRu+/vprLFy4EAsWLMDAgQPx9ttvY8mSJWKd8PBw/Prrr1i8eDGWLVsGa2trtGrVCs8//7zRuRYtWoRt27bhhRdegI+PD77//nu0adMGAGBlZYXPPvsMixcvxoIFC9C7d28cPnzYhHdK58cff0RSUhK2bNli1D3WtGlTXL9+3eTXM8RZXUWYa1ZXXTRlzxRsOLMBn6//HG1vtS22v8XaFmg8o3Gpx2+dsxWNV+r2p7yXglH/M820feW3SsQ+H1sjCxiWpW9BX6Op9HMPzMWKf1cAAP6a+Bd6N+1t3oCIapmyZuCQZUgkEuzatavOPn6Cs7rIrPQtGju67UC7zHYQ1IJu3ZwH8lR5pRypYzgITiaVlVGzcnwm+cBtiBvy79X8bK7YKbG4/999AIA2VwuZfeH7kEoKp72xxYeIqHZi4mMOd+8CJ09aOopqk9y6AQD4K/gvuI08g3Z2TaG+YIWz7+ie26U9FwvsPlvq8do7dwDomnilN+KB3btNFpvNg6+aZlXgAP2zO7S7foXMoTDzkyqviq+1//wFnKn4lPx6zcMD6NEDkFh+xh1RbTV06FBxzaCi3nrrLbz11ltmjqj+YuJjDidOACVML6xrpMMBdNa9fuWPWXDJBbzvtcY4rAEAnN+fjMMn46GVaHAx4A/ENz5mdHyT22PQFLpFvmQ//wysO2TO8E1CivcA9AQAXHo2BhIUtjJ1bNQRixt1wNGWR6H9bgEQb6Ega6OFC4F337V0FES11jfffIPs7OwS95lyNWOObmHiQ5UgN5jdePjBRIWAhByMi9C9ds1sDNdM3RiexokPY+SckcizLuz+eiKl8C9+qzraFSRDjvg6BV2N9nne0331jOkJjf9pAIlmjq4WO3LE0hEQ1WqNG5c+PpJMi4mPOQQHA0uXWjqKahunvY4t+d8h1eCX/3WP6zjT9Aw63uhoVNc+zx5O2U5Iti58iJ5UKBwD4xbcB3jVdAt3Gbpy9ao4NbM0Q4cMwV6DqaBFtwHg+SlTiq2H4RXriqSt+RDyjRfyMiSFFKqHhwEzH6pC9LVf0ftb0n0CAOTnAwsWmDEyIqIKEMhIWlqaAEBIS0uzdCi1UnZ+thBzO0bwDPQU4ADBK8hLOH7huBDUNEhQ2CuERVaLhEM4JBzCISG4SbBY50T0CWGq21RxX/zm+BqLMSUlRfDx8REACFKpVAAgeHt7C97e3gIAwdfXV7h27ZpYR7/t5eUlQDdcW/D29hZSUlJKPP+9O/eEhxo9JCigEBRQCO4Sd0EBhTDLd5b4/n5a/1ONvT9LM7y/vr6+pd4nITtbEADdV9++Zo2Raofs7Gzh4sWLQnZ2tqVDoXqirJ+piv7+ZosPVYqtlS1aNm6JmFMxiIqKEtfd+e/0f4iKioLzOmdk7sgEAGx5eAtS8lPg4eEBm89t8Hyz55GVkgUAcHR2rLEYS1sjCYBRzPo6+u1Lly7hyIMumb59+5a6npC7rzuOXz4u1u3QoQOuXbuGa2uuAT89uE/W9Xfqbkn3joioruA6PkVwHZ/qufzSZdxdfbfceu1+awf3Ryr2cL66YvP4zfDbrJu1lrUhC49MesTCEVlYbi6gX2ejTx+O82mAuI4PmZop1vGRlrqHqAoajWgEiXXZ05bl3nK49KqHTy43WJpIKODfE0REtRG7usik3Aa6ofvd7si9nVtqHYfWDpDa1MOc2+BfExOfItiwTGRyGzduxKxZs5Camlrj15o4cSJSU1Ox24Trr1kKEx8yOXkjOTJlmYiMjERoaCgAiK8tNR5ErVbXfAwGLT7x6+Ox9q+1yLHKwbA3h+GhtnV7hpf6TzVUESrcvXsXbm5uSElJga+vLwDg7t278PX1hZ2dHZx7OMNt4IM1R7hgIVGdc/36dQQEBOD06dPo2LFjjV5LUsJnxPfff49x48bV6HWZ+JDJqdVqBAcHQ6lUwsvLCxKJBCqVCj4+PoiOjjZ78mMYT03GILEq/EfcLrIdEKl7vfXvrZh1eladHQSccT4DZwfqVuSWQYY0pEEGGRKQIJbpXwNA53Od4diu5gavE1H98e2332LIkMKlTVxdXWv8mvWwv4EsLTIyEkqlEgCQkJAAlUoFAFAqlYiKirJoPDUZQ8tHW0Ij0RQr97/vb5H3bSqZFzIrVT/rom7mnlGLD7u6qI7p168fXn75ZcyapfujxcvLC19//TUyMzMxadIkODk5oXnz5uLT1zUaDaZMmYKAgADY2dmhZcuWWLVqlXi+nJwcBAcHY9q0aWJZXFwcnJycsGHDhgrFtHHjRvj7+8Pe3h4jR45EcnJysTp79uxBSEgIbG1tERgYiEWLFqGgoEDcL5FIsHbtWgwdOhR2dnYIDAzEjz/+KO4PCNCtTtupUydIJBL069fP6PwrV66Ej48P3N3d8eKLLyI/v3rPSHR1dYW3t7f4ZZZB8DUz077u4jo+1We4zkvR9XNKXfPFTPHUdAyn/z0tDHhogNDFp4vwh+wP4RAOCRvcNljkfZuKcrNSXJ9oFmYJ3STdhC7oIoQrwoVwRbjQBV2Et+3fFuuo/k+lOzAvr3Adn169LPsmyCLq8jo+ffv2FZycnIQlS5YIly9fFpYsWSLIZDJh6NChwldffSVcvnxZmDlzpuDu7i5kZmYKeXl5woIFC4T//vtPuHbtmrBlyxbB3t5e+OGHH8Rznj59WpDL5cLu3buFgoICoVu3bsLIkSMrFM/x48cFqVQqLFu2TIiNjRVWrVoluLq6Ci4uLmKdv/76S3B2dhY2btwoxMXFCfv37xeaNWsmvPvuu2IdAIK7u7vw9ddfC7GxscLbb78tyGQy4eLFi4IgCMLJkycFAEJERISgVCqF5ORkQRAEYcKECYKzs7MwY8YM4dKlS8Ivv/wi2NvbC1999ZV47unTpwsODg5lfhnSfya7u7sLDz/8sLB+/XpBq9WWeR9MsY4Pp7MXwenspqFWq8V1XgBYfM0Xw3hqOgb9tXKH5cI+1x53ve7iadXTNXrNmqT6ToWYiTEAAO0rWgTMCii2NpLfKT/cnadbxqD1ltbwesYLKCgArB+scN2zJ/DPPxaJnyyntKnHnb/qDFWGyuzxeDt649S0UxWq269fP2g0GvHBoRqNBi4uLhg1ahQ2bdoEAGIX/rFjx9CtW7di53jppZegUqmMWlRWrFiB5cuXY9y4cdi5cyfOnz8Pd/fyl/Z4+umnkZaWht9++00sGzduHPbt2ycObh44cCDCwsIwf/58sc6WLVswd+5c3L2r+/cpkUgwY8YMrF27VqzTrVs3hISEYM2aNaWO8Zk4cSIOHz6MuLg4yGS6AY1PPvkkpFIptm3bBgBITExEenp6me/DcJX3JUuWYMCAAbC3t8f+/fuxcOFCLF++HK+88kqpx5tiOjvH+FCNUCgUCAsLE7cNX1tC0XjMca3fJLoPKMNHddRFgqbwb6NWwa3gG+ArNocDuv+3d2LuFNbX8m8pKpsqQ4U79++UX9HC2rdvL76WyWRwd3dHu3btxDIvLy8Aul/4ALB69Wps2LABN2/eRHZ2NvLy8ooNEJ49ezZ2796NL774Anv37q1Q0gMAly5dwsiRI43Kunfvjn0Gj9o5e/Ysjh49ivfff18s02g0yMnJQVZWFuzt7cXjip7nzJkz5cYQHBwsJj0A4OPjg/Pnz4vbnp6e8PT0rND7AYB33nlHfN2pUydkZmZixYoVZSY+psDEh6iGaCW6B7FKhLo9u8lwar5EVsp7Mczt9NU5xodK4e3oXSeua21t/Ew+iURiVKaflaTVarFt2za88cYb+Oijj9C9e3c4OTlhxYoVOHHihNE5EhMTcfnyZchkMly5csVoYG91ZWRkYNGiRRg1alSxfaYYO1PS/dBqCx84PWPGDGzZsqXcGEvTtWtXLFmyBLm5ubCxsalesGVg4kNUQwSJ7pd9nU98DFp8DKfsG5JIC98jW3yoPBXtbqpLjh49ih49euCFF14Qy+Li4orVmzx5Mtq1a4cpU6Zg6tSpGDhwIFq3bl3u+Vu3bl0siTp+/LjRdkhICGJjY0t+aHCR48aPH2+03alTJwCAXC4HoGspqqzFixfjjTfeqPRxemfOnIFCoajRpAdg4kNUY/SJj6ARoFarSxxbpFarcfjwYQC6MQWVHX+kX58oKCgIcXFxRusmGZZV5Lwx92Jw5uYZsem6Xbt2cHR0hPa6Fs7Q9ZefTTqLyMuRxY7V3NLABbrVuM/efVBHqwEeAjwygS4QULfTP6KytWjRAps2bcIff/yBgIAAbN68Gf/9959Rt/Dq1atx7NgxnDt3Dn5+fvjtt9/wzDPP4Pjx42LCUZpXXnkFPXv2xMqVK/H444/jjz/+MOrmAoAFCxZg+PDh8Pf3x5gxYyCVSnH27FlcuHAB7733nlhvx44d6Ny5M3r16oWtW7fi5MmTWL9+PQBdd5WdnR327duHJk2awNbWFi4uFVtpvzJdXb/88gsSEhLQrVs32Nra4sCBA/jggw+qlThVFBMfohoiJj4FAoKDg4utH6RWq9G6dWskJOjWwPH29sbFixcrnPwYrk8klUqh1WqN1k3Sl1Vk7aJfYn/BY9seMy68rvs2+txovISXAAArTqzAwayDxY5/5PwjmIM5AIDPj3+O3/N/1+14MKZ78ZXbeKfYUUT1x/Tp03H69GmMHTsWEokETz31FF544QVxuntMTAzmzJmD9evXw89P90y/NWvWoH379njnnXewbNmyMs/frVs3fP3111i4cCEWLFiAgQMH4u2338aSJUvEOuHh4fj111+xePFiLFu2DNbW1mjVqhWef/55o3MtWrQI27ZtwwsvvAAfHx98//33aNOmDQDAysoKn332GRYvXowFCxagd+/e4h9npmRtbY3Vq1fjtddegyAIaN68OT7++GNMnTrV5NcqirO6iuCsLjKVnS474Z7ujgSnBIy7Pw4RERFGA6wjIiIwaNAgo2OK1ilLSceXVbes87627zX83x//B59Un2L7+kX3w4j/RgAAFo1ZhMNtDxerM+T0ELy5500AwEfDP8KvnX812t83xRmHV6VVKFaqP/iQ0tpHIpFg165dGDFihKVDqRLO6iKqzR707UgFKXx9fcXp33qhoaHw8vIyavEpWqc0giAg4GoA5trPRWZWJiSQQIAAB3sHADAuc3CA9y5vpDunw/nhkj8M3P5zw/effg9pOWuajmw1EgP7DzQqy87JxvmfCmd2PBLwCLr174YCbT7ePbJIFy/49xUR1Q5MfIhqiCDV/bKXSWS4cOFCsa4mhUKBS5cu4ciRIwCAvn37VribK/VQKm7NvIWhGGq8I6uEyplA0uokqLep0eNuD0jlxZMbz1Oe5SY9ADBl3BQ4BDsUK4+7FodbM28BAB5r9Rga92mM3Pwcg8SHiMoydOhQcc2got566y289dZbZo6o/mLiQ1RD9GN8pIK01IRGoVBUqck5K6akDKdsBckFKEgtgNyzhEGUBqvO24y1gWez4gMUXfu4lpj0AICjU+GzufSzuqTSwilgTHyIyvbNN98gOzu7xH1ubm4muw5HtzDxIaoxNTmdXZtXuHZGsyXN4Dao9A/GuDfjkHZEN77GaGq6ocJH+cBpphOC+gZVLiDDxqIHoRk+eZldXURla9y4saVDaDCY+BDVEH1XV00kPkJuYSLhEOwA566lD+SzbmSw6Ji25DqS/MIYreSV/1goaR0fCQwTHyKi2oGJD1EN0bf4OOQ44KvWX0Gj0YhTzPXfZTKZ2DIiCEKpdQDdgmL6+ookBRqhEQDgjUNvICY5BgUFBcjKzIK9gz2srAr/aT91/Sl0REcAwGNbHkOqe+qDAAG7FDvkZOZgROIIsb6Vre5Y/RpBFVoHyKDF50rkFeQcz0H8nXixTCth6kNEtQMTH6IaorHWrXwq08rwUMxDNXads+lncfbO2cKCIivCD84dXFhXeRYJOQmAAHz03UcIuV58Fll+fr7RGkEVWQfIsMVHukWKO1vuQA45pvWchq8GfcUWHyKqNer20xOJajG7SXbItcqt0Wtc8LuAaP9oXbeSAPFLYvCfYNDaYiVYQQIJ/JL9Skx6smXZuJt4F5GRkVAqlQAApVKJqKioMuOwaVLyEvPDIocBYFcXEdUebPEhqiGjloyC9m0tUhJT8PDDD0OVoIJUIoVW0Irffbx9cPLkSQAotY6Xp+4J0AmJCfDx9sGBAwcwcOBAqBJUcNO4IfE13ZOh9S00vr6+4vR5tVqNL5Z9IcZ06rlT8O7sjYzzGTj1he55SUoocQVXoIEGUS5R2NRzEwDdk5f15ytvfSGnLk7w/cAXuxfvRk5ODkIQAkc4wlqjG19Uxx9XRkT1CBMfohoktZGikV8jRF2KQlRUFAIDA3Ht2jXxe0hIiNiFVFYdAIiKihLr6+saHh8dHV2sTKFQ4LERj0H9vRoA4OToBMD4ietej3qh26puuHbtGmaFzCrzfKWRSCR4aP5DmDpjKqKiomA3yw55F/Ig0+rGJ3FWF5Hpbdy4EbNmzUJqamqNX2vixIlITU3F7t27a/xaNY2JD5EZKBQK8ZER+ocWGj68sCJ1DB85YVi3rDIAsLEz6IZ6MKvLMPHxa+aHgICAMuOpKP0xkXaRyENh4lPKZDIiqmWuX7+OgIAAnD59Gh07dqyx62zcuBGTJk0qcV9CQkKFH3ZaFUx8iOq5kqaaGyY+EivT90PpzykTZJBojccZERGNHTsWQ4YMMSqbOHEicnJyajTpATi4maj+M/xXrptoZrbEB9CtXM20h+qafv364eWXX8asWbruXy8vL3z99dfIzMzEpEmT4OTkhObNm4tPX9doNJgyZQoCAgJgZ2eHli1bYtWqVeL5cnJyEBwcjGnTpollcXFxcHJywoYNGyoU08aNG+Hv7w97e3uMHDkSycnJxers2bMHISEhsLW1RWBgIBYtWoSCgsIVSiUSCdauXYuhQ4fCzs4OgYGB+PHHH8X9+pbfTp06QSKRoF+/fkbnX7lyJXx8fODu7o4XX3wR+fn5qAo7Ozt4e3uLXzKZDAcPHsSUKVOqdL7KYOJDVMup1WpERERArVYbva4oiawwCTkYcRC7du2C8paycH8NJz4yrYyJD9VJ3333HRo1aoSTJ0/i5ZdfxsyZM/HEE0+gR48eiIqKwuDBg/Hcc88hKysLWq0WTZo0wY4dO3Dx4kUsWLAAb731FrZv3w4AsLW1xdatW/Hdd99hz5490Gg0ePbZZzFo0CBMnjy53FhOnDiBKVOm4KWXXsKZM2fQv39/vPfee0Z1/v77b4wfPx6vvvoqLl68iHXr1mHjxo14//33jeq98847GD16NM6ePYtnnnkG48aNw6VLlwBAnGwREREBpVKJn376STzu0KFDiIuLw6FDh/Ddd99h48aN2Lhxo7h/xowZcHR0LPOrNJs2bYK9vT3GjBlT7r2oLonAB3cYqehj7YnMwXA9HS8vL0gkEqhUqgqtraN3+aXLuLv6LgAgDWnQQANrWMMJuoHOXm94ofWK1iaN+1T/U8g4rFtQSOWiwvbBH+On7SdNeg2q/XJychAfH4+AgADY2tqK5ac6n0KeKs/s8ci95eh8qnOF6vbr1w8ajUZ8cKhGo4GLiwtGjRqFTZt0Mx/1/xaPHTuGbt26FTvHSy+9BJVKZdSismLFCixfvhzjxo3Dzp07cf78ebi7u5cbz9NPP420tDT89ttvYtm4ceOwb98+cXDzwIEDERYWhvnz54t1tmzZgrlz5+LuXd1ngEQiwYwZM7B27VqxTrdu3RASEoI1a9aUOsZn4sSJOHz4MOLi4sRFVZ988klIpVJs27YNAJCYmIj09PQy30fz5s1LLG/Tpg369euHNWvWlHl8aT9TQMV/f3OMD1EtZrieTkJCgliuX1unIoOPrVwL/5m7wKXYfmWGEq1h2sQnXZsuPu3dO80b/U+NNun5qW7LU+Uh7475E5/Kat++vfhaJpPB3d0d7dq1E8u8vHRLTSQm6paUWL16NTZs2ICbN28iOzsbeXl5xQYIz549G7t378YXX3yBvXv3VijpAYBLly5h5MiRRmXdu3fHvn37xO2zZ8/i6NGjRi08Go0GOTk5yMrKgr29vXhc0fOcOXOm3BiCg4PFpAfQLXlx/vx5cdvT07NK43OOHTuGS5cuYfPmzZU+tiqY+BDVYqGhoeJ6Ot7e3gB0f2VWZG0dPZ/nfZDyTwqu/X0NGq3GaJ/KRoVnZj1j8rhbLmiJP4b+gcD8QACAXW7JT3WnhknuLa8T17W2tjbalkgkRmX6x81otVps27YNb7zxBj766CN0794dTk5OWLFiBU6cOGF0jsTERFy+fBkymQxXrlwpNsC3OjIyMrBo0SKMGjWq2L6irSNVUdL90GoL52zOmDEDW7ZsKTfGor755ht07NgRoaGh1Y6xIpj4ENViCoXCaD0dABVeW0fPrpkdOh/ujCB1EI4cOQIA6NChA65du4YhIUMqfJ7KaBzWGCOUI3Cu0TkAgFSQlXMENSQV7W6qS44ePYoePXrghRdeEMvi4uKK1Zs8eTLatWuHKVOmYOrUqRg4cCBaty6/xbV169bFkqjjx48bbYeEhCA2NrbU7iTD48aPH2+03alTJwCAXK5LDjUaTYnHlmXx4sV44403KnVMRkYGtm/fjqVLl1b6elXFxIeoliu6nk5l19YxPM+IESPE7aLr9piam7sbNBINZIJMXM+HqL5q0aIFNm3ahD/++AMBAQHYvHkz/vvvP6N/Z6tXr8axY8dw7tw5+Pn54bfffsMzzzyD48ePiwlHaV555RX07NkTK1euxOOPP44//vjDqJsLABYsWIDhw4fD398fY8aMgVQqxdmzZ3HhwgWjgdA7duxA586d0atXL2zduhUnT57E+vXrAei6q+zs7LBv3z40adIEtra2cHEp3kVekqp0df3www8oKCjAs88+W6njqoOzuoioxmilur8aJQI/aqh+mz59OkaNGoWxY8eia9euSE5ONmr9iYmJwZw5c7BmzRr4+fkBANasWYN79+7hnXfeKff83bp1w9dff41Vq1ahQ4cO2L9/P95++22jOuHh4fj111+xf/9+PPzww+jWrRs++eQTNG3a1KjeokWLsG3bNrRv3x6bNm3C999/jzZt2gAArKys8Nlnn2HdunXw9fXF448/Xt1bU6b169dj1KhRcHV1rdHrGOKsriI4q4vIdPbJ98I23w63G8Xj2aSSV2ml+qusGThkGRKJBLt27TJq/a1LTDGri3+GEVGN0Uh0LT5SLT9qiKh24KcREdUYfVeXe7onjvc7joNdDuLS/EviozOISGfo0KGlLvr3wQcfWDq8eoWDm4moxuRZ6dZqsSmwQ86RHEghRcJ/CXDo6gD/Ef4Wjo6o9vjmm2+QnZ1d4j43NzeTXYejW5j4EFEN+qPTHjx5dCKstMYfNVePX2XiQ2SgcePGlg6hwWBXFxHVmN3dtuLReY/i0TcfxReDvxDLP4n9BJP3lP98IiIiU2PiQ0Q1xj1Hghx5DjLsMpBlmyWWCxoB3575FtdTr1suODIbw9V9iarDFD9L7OoiohrzyUE5lj6ciwwXWzRxayKW6xc0zMrPKu1QqgfkcjmkUinu3r0LDw8PyOVy8TEPRJUhCALy8vKQlJQEqVRa7oKPZWHiQ0Q1Zki8DEOiAbRtjoT5S3Bp4yUAhYmPVmBLQH0mlUoREBAApVIpPh2cqDrs7e3h7+8PqbTqHVZMfIio5gkCJFaFf+kz8Wk45HI5/P39UVBQUKXnPxHpyWQyWFlZVbvVkIkPEdUcgw8ow8Tn+T+fxzn/c0x8Ggj9U82LPt2byBI4uJmIzMIw8bEpsMEn332C1DuplguIiBokJj5EVHP0LT6CAOcezhDsCxdPs8+zR9yxOAsFRkQNFRMfIjILeSM52kW3w12HwkGuzfyaWS4gImqQmPgQUc0xaPEBgEbNGiGzT6a4215ub4moiKgBY+JDRGYlk8vE19oCDm4mIvOqM4nP+++/jx49esDe3h6urq4l1rl58yaGDRsGe3t7eHp6Ys6cOSgoKDBvoERUqEiLDwCgMO+BNp+JDxGZV52Zzp6Xl4cnnngC3bt3x/r164vt12g0GDZsGLy9vfHvv/9CqVRi/PjxsLa2xgcffGCBiImoJIKsMAkSCvikaCIyrzqT+CxatAgAsHHjxhL379+/HxcvXkRERAS8vLzQsWNHLFmyBG+++Sbefffdai1vTUQmZNDiE78tHumR6ejQpwOaDG2C1LRUREZGIigoCHFxcQgNDQWAYmUKhQJqtbrEciKistSZxKc8x44dQ7t27eDl5SWWhYeHY+bMmYiOjkanTp1KPC43Nxe5ubnidnp6eo3HStRglNPV1XRXUwBA3PI4JE1PwvCfh0OpVEIqlUKr1cLLywsSiQQqlUos8/HxwdGjR9GzZ0+juj4+PoiOjmbyQ0RlqjNjfMqjUqmMkh4A4rZKpSr1uKVLl8LFxUX88vPzq9E4iRq6jOYZJZbf/f0ulEolgMInMCckJIj/fvVlSqUSO3bsKFZXqVQiKiqqRmMnorrPoi0+8+bNw7Jly8qsc+nSJbRq1arGYpg/fz5ef/11cTs9PZ3JD5GplNDic6/XPcx/ej6aJjUFLgKT70yGHHI4pDtgvmI+srOzIZFIIAgCbG1tAQA5OTlimZ2dHUL/CzWqm4tcnPQ5CbumdohOjIaPkw/c7Nws8Y6JqJazaOIze/ZsTJw4scw6gYGBFTqXt7c3Tp48aVSWkJAg7iuNjY0NbGxsKnQNIqo+qUyK4w8dx/GHjgM9gSdWPgH3DHdI0iQYjMHGlXNKOEEOgB9RrG6vlF7oubUnAEAuk2PPuD0Y0nxIzbwJIqqzLJr4eHh4wMPDwyTn6t69O95//30kJibC09MTAHDgwAE4OzujTZs2JrkGEVVSCS0+AYoAoyoH2x7EE8efqPalfFJ9INVKoZVqkafJw0+XfmLiQ0TF1JnBzTdv3kRKSgpu3rwJjUaDM2fOAACaN28OR0dHDB48GG3atMFzzz2H5cuXQ6VS4e2338aLL77IFh2iWmRc23FIyU7BxaSLAIDcTrnYrdwN6+yqPbm72+pucL/qDgAY3WI0dsTtAAAUaLmGFxEVV2cSnwULFuC7774Tt/WztA4dOoR+/fpBJpPh119/xcyZM9G9e3c4ODhgwoQJWLx4saVCJiI9gxYfWytbvN799TIqV87ZvWehvqoGALzb410x8dEKXByRiIqrM7O6Nm7cCEEQin3169dPrNO0aVP8/vvvyMrKQlJSElauXAkrqzqT2xHVP/qurnKo1WpERERArVaXW160TCov/Bg79sMxeKm9YJtrW+nEp7QYiKh+YVZARBalVqsRHBwMpVJptBZPSeUAipVJ5IXJVdBbQdiGbci2zsb+ufuBkdWLgYjqnzrT4kNEdVBJCxgWERkZKa7JY7gWT0nlJZXZNrMtdk67fDs0OdykwmGWFgMR1T9MfIjIokJDQ+Hj4wMA8PX1RUhISKnlJZX5z/WHx0seOGpzFMetjovntZPZVTsGIqp/2NVFRDWnAi0+CoUC0dHRiIqKQkhIiNjFVFp5SWXBnwfDd7Evfv7uZ+A13Xmllfi7rrRrEVH9IxGEMj6RGqD09HS4uLggLS0Nzs7Olg6HqG7z8ADu3QMCA4G4uBq/3PWz13G943UAQEzPGMz4Z0aNX5OIaoeK/v5miw8R1ZwKtPiYktSqsJVHoq3YjDJtvha3VtxCxtnizxCz8bOB/1x/yD3lJouRiCyLiQ8R1RuGy1dINBVLfO7tuYf4/8WXul8ikyBoWVC1YyOi2oGJDxHVG4YtPvnZ+VCr1eLU+MjISAQFBSEuLg6hoaEAdLO5Gp1qVOY5c2/l1mjMRGReTHyIqObou7quXwfcav5p6VIrJwC6Fd5l6lTcaeaGdCcn3L9/H14AMgB4AbiS+xSy88bAWrBCKhIA6B5r46H4GAX5J6DRNkJ61moAgPDjT8C+XtULzNcXWL8e6Nq1euchompj4kNENcfVFUhM1I3xMcOKyFZyjfg61U6Gds8DwH3jOgVW+G3pRMiF4uN2Hh97EXHeiWiUpsWOT3RlKrkGwdWNXa0GVq9m4kNUCzDxIaKas2wZsGQJkFF84HBNsNPaAld1r0OuhWDbx9uK1dFINZBrdElPjlUOEl0SAQDHHjqGOC/dzDOttPBxF7fc5EDjh6oWUEEBcO2a7nVmZtXOQUQmxcSHiGrOiBG6LzOR52ggOP8FSb4Eco0cXuleZda/1eIWds3dhcyMTLgqXDFGPgZ5eXlIu5pWWMnTBzgVW7WAlEpdNxcR1RpMfIio3pDZytB8aXPc+eIOtHnFH1KadzfPaLtbUDdMnTi1WL1b128h7t0H6w6Z6iHvXDKNqFZg4kNE9YrfbD/4zfYrcd8/jf5BQXKBuC2xKnnKu5W1wUejpsQqRFRH8VldRNRgSK2NP/JKS3ysra0LN0zV4kNEtQITHyJqMCRy40SnQolPdVp8JAbnZ1cXUa3AxIeI6i21Wo2IiAioH0xHl1hXLPEx7OpqdqkZ1j2+DpnpnJVFVB8w8SGiekmtViM4OBiDBg1CcHCwLvmxNa6TL80v8Vi5jRwaaWFTT8ufW2LPyj01GS4RmQkTHyKqlyIjI6FUKgEASqUSUVFRyByUiRzkAABSkIKkkKQSj7W2tsa5sHNGZQmxCZUPQlKx54URkflwVhcR1UuhoaHw8fGBUqmEr68vQkJCgBCg/bb2uKe6h0Y+jXBu/LlSj5/4w0Q82/1ZzImdAwBwdnCuXkAc40NUKzDxIaJ6SaFQIDo6GlFRUQgJCYFCoQAAnLt4rlhZacc/P/N5YJZuWyaRmSFqIqppTHyIqN5SKBQICwsrt6w0Ds4O4muhoAotNuzqIqp1OMaHiKgUMqvCVp4qJT6G2NVFVCsw8SEiKoXM2qB7iys4E9ULTHyIiEphmPgE/hCIX9b9YrQ/MyYTl+ZcwsGxBxG3Ng6Chq06RLUdx/gQEZXCysYKGoOmHvuZ9jjT4Qw6dusIADj36DnkXs2FFFLc2n4LMkcZmj3XrPAEXLmZqNZhiw8RUSk69u+Iey73xG2ZIMOJP04AAAStgNyruUb1rx25Ztb4iKjymPgQEZXCzsEO3c51wxmfM2KZt5c3AJTYreXr5Wuu0Iioipj4EBGVoYl/EzgNdBK35TI5gJJnedlY2xgXsKuLqNZh4kNEVA65rVx8rcnXjfkpKfGp9pR3IqpxTHyIiMohtS78qCzILwDAxIeormLiQ0RUDqlV4UflqqOrYLXYCt4feher99HfH2HY/w2DRvtgJhhXbiaqdTidnYioHA72hY+uaHejHSRaCRxzHIvVG3h2IKZHTsexXsfQy7+X8U6O8SGqFZj4EBGVo71ve1zHdQDAqJOjMOrkqBLruWW6YctnW5AwPAHwN2OARFRh7OoiIiqH4uHSn+JelE2BDVR/qmowGiKqDrb4EBGVw7mrM4J+C8LCpxYiPT3daF++az6Wf78cMY/HwCXPBQDg7flg/A+nsxPVOkx8iIjKIZFI4PeIHz66/hGioqIQGBiIs2fPAgD69u0LhUKBo88chcu3usTHxsqmrNMRkQUx8SEiqiCFQoGwsDAAQEBAgNE+uV3xtX6IqPbhGB8iIhOQWBV2a2kLtA8K2dVFVNsw8SEiMgGJrDDJ4UKGRLUXEx8iIhOQWBcmPtePXUdycrIFoyGi0jDxISIyAams8OM0ZE8Ivun4DVJTUwsrsKuLqFZg4kNEZAJuD7kZbXe93RX//HXMQtEQUWmY+BARmcCA5wbg+ivXjcqCAptbJhgiKhUTHyIiE5DJZJi4aiIud74sltnb2lkwIiIqCRMfIiITkloXfqxqNNrCHRzjQ1QrMPEhIjIlg2VhCwq4kCFRbcPEh4jIlGSFLwvymPgQ1TZMfIiITMkg8fn3X4NZXezqIqoV+KwuIiJTMvhU9VvUEnutf0e6wz14Z+9GX8tFRUQPVKnFZ9OmTcjNzS1WnpeXh02bNlU7KCKiukrqVvixalNgA7t8O3il+iH2bgcLRkVEelVKfCZNmoS0tLRi5ffv38ekSZOqHRQRUV3V761+uNLpCuLd43FDcUMsl2o5tZ2oNqhSV5cgCJAYPnX4gdu3b8PFxaXaQRER1VWBbQMRGBUItVqNvdt+BF7QlUsFWdkHEpFZVCrx6dSpEyQSCSQSCcLCwmBlVXi4RqNBfHw8hgwZYvIgiYjqGoVCgUGDByIaulYfiZZzSYhqg0olPiNGjAAAnDlzBuHh4XB0dBT3yeVyNGvWDKNHjzZpgEREdZXMqjDZkWjZ4kNUG1Qq8Vm4cCEAoFmzZhg7dixsbW1rJCgiovpAJi/8iJUKbPEhqg2q9C9xwoQJyMnJwTfffIP58+cjJSUFABAVFYU7d+6YNEAiorpKZl3YysMWH6LaoUqDm8+dO4eBAwfCxcUF169fx9SpU+Hm5oaffvoJN2/e5JR2IiLoHlyq53nPH8e6HENOTg68H/FGq6WtIJFIoFarERkZidDQUCgUCgtGS9QwVKnF57XXXsPEiRNx5coVo+6uRx55BH/99ZfJgiMiqstkMitkW2cDAGzy7ZH7Xy4k5yVIWJaAuwfvQq1WIzg4GIMGDUJwcDDUarWFIyaq/6qU+Jw6dQrTp08vVt64cWOoVKpqB0VEVB/IJDJs67kNebK8YvtijscgMjISSqUSAKBUKhEVFWXuEIkanColPjY2NkhPTy9WfvnyZXh4eFQ7KCKi+kAqkWJTv00Y+tZQvDh5INZL1ov7gpoGITQ0FD4+PgAAX19fhISEWCpUogajSmN8HnvsMSxevBjbt28HAEgkEty8eRNvvvkmp7MTET0gkUggEQCtTIu73jI88UQQoPvYxLrT65CUloQ3g9+EzEcGubUcO4fthNVDVhi9ajScXJwsGzxRPVWlFp+PPvoIGRkZ8PT0RHZ2Nvr27YvmzZvDyckJ77//vqljJCKqmyQSyDW6l6lyDS6kXRB3nbhxAo3XNkaHiA5oG9UWD514CM2PNUez75rh9xW/WyhgovqvSi0+Li4uOHDgAP755x+cO3cOGRkZCAkJwcCBA00dHxFRnfZ8FLC6i+61RqoRy2VaGbxTvUs8JutmljlCI2qQqpT46PXq1Qu9evUyVSxERPXOF78DC44AOb27I33wEtzbew8A8OnAT5F2OQ15d/IgsZEg5d0UKOY/mM6utWDARPVclRKfzz77rMRyiUQCW1tbNG/eHH369DFaw4KIqMF58DBnz0wAuba46+SGe9AlPgnfJMDqtu4jWGonhbyRXDxM0AhmD5WooahS4vPJJ58gKSkJWVlZ4oJbarUa9vb2cHR0RGJiIgIDA3Ho0CH4+fmZNGAiorpKal04rFJ6Wgrtg6adpPQkfLL8EyzBEgBAQX6BReIjagiqNLj5gw8+wMMPP4wrV64gOTkZycnJuHz5Mrp27YpVq1bh5s2b8Pb2xmuvvWbqeImI6iZBgGuYKwS74q05R7RHkJqWKm5n3ecYH6KaUqUWn7fffhs7d+5EUFCQWNa8eXOsXLkSo0ePxrVr17B8+XJObSeihu1BV5eebRNbtItph5EhI5GcnAyJRIJMIRO5Xrlo5tQMSNTVs7OxM3+sRA1ElRIfpVKJgoLiTbEFBQXiys2+vr64f/9+9aIjIqpnGvk3ws9XfkZUVBQCAwNx7do1hISEIPKPSOApXR2ZhOMjiWpKlbq6+vfvj+nTp+P06dNi2enTpzFz5kwMGDAAAHD+/HkEBASYJkoionpEoVAgLCwMAQEBCAsLg0KhMF6wkLO6iGpMlRKf9evXw83NDaGhobCxsYGNjQ06d+4MNzc3rF+vW5Ld0dERH330kUmCvH79OqZMmYKAgADY2dkhKCgICxcuRF6e8fNvzp07h969e8PW1hZ+fn5Yvny5Sa5PRFRtQtkztYxmwTLxIaoxle7qEgQBeXl5+Pnnn3Hz5k3ExsYCAFq2bImWLVuK9fr372+yIGNiYqDVarFu3To0b94cFy5cwNSpU5GZmYmVK1cCANLT0zF48GAMHDgQX375Jc6fP4/JkyfD1dUV06ZNM1ksREQVVmSMT5lVZQZ1NaXXI6LqkQhCOX+GFKHVamFra4vo6Gi0aNGipuIq14oVK7B27Vpcu3YNALB27Vr873//g0qlglyuWw9j3rx52L17N2JiYip83vT0dLi4uCAtLQ3Ozs41EjsRNRC5uYCtre51377A4cOlVj1z5AxS+6UCAK4GXoVsjAzp6elwdnZGRkEGRrw8An7NuDwIUWkq+vu70i0+UqkULVq0QHJyskUTn7S0NLi5uYnbx44dQ58+fcSkBwDCw8OxbNkyqNVqcb2honJzc5Gbmytul/TUeSKiaiuvq8uqsKur+bXmQJGe+q3bt2L6uemlfpYRUcVUaYzPhx9+iDlz5uDChQvlV64BV69exeeff47p06eLZSqVCl5eXkb19Nv6mWYlWbp0KVxcXMQvLrhIRCZTia6uwHaBSLcr/Q+vVsmtEBUVZYqoiBq0Kk1nHz9+PLKystChQwfI5XLY2RmvOZGSklKh88ybNw/Lli0rs86lS5fQqlUrcfvOnTsYMmQInnjiCUydOrXywRcxf/58vP766+J2eno6kx8iMjsHZwf4HfDD0ilLkZudC4lEAkEQMOHeBLhluUEqSBESEmLpMInqvColPp9++qlJLj579mxMnDixzDqBgYHi67t376J///7o0aMHvvrqK6N63t7eSEhIMCrTb3t7l/wEZADirDQiohpVgeGUnXp2wrpj64zW+FE9owKyACvBit1cRCZQpcRnwoQJJrm4h4cHPDw8KlT3zp076N+/P0JDQ/Htt99CKjXupevevTv+97//IT8/H9bW1gCAAwcOoGXLlvywICLLqERXl55+jR8ACAgIwBarLQAAmZaLGhKZQpXG+BjKyclBenq60Zep3blzB/369YO/vz9WrlyJpKQkqFQqo7E7Tz/9NORyOaZMmYLo6Gj88MMPWLVqlVE3FhFRXSNIdS1FUm21P66JCFVs8cnMzMSbb76J7du3Izk5udh+jca0i1AcOHAAV69exdWrV9GkSROjffrZ+C4uLti/fz9efPFFhIaGolGjRliwYAHX8CGi2qFyK4eItDLdaoZs8SEyjSr9CTF37lwcPHgQa9euhY2NDb755hssWrQIvr6+2LRpk6ljxMSJEyEIQolfhtq3b4+///4bOTk5uH37Nt58802Tx0JEZE76xEcqSBH7eywivo7Avev3AABqtRoRERGIj49HREQE1Gq1JUMlqhOq1OLzyy+/YNOmTejXrx8mTZqE3r17o3nz5mjatCm2bt2KZ555xtRxEhHVPVUY41OUVlr4/ArlMCWsYIUoRMH/J38MeHEAlEolpFIptFotfHx8EB0dzXGNRGWoUotPSkqKONvK2dlZnL7eq1cv/PXXX6aLjoiogUt0TSxWJoccUZ9FQalUAtCtqA8ASqWSa/0QlaNKLT6BgYGIj4+Hv78/WrVqhe3bt6NLly745Zdf4OrqauIQiYjqgSqO8Tn0xCHE2cbBNdMVrtdd0SulFwDALtEOz7R8Brk5uZBAgmxpNk43O404+zj0yO8BO2u7cs5M1DBVKfGZNGkSzp49i759+2LevHl49NFH8cUXXyA/Px8ff/yxqWMkIqqbTNDVleeRh/Vh6wEA/kn+6LVal/goLirwPJ43qntaOI3p+6fj8v3LWDl4ZbWvTVQfVSnxee2118TXAwcORExMDCIjI9G8eXO0b9/eZMERETV0vf1748iNIwCAu4q7SHJKgsf9ktc/a6HUPT/xjOqMucIjqnMqnfhotVps3LgRP/30E65fvw6JRIKAgACMGTMG7dq1q4kYiYjqvip2dS3qvwhhgWFIzHww1mcokHYyDTBYNcTxI0fIlDJYaXQf6VpBW8KZiAioZOIjCAIee+wx/P777+jQoQPatWsHQRBw6dIlTJw4ET/99BN2795dQ6ESETU8UokU/Zr1My7sYbwZuS0S95X3Ya3RrVrPxIeodJVKfDZu3Ii//voLf/75J/r372+07+DBgxgxYgQ2bdqE8ePHmzRIIqI6yQRjfEqiVqsRGRmJ0NBQKBQKSOS668gEGaRaKRMfojJUajr7999/j7feeqtY0gMAAwYMwLx587B161aTBUdEVG9UsaurKLVajeDgYAwaNAjBwcFQq9XQSAv7vX5a8ROanmlqkmsR1UeVSnzOnTuHIUOGlLp/6NChOHv2bLWDIiKikkVGRorr9+jX7bkvuy/ud8l2QZcDXSwVHlGtV6nEJyUlBV5eXqXu9/Ly4pLpRER6NdDVFRoaCh8fHwCAr68vQkJC0Oq9VoiWR4t17DRcw4eoNJVKfDQaDaysSh8WJJPJUFBQUO2giIjqHRN1dSkUCkRHRyMiIgIXLlyAQqGAby9fPHX7KbEOH2hKVLpKz+qaOHEibGxsStyfm5trkqCIiKh0CoUCYWFhxmWNCp/PJdHUzKBqovqgUonPhAkTyq3DGV1ERA/U0Kyuki8lgUaiEWd2EVHJKpX4fPvttzUVBxERVZNGqoFMI4NUw8SHqDT810FEZA4mGuNTFq1Ut36PRMuuLqLSVOlZXUREVPvo1/NpfLcxzjx5BrYOtkg/l47MnEw0mdAELea2sHCERJbHxIeIqJ7IkefAIdcBAJC6I1Usl0CCW2/egssIF3g+5Gmh6IhqB3Z1ERGZgxm6un7s/WOp+6SQ4vy/52s8BqLajokPEVE9sa/3Przw/Aul7m/9UGszRkNUOzHxISKqSWac0u7j5GP03K6iMjQZZouFqLZi4kNEZA5m6Or6cviX6BPUp9T9eXl5NR4DUW3HxIeIqJ7o07QPPnnkk1L3a/O1ZoyGqHZi4kNEVJPM2NUFABKr0q+nLWDiQ8TEh4jIHMzQ1QWUnfioZqmg/FdpljiIaismPkRE9YhUXvrHum2cLfb33Q+1Wm3GiIhqFyY+RET1iI2fDYRWpbcueRZ4IioqyowREdUuXLmZiKgmmXuMj0SCDv90wNBWQ5F8LxkpI1OQ/1A+fln2CwBABhlCQkLMGhNRbcIWHyIiczDTGB8AcHN3w77L+7AuYh2enPAkMuwyEOMbAwCQy+RQKBRmi4WotmHiQ0RUDykUCoSFhcHBVvfsLnFhQw0gmDEJI6ptmPgQEdUkM3d1FSWV6D7mDVd0FjRMfKjh4hgfIiJzuH0b+N//zH5ZqewfQFYk8fnfQsCqHq/p07gxMH484Oho6UioFmLiQ0RUk/QtPgkJwAcfmP3ysjAAvY0Tnx0/HMd9xWFAWgAA6HoHaJ9g9tBqlkoFLF5s6SioFmJXFxFRTRoyxKKXlz7o1dJKClt4vG/8D6ftpmLaY8C0x4AOM4GYRhYKsKbExFg6Aqql2OJDRFSTdu0CTp4EsrMtcvmuyf8CF9/BxSYX0SWui1je+nZro3o/zh6Ht7tMrZEYIiMjMWfu3GLlK1esMO3U+sRE4KmnTHc+qpeY+BAR1SSZDOje3WKXHy70x9HbAxDZNxJLXlmCd86/AwAIsAuA3WU7ZD+kS8jc+/QBegyokRgCO3VCzCefQKlUQiqVQqvVwtfXFwFTpgCmnFp/61bha85co1Iw8SEiqsckEgl6+PVAD78eePbIszjjewaSHAncc93xebvP8c25b3DF5wps7WxNfm1BKyDtaBo0aRoc+/gYrsZdhbeXN1QJKjQPag7hlABtHy2kNhx1QebDxIeIqIFQKBSwtrdGQU4Bcm/kImh+EJZiKQqkBbjT7w7QybTXu/zCZSjXFT4UVQYZkpAEGWSIRzwAwKWXCzr9baILW3jpAKobmGYTETUgjh2KT/G20lrBJsrG5NdK/TO13Dpp/6RBm1cDU+vZ1UWlYIsPEVED0vr/WiPphyRoMjS4cPACHA7qVnYWck2fKAha3Tml9lI0faup0T7leiVy4nN09bigIpkREx8iogbExtsGDuMdEBkZidSCVDHxyfsnDylJKXDzcKvwudRqNSIjIxEaGlri87/0CY3GRgPnF5yN6iTtT8KD3i7AVA0+7OqiCmBXFxFRA6JWqxEcHIxBgwZh8w+bxfKmfzfFr76/IuVeSqXPExwcDLVaXayOtkCX0SSrk43qqNVq/Hv838Jz3St+bLWxq4tKwcSHiKgBiYyMhFKpG3Acmx9rtM+/wB+nfz5d6fMolUpERUUVq5OXkwcA0EJrVCcyMhI5eTlivbNnzlb+jRBVERMfIqIGJDQ0FD4+PgCANO80LHxiodH+1i1bl3RYmefx9fUtcSFCaytrALrEx7BOaGgorG2sxXrt27av/BspiWFXF1t8qBRMfIiIGhCFQoHo6GhERETgk48/wV/Bf2FP5z3ifid7p0qf58KFCyWO8ZFodYmIl7eXUR2FQoG+/fuK9VycXKrzlogqhYkPEVEDo1AoEBYWBmdHZwBFntxeUPGWEv15Skp6gMJZXXYOdsXqGLb46OtVGwc3UwVwVhcRUQMllej+9jVMfF7+5WXcuXTHJOefnT0bdrDDncw7GLhpoNG+0XdGozV03WrTdk/Dq4+/ihAfEz63i11dVAomPkREDZSdtR0A4ye3R92OwgXZBZOcf5ZmFgAgoyADf8b/abSvV1YvMfHZe3kv7hy4g4jxESa5LlFZ2NVFRNRA9WnaB10adzFq8ZEJMpOdX6bVncswsdIzLJNqpbibfrf6F2RXF1UAW3yIiBooWytbHJ9yHJfjLkN5VDc1veOmjnCWOEMikUAQBLi4umDFihVwcHBAZmYm5rwxB2lpaQAAF1cXLHp3ERa+uxBpqWniMfrvMo0u8ZGmSnFr5i0oXAvH+cTFxCElWrdm0LZV2/Dh4A+hfkZd6nihSmNXF5WCiQ8RUQMmkUggl8vF7YnaicYVkgHVZJW4ORuzjfalv5xuXFaCvPw8xJ6PRVhYmFhm52VnVGfk6ZGIiooyqkNUE9jVRUTUwDl2LP7gUlNS2imLrfPTZFYTuI50FbdtNbYlrgVUKezqogpgiw8RUQPX6PFGaPdrO9w7dQ/Xrl0DAPj4+iAlOQWNGzeGnX1h60x2VrZYJzAwEHb2dsjOysadO3fg5u6GlOQU4+/5KXjh5ReKdWHZNbNDx5864heHX+CU5QQbmY3purkAdnVRqZj4EBE1cBKpBO7D3OE+zB0t0bLc+iXVqchxJdEPrNYPhK4WtvhQBbCri4iILEYr1c3ukmpM/OuILT5UCiY+RERkMfoWH6mWv47IPPiTRkREFqOV6Vp82NVF5sLEh4iISqVWqxEREYH4+HhERERArVab9Pz6ri7nDGdEPRKF7GvZxa5d0jXL2geAXV1UKg5uJiKiEqnVagQHB0OpVEIqlUKr1cLHxwfR0dEmm4GVY5Mjvk7fm464FXFou7at0bWLXrOsfUTlYYsPERGVKDIyEkqlbkVnrVbXMqNUKhEVFWWya/zS6xej7cSricWuXfSape5jVxdVABMfIiIqUWhoKHx8fAAAUqnu14Wvr2/1Fxo0cLrLaYx7dZy47ebsVuzaRa9Z1j4Ru7qoFOzqIiKiEikUCkRHRyMqKgqBgYG4du0aQkJCTNqtZGVlZfSQVGupdbFrF71m9o5s/NL2F6T7pcPZ2Rm3J96GZooGjXqyxYfKx8SHiIhKpVAoxOdnBQQEmPz8UonUKPERCgpbagyvrZd9PRuXp18GAEggwX3cBwCkHk5Fz5hW7MagcjHxISIiiyma+MQlxeHP43+WWt/+rD1aoEWxck26BppsoTDxYVcXlYKJDxERWYxUIhWntANATEIM5v0xr9T6IddC8BE+AgBs774dAQkBePjawwAArUZb6nFEekx8iIjIYnr69UT87XhxOzAhEHP2zCm1vkeah/j6vu195FnlFW7nZsBGv8EWHyoFEx8iIrKY1Y+sxqjAUcBS3bbHfQ88cvqRCh079KGhiL9emDSpU9RoVBNBUr3CcWBERGQx1jJrDAkeAm3vynVTZSIT95zuQZNfOD7o4qUYU4dH9RBbfIiIyOI67u6IsFZhUCepdeN+BC08PTyxectmPPvMs0i6l4RGjXTtOffu3YPUW4o/X/gTm3dsFs/RPKh54QnZ1UWlYOJDREQW5+bmhoOxB0tcM2j/5f3iej4AjNb28fT2BG7ozmFnb2/Bd0B1BRMfIiKqFUpbM6joej6Gr2XWhU9113BWF1VAnRnj89hjj8Hf3x+2trbw8fHBc889h7t37xrVOXfuHHr37g1bW1v4+flh+fLlFoqWiIjMwuC3mKagcLwPu7qoNHUm8enfvz+2b9+O2NhY7Ny5E3FxcRgzZoy4Pz09HYMHD0bTpk0RGRmJFStW4N1338VXX31lwaiJiKhGFTb4QKNliw+Vr850db322mvi66ZNm2LevHkYMWIE8vPzYW1tja1btyIvLw8bNmyAXC5HcHAwzpw5g48//hjTpk2zYORERFRdarUakZGRCA0NNX5WmMGf7/uWH8I5/xFw1iRhoIDCNX2IDNSZFh9DKSkp2Lp1K3r06AFra90D7Y4dO4Y+ffpALpeL9cLDwxEbGwu1Wl3quXJzc5Genm70RUREtYdarUZwcDAGDRqE4OBgo890ibTwwaSh+7vC5+arcLjzHr5Pal7SqYjqVuLz5ptvwsHBAe7u7rh58yb27Nkj7lOpVPDy8jKqr99WqVSlnnPp0qVwcXERv/z8/GomeCIiqpLIyEgolUoAgFKpRFRUlLjPpYdLicfkpfqaJTaqeyya+MybNw8SiaTMr5iYwgWp5syZg9OnT2P//v2QyWQYP348hGoOYJs/fz7S0tLEr1u3blX3bRERkQmFhobCx8cHAODr6ytOaweA0QtGI3dTLj5+6GOs9l8llkvrzkgOMjOL/mTMnj0bEydOLLNOYGCg+LpRo0Zo1KgRHnroIbRu3Rp+fn44fvw4unfvDm9vbyQkJBgdq9/29vYu9fw2NjawsWFPMBFRbaVQKBAdHW20fo+eVCpF+HPh6DK8C/Zt2wm8oCuXCHWqQ4PMyKKJj4eHBzw8PMqvWALtg9H7ubm5AIDu3bvjf//7nzjYGQAOHDiAli1bGg+EIyKiOqfoWj4l7R80aCAu4DoAQCLISq1LDVudSIlPnDiBL774AmfOnMGNGzdw8OBBPPXUUwgKCkL37t0BAE8//TTkcjmmTJmC6Oho/PDDD1i1ahVef/11C0dPRETmoP+jFwCgrRO/3sgC6sRPhr29PX766SeEhYWhZcuWmDJlCtq3b48jR46I3VQuLi7Yv38/4uPjERoaitmzZ2PBggWcyk5E1EBY2xQmPuzqotJIhOqODq5n0tPT4eLigrS0NDg7O1s6HCIiqqD8FDWOup8FAGgkGjQ51wQt27a0cFRkLhX9/c2UmIiI6gWZVeG4Hpkgw42ON3BkzxELRkS1ERMfIiKqF6QyGRJcC5ckkWvkiNoSVcYR1BAx8SEionqjteQd3HGPE7ed7J0sGA3VRkx8iIiofpBI0F59Ax7ydWKRlYQLGZIxJj5ERFSvyASN+Foo4PwdMsbEh4iI6hUmPlQWJj5ERFQ/SHRPamfiQ2Vh4kNERPWKYeJzP+k+1Gq1uJ1yLwURv0fgWsw1RPwegZSUFEuESBbExIeIiOoVw8Sn418dsaXNFiQoE3Bt/TUc9zwOq2FWuNn6JqyGWWG/536ozqgsGC2ZGxMfIiKqHx50dXnkphoVt1O1w+6vduPGqhuwF+yN9nlrvHFx9UVzRUi1ABMfIiKqVwLvJ+JO6BajMg83D9hbFSY913BNfO3j5mO22MjymPgQEVH98KDFBwCecbyK+Enx4raV1AoyQfdIC8FaQLdN3cR9NtY25ouRLI6JDxER1Us29oUJjTpTjby8PACAVC6FlVvhwobpmenQClqzx0eWwcSHiIjqJZl14UNLvz31La4kXgEA3C+4j9E7R4v71p1Yhzar2yArP8vsMZL5MfEhIqL6waCrC4IANwc3cVOmlUGm1SVCGqkGGqnGaF9sciz+vvG32UIly2HiQ0RE9VJr79bi624+3eAscwYAWMut0a95P3GfPiHK0+SZNT6yDD69jYiI6h9BgNS68G/7gf83EJJ0XYuQi70Llg1Zhsj5kQCAkf+NhCARoHlCU+KpqH5hiw8REdUPhl1dAGROhWN8JCkSoED3+nridWRqM43qjjo5Cjn/5tR4iGR5THyIiKhecn/UHdqOWmQa/JeEJGzUbES0OhraYcYzuRJiEywUKZkTu7qIiKh+KDK42crJCp0OdkJwcDCUSiWkUim0Wi18fX0REhICbAZe6/oaJl6ZCADwdPe0TNxkVkx8iIio3lIoFIiOjkZUVBQCAwNx7do1hISEQKFQAAD6D+wP6Ga5Q24lt2CkZC5MfIiIqF5TKBQICwsDAAQEBBjtM1zkUCgQzBoXWQbH+BARUf1QpKurQofICo8R8pn4NARMfIiIqMGSWBcmPloNH1vREDDxISKiBsuwxcdrkRd+/vLnap1PrVYjIiICarVafB0fH2/0Xa1WVzdsszF8PxUprws4xoeIiOqHKnR1yWxkxtuvynD7kdto4t+k0pdXq9XiDDIvLy9IJBKoVCpxNpn+u4+PD6Kjo8UB1rWV4fsxjLm08rqCLT5ERNRgdXuqG9SOha0WDnkOOPHXiSqdKzIyEkqlEgCQkJAAlUoFANBqtUbflUoloqKiqhO2WRi+H8OYSyuvK5j4EBFR/VCFFh/fAF90j+2OKx5XxLKWLVpW6fKhoaHw8fEBAHh7e8Pb2xsAIJVKjb6L6wjVcobvxzDm0srrCnZ1ERFRg+bt642C5gVAkm7b0daxSucxXDNInwwYrh9U0jpCtVnR96OPubTyuoKJDxERNXjVmd2VcyMHyb8nQ9DoWplaoiUyL2WKr3HJ+HvmJd3jM8ri3NUZzg87V/JdmJ7hGkgVKa8LmPgQEVH9UIWuLrG6rLC+Nr/iiY8mR4PIzpHIv5dfqetVROfzneHYtmqtT1Q6jvEhIqIGzzDxqcxChrm3cmsk6QGAjNMZNXLeho4tPkRE1OAZJj6xH8TC9QtXeAR6lH+gQeOQ0FZA05ebwsHBAZmZmYiPj0dAQAAcHByMDtHv8/T0xM0bNwEA/k39kZiYCOerzsj8MbPYuU1JrVYjMjISoaGh4vT0yMhIBAUFIS4uDqGhoQBQ4TqGZXVhvA8THyIiqn+q0dXluNcRW9tsxQTlhHJ/kevH9QDAvgv7sPndzTh69Ch69exV4jo3arUanYI7QalUQiKRQHgQp36Nn0clj+J1vA4AyEg3fYtP0TV4jh49ip49exo9vd5wDaKK1Klr6xMx8SEiogYvoXUC2v7eVtz2y/VDVFRUuQN4DRMfLbRQKpXYsWNHsXVu9OcxXANHMEjO9Gv8aASNWHbz+k00R/NqvjNjkTsiMUE5AQ5wAJTAmeFn8ILyBf0b0EkwOKAidbTGdRt5NILUWgrvSd5wf8TdpPGbAhMfIiKqPySSSrf2AMCNnjcw/f50rPtqHQDAWmpdofVpiiY+vr6+eOKJJ/Dpp59CqVQWW+dGvwZOaS0+gkQAHpzSv4l/pd9HeVw2uSAc4YUFF4Fe6FX2QRWpo/cvkIxkAEDKgRT0TOwJqbx2DSdm4kNERPXPhQtAz54Vri5pewWXfZNw0/0m/JP9oZBYQTF8eJnH/J93EjbZ22IePgMA2HcE5IPvYcC61rB5ToC/YA2p5B5ClvkYHaffJ5FIIGh1WY5EqkuCFNES4HddvQ/2vYlDCb9V/D1XwIfRG+AFX5OeszSaNA00vQdBapVTfOfChcDgwWaJoygmPkREVH/Y2gLZ2UBmJvDvvxU+TOoBwBfQSh/022hQ7vHzXgMc7rcSt9Pk+bhun1eFoAsl2RTOEFNbaXHdLrda5ytKC92U/1T7VEx+YbJJz6339s63ERKva+XKiTwJa00JY5Xu3auRa1cEEx8iIqo/3nwT+OADIK9yCYh+BSCNVDfGRqjAai9qW8ApvbCebYEWXtUcj+yUVziVyzlHUu3zFSXX6B7KqpXmQ46aebJ6vqzw3udaSeGkKaOyBTDxISKi+mPhQuCddyp9mPSXqcCZDYWJj7UdkFP2b2zNUkdIhcLEZ1rfV7F82WeVvrahhG2JuPRbDADgveGf4rtXf6zW+Yr6d+tx5N3Pg49bE6iW1UxG8s2fG8TXQuxlwK+EZQEMF5s0MyY+RERUv0grP5hWItEdIyY++QKUpxLg08Wn1GO0Gi1a325deA4raZWubRSHVeHxl2OvoOCGBmfOnAEA9OvXz2hNHcN1c4qus1P0u76uflVqQSJAnZZW7DyG56rsujz647RCYauVVkC174mpMfEhIqIGT1ok8QGA2K6xyFiRgRZvtCjxmLk/zsWA8wPE7dz86o/HkcgKW0K+Xvc1tn+1XZz55e3tjX///VdcU0e/bg4AcW0e/eywot/16/Gok9VwghNu3L6B0W1Gi2v16NffKbrOT0XX5TE87gO/D8RyoQoz7Gpa7UrDiIiILEDyoOvlZqObRuW3f7xd6jFdLncx2lbJVdUPxOC3sgQSo8RBpVKVuEaQ4dpA+vWAin7Xry8kEXTvM1eTC5VKZXQewHidIcPy8hgeVyAUiOWGrT+1BVt8iIiowdO3+KwbtA5Zt7MwJmkMAMDZoeQnpGsFLWRambi9znUdvnj9i2rHYdjiMwzDEIpQCA8W9rGR26DLL12wSr4KuXm5sLWxhct7LgAglkkggQCh2HdbG1s8/MvDyEKW7v1aSeHdyBsqlcporSHDdYaKrkFUFsPjpAZdW5V90r05MPEhIqIGT/JgXle6fTpG/zEaePD7XiaRlVhfo9WIA5vv+NzBmug1JnlUg9SmMGlo8uA/UR6Q808O2qO9bjsXyDism/YllpUmV3es9EGTUst2LXHxz4uIiopCSEiIGLtCoUB0dHSx8vIYHnd1/lXgQcMZu7qIiIhqIX2LDwA4ujiKr4WCkn9xF2gLINXqjpHKpSZ7PpVLXxc4dXYyyblKI7WXwv8lfygUCoSFhRWLvbTy8uiPM2zxMVzZurZgiw8RETV4EoPp1buv7sYgDAIAqFJV+Dry62L1czW5aC3oZnQJUtP9cpfZyhByMgSajJpb/EYqlxq1LJmcwUx1/Rij2oSJDxERNXgSg9/WH/z7gZj4xN+Lx4u/vlj8AAE4JBzSvTRh4gPokjArp7r761mQFN4PdnURERHVQl0aG8zQkgAaia7FxVpjDbtcO9jl2okPDwVgtHChg62DWWJUq9WIiIiAWq022o6Pjzcqr8ixNclwJhe7uoiIiGqhp9s9DT8XP1xNuQoAkHwgAfKAFqoW+H2p7qmhcY5xSNmagvc+fg9ZqVnisb5ONf/Qz6Lr6xw9elRcz8dwrZ6S1t2p6to8VY1TqVKiFXTPMEtLT6uR61QHW3yIiKjBk0gk6NO0DyZ3mozJnSZD4lb8kQpBGUFw+ckF6UfSIT1b+OszMzuzxuMrur6O4Xo+hmv1lLTuTlXX5qlqnAXawnV8YmNia+xaVcXEh4iIqIigtUE4ZXMK/+E/3MANsTxUEorhLsPRG73FMifXmp2FBRSukwMAvr6+eOKJJ8Rt/Syq0tbdKXpsRdfmqWqcUllhatGiecmrXlsSu7qIiIiK8B/hjynKKYiKioJnlCeS5yYDAO5vvI/ZmG1U19rGusbjKWl9Hf12YGAgrl27Vuq6O1Vdm6eqcTZu0hiI1207OjqWfYAFMPEhIiIqgX5dmgyPDDHxKYljB/P8ctfHU9J2QEBApY6tSYYtPly5mYiIqI5xbO+Ijn91RPrx9GL75F5yeIzxsEBUtZjBIJraOJ2diQ8REVE5XHu7wrW3q6XDqBsMxoUL2tqX+HBwMxEREZlOLV+5mYkPERFRBZhzEcA6zSDxuTfgHm78cKP0uhbAxIeIiKgc+kUABw0ahODgYCY/Zci3yxdfSwokOPTsoVp1v5j4EBERlcOciwDWdVcHXUWMb4y4bVtgW6vuFxMfIiKicphzEcC67r7/fcycNhOJzokAALlUXqvuFxMfIiKicugXAYyIiMCFCxdqdBHAuk4q0aUWGumDB706WuOFgy/gmvqaJcMScTo7ERFRBZhzEcC6zNbKFkBh4qPN12LbhW1Q2CqwZtgaS4YGgC0+REREZEITOkxAE+cmYuIj08oAAImZiZYMS8TEh4iIiEwm1DcUN2bdQGvv1gAKEx+NoLFkWCImPkRERGRSUokUUitdimGXb4cX9r0AW7WthaPSYeJDREREJqeVFa7a/MTxJ9BpVycLRlOIiQ8RERGZ3P2e94227VR2ForEGBMfIiIiMrmQd0Pwms9r4rZcKrdgNIWY+BAREZHJKRQK7D60W9yWCrUj5agdURAREVG949bITXwt0UjKqGk+dS7xyc3NRceOHSGRSHDmzBmjfefOnUPv3r1ha2sLPz8/LF++3DJBEhEREazkheskS7RMfKpk7ty58PX1LVaenp6OwYMHo2nTpoiMjMSKFSvw7rvv4quvvrJAlERERGRlXZj4SDW1I+WoU4+s2Lt3L/bv34+dO3di7969Rvu2bt2KvLw8bNiwAXK5HMHBwThz5gw+/vhjTJs2zUIRExERNVwya5n42iHBAesmrkNmZia6Tu6KnkN7WiSm2pF+VUBCQgKmTp2KzZs3w97evtj+Y8eOoU+fPpDLC0eNh4eHIzY2Fmq1utTz5ubmIj093eiLiIiIqk8qk0IL3Xo+nqmeaPldS4T8GIJlry0r83dzjcZkkatWkiAImDhxImbMmIHOnTuXWEelUsHLy8uoTL+tUqlKPffSpUvh4uIifvn5+ZkucCIiogYurnlcsbKsrCxERUVZIBoLd3XNmzcPy5YtK7POpUuXsH//fty/fx/z5883eQzz58/H66+/Lm6np6cz+SEiIjKRYYeG4bmw55CbmQuJRAJBEKCWqRESEmKReCya+MyePRsTJ04ss05gYCAOHjyIY8eOwcbGxmhf586d8cwzz+C7776Dt7c3EhISjPbrt729vUs9v42NTbHzEhERkWn4NvHFj8d/RFRUFAIDA3Ht2jWEhIRAoVBYJB6JIAiCRa5cCTdv3jQae3P37l2Eh4fjxx9/RNeuXdGkSROsXbsW//vf/5CQkABra2sAwFtvvYWffvoJMTExFb5Weno6XFxckJaWBmdnZ5O/FyIiIjK9iv7+rhOzuvz9/Y22HR0dAQBBQUFo0qQJAODpp5/GokWLMGXKFLz55pu4cOECVq1ahU8++cTs8RIREVHtVCcSn4pwcXHB/v378eKLLyI0NBSNGjXCggULOJWdiIiIRHWiq8uc2NVFRERU91T093edmM5OREREZApMfIiIiKjBYOJDREREDQYTHyIiImowmPgQERFRg8HEh4iIiBoMJj5ERETUYDDxISIiogaDiQ8RERE1GPXmkRWmol/I2vChqERERFS76X9vl/dACiY+Rdy/fx8A4OfnZ+FIiIiIqLLu378PFxeXUvfzWV1FaLVa3L17F05OTpBIJCY7b3p6Ovz8/HDr1i0+A6wG8T6bB++z+fBemwfvs3nU5H0WBAH379+Hr68vpNLSR/KwxacIqVSKJk2a1Nj5nZ2d+Y/KDHifzYP32Xx4r82D99k8auo+l9XSo8fBzURERNRgMPEhIiKiBoOJj5nY2Nhg4cKFsLGxsXQo9Rrvs3nwPpsP77V58D6bR224zxzcTERERA0GW3yIiIiowWDiQ0RERA0GEx8iIiJqMJj4EBERUYPBxMdMVq9ejWbNmsHW1hZdu3bFyZMnLR1Snfbuu+9CIpEYfbVq1Urcn5OTgxdffBHu7u5wdHTE6NGjkZCQYMGI64a//voLjz76KHx9fSGRSLB7926j/YIgYMGCBfDx8YGdnR0GDhyIK1euGNVJSUnBM888A2dnZ7i6umLKlCnIyMgw47uo/cq7zxMnTiz28z1kyBCjOrzP5Vu6dCkefvhhODk5wdPTEyNGjEBsbKxRnYp8Vty8eRPDhg2Dvb09PD09MWfOHBQUFJjzrdRqFbnP/fr1K/YzPWPGDKM65rrPTHzM4IcffsDrr7+OhQsXIioqCh06dEB4eDgSExMtHVqdFhwcDKVSKX79888/4r7XXnsNv/zyC3bs2IEjR47g7t27GDVqlAWjrRsyMzPRoUMHrF69usT9y5cvx2effYYvv/wSJ06cgIODA8LDw5GTkyPWeeaZZxAdHY0DBw7g119/xV9//YVp06aZ6y3UCeXdZwAYMmSI0c/3999/b7Sf97l8R44cwYsvvojjx4/jwIEDyM/Px+DBg5GZmSnWKe+zQqPRYNiwYcjLy8O///6L7777Dhs3bsSCBQss8ZZqpYrcZwCYOnWq0c/08uXLxX1mvc8C1bguXboIL774orit0WgEX19fYenSpRaMqm5buHCh0KFDhxL3paamCtbW1sKOHTvEskuXLgkAhGPHjpkpwroPgLBr1y5xW6vVCt7e3sKKFSvEstTUVMHGxkb4/vvvBUEQhIsXLwoAhP/++0+ss3fvXkEikQh37twxW+x1SdH7LAiCMGHCBOHxxx8v9Rje56pJTEwUAAhHjhwRBKFinxW///67IJVKBZVKJdZZu3at4OzsLOTm5pr3DdQRRe+zIAhC3759hVdffbXUY8x5n9niU8Py8vIQGRmJgQMHimVSqRQDBw7EsWPHLBhZ3XflyhX4+voiMDAQzzzzDG7evAkAiIyMRH5+vtE9b9WqFfz9/XnPqyE+Ph4qlcrovrq4uKBr167ifT127BhcXV3RuXNnsc7AgQMhlUpx4sQJs8dclx0+fBienp5o2bIlZs6cieTkZHEf73PVpKWlAQDc3NwAVOyz4tixY2jXrh28vLzEOuHh4UhPT0d0dLQZo687it5nva1bt6JRo0Zo27Yt5s+fj6ysLHGfOe8zH1Jaw+7duweNRmP0PxMAvLy8EBMTY6Go6r6uXbti48aNaNmyJZRKJRYtWoTevXvjwoULUKlUkMvlcHV1NTrGy8sLKpXKMgHXA/p7V9LPsn6fSqWCp6en0X4rKyu4ubnx3lfCkCFDMGrUKAQEBCAuLg5vvfUWhg4dimPHjkEmk/E+V4FWq8WsWbPQs2dPtG3bFgAq9FmhUqlK/JnX7yNjJd1nAHj66afRtGlT+Pr64ty5c3jzzTcRGxuLn376CYB57zMTH6qThg4dKr5u3749unbtiqZNm2L79u2ws7OzYGRE1Tdu3Djxdbt27dC+fXsEBQXh8OHDCAsLs2BkddeLL76ICxcuGI0FJNMr7T4bjj9r164dfHx8EBYWhri4OAQFBZk1RnZ11bBGjRpBJpMVmyWQkJAAb29vC0VV/7i6uuKhhx7C1atX4e3tjby8PKSmphrV4T2vHv29K+tn2dvbu9ig/YKCAqSkpPDeV0NgYCAaNWqEq1evAuB9rqyXXnoJv/76Kw4dOoQmTZqI5RX5rPD29i7xZ16/jwqVdp9L0rVrVwAw+pk2131m4lPD5HI5QkND8eeff4plWq0Wf/75J7p3727ByOqXjIwMxMXFwcfHB6GhobC2tja657Gxsbh58ybveTUEBATA29vb6L6mp6fjxIkT4n3t3r07UlNTERkZKdY5ePAgtFqt+EFHlXf79m0kJyfDx8cHAO9zRQmCgJdeegm7du3CwYMHERAQYLS/Ip8V3bt3x/nz540SzQMHDsDZ2Rlt2rQxzxup5cq7zyU5c+YMABj9TJvtPpt0qDSVaNu2bYKNjY2wceNG4eLFi8K0adMEV1dXo9HrVDmzZ88WDh8+LMTHxwtHjx4VBg4cKDRq1EhITEwUBEEQZsyYIfj7+wsHDx4UTp06JXTv3l3o3r27haOu/e7fvy+cPn1aOH36tABA+Pjjj4XTp08LN27cEARBED788EPB1dVV2LNnj3Du3Dnh8ccfFwICAoTs7GzxHEOGDBE6deoknDhxQvjnn3+EFi1aCE899ZSl3lKtVNZ9vn//vvDGG28Ix44dE+Lj44WIiAghJCREaNGihZCTkyOeg/e5fDNnzhRcXFyEw4cPC0qlUvzKysoS65T3WVFQUCC0bdtWGDx4sHDmzBlh3759goeHhzB//nxLvKVaqbz7fPXqVWHx4sXCqVOnhPj4eGHPnj1CYGCg0KdPH/Ec5rzPTHzM5PPPPxf8/f0FuVwudOnSRTh+/LilQ6rTxo4dK/j4+AhyuVxo3LixMHbsWOHq1avi/uzsbOGFF14QFAqFYG9vL4wcOVJQKpUWjLhuOHTokACg2NeECRMEQdBNaX/nnXcELy8vwcbGRggLCxNiY2ONzpGcnCw89dRTgqOjo+Ds7CxMmjRJuH//vgXeTe1V1n3OysoSBg8eLHh4eAjW1tZC06ZNhalTpxb7Q4n3uXwl3WMAwrfffivWqchnxfXr14WhQ4cKdnZ2QqNGjYTZs2cL+fn5Zn43tVd59/nmzZtCnz59BDc3N8HGxkZo3ry5MGfOHCEtLc3oPOa6z5IHQRMRERHVexzjQ0RERA0GEx8iIiJqMJj4EBERUYPBxIeIiIgaDCY+RERE1GAw8SEiIqIGg4kPERERNRhMfIiIiKjBYOJDRHXKxIkTIZFIIJFIYG1tDS8vLwwaNAgbNmyAVqut8Hk2btwIV1fXmguUiGolJj5EVOcMGTIESqUS169fx969e9G/f3+8+uqrGD58OAoKCiwdHhHVYkx8iKjOsbGxgbe3Nxo3boyQkBC89dZb2LNnD/bu3YuNGzcCAD7++GO0a9cODg4O8PPzwwsvvICMjAwAwOHDhzFp0iSkpaWJrUfvvvsuAGDz5s3o3LkznJyc4O3tjaefftroidFEVLcx8SGiemHAgAHo0KEDfvrpJwCAVCrFZ599hujoaHz33Xc4ePAg5s6dCwDo0aMHPv30Uzg7O0OpVEKpVOKNN94AAOTn52PJkiU4e/Ysdu/ejevXr2PixImWeltEZGJWlg6AiMhUWrVqhXPnzgEAZs2aJZY3a9YM7733HmbMmIE1a9ZALpfDxcUFEokE3t7eRueYPHmy+DowMBCfffYZHn74YWRkZMDR0dEs74OIag5bfIio3hAEARKJBAAQERGBsLAwNG7cGE5OTnjuueeQnJyMrKysMs8RGRmJRx99FP7+/nByckLfvn0BADdv3qzx+Imo5jHxIaJ649KlSwgICMD169cxfPhwtG/fHjt37kRkZCRWr14NAMjLyyv1+MzMTISHh8PZ2Rlbt27Ff//9h127dpV7HBHVHezqIqJ64eDBgzh//jxee+01REZGQqvV4qOPPoJUqvv7bvv27Ub15XI5NBqNUVlMTAySk5Px4Ycfws/PDwBw6tQp87wBIjILtvgQUZ2Tm5sLlUqFO3fuICoqCh988AEef/xxDB8+HOPHj0fz5s2Rn5+Pzz//HNeuXcPmzZvx5ZdfGp2jWbNmyMjIwJ9//ol79+4hKysL/v7+kMvl4nE///wzlixZYqF3SUQ1gYkPEdU5+/btg4+PD5o1a4YhQ4bg0KFD+Oyzz7Bnzx7IZDJ06NABH3/8MZYtW4a2bdti69atWLp0qdE5evTogRkzZmDs2LHw8PDA8uXL4eHhgY0bN2LHjh1o06YNPvzwQ6xcudJC75KIaoJEEATB0kEQERERmQNbfIiIiKjBYOJDREREDQYTHyIiImowmPgQERFRg8HEh4iIiBoMJj5ERETUYDDxISIiogaDiQ8RERE1GEx8iIiIqMFg4kNEREQNBhMfIiIiajCY+BAREVGD8f/1z7iTJkpzmwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_2.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "steps=250\n",
    "\n",
    "distance=0\n",
    "x=0\n",
    "distance_list=[]\n",
    "steps_list=[]\n",
    "while x<steps:\n",
    "    distance+=np.random.randint(-1,2)\n",
    "    distance_list.append(distance)\n",
    "    x+=1\n",
    "    steps_list.append(x)\n",
    "plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
    "\n",
    "steps_list=np.asarray(steps_list)\n",
    "distance_list=np.asarray(distance_list)\n",
    "\n",
    "X=steps_list[:,np.newaxis]\n",
    "\n",
    "#Polynomial fits\n",
    "\n",
    "#Degree 2\n",
    "poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly=poly_features.fit_transform(X)\n",
    "\n",
    "lin_reg=LinearRegression()\n",
    "poly_fit=lin_reg.fit(X_poly,distance_list)\n",
    "b=lin_reg.coef_\n",
    "c=lin_reg.intercept_\n",
    "print (\"2nd degree coefficients:\")\n",
    "print (\"zero power: \",c)\n",
    "print (\"first power: \", b[0])\n",
    "print (\"second power: \",b[1])\n",
    "\n",
    "z = np.arange(0, steps, .01)\n",
    "z_mod=b[1]*z**2+b[0]*z+c\n",
    "\n",
    "fit_mod=b[1]*X**2+b[0]*X+c\n",
    "plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
    "plt.title(\"Polynomial Regression\")\n",
    "\n",
    "plt.xlabel(\"Steps\")\n",
    "plt.ylabel(\"Distance\")\n",
    "\n",
    "#Degree 10\n",
    "poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
    "X_poly10=poly_features10.fit_transform(X)\n",
    "\n",
    "poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
    "\n",
    "y_plot=poly_fit10.predict(X_poly10)\n",
    "plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#Decision Tree Regression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "regr_1=DecisionTreeRegressor(max_depth=2)\n",
    "regr_2=DecisionTreeRegressor(max_depth=5)\n",
    "regr_3=DecisionTreeRegressor(max_depth=7)\n",
    "regr_1.fit(X, distance_list)\n",
    "regr_2.fit(X, distance_list)\n",
    "regr_3.fit(X, distance_list)\n",
    "\n",
    "X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
    "y_1 = regr_1.predict(X_test)\n",
    "y_2 = regr_2.predict(X_test)\n",
    "y_3=regr_3.predict(X_test)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure()\n",
    "plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
    "plt.plot(X_test, y_1, color=\"red\",\n",
    "         label=\"max_depth=2\", linewidth=2)\n",
    "plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
    "plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
    "\n",
    "plt.xlabel(\"Data\")\n",
    "plt.ylabel(\"Darget\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a tree, regression\n",
    "\n",
    "There are mainly two steps\n",
    "1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$.  \n",
    "\n",
    "2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
    "\n",
    "How do we construct the regions $R_1,\\dots,R_J$?  In theory, the\n",
    "regions could have any shape. However, we choose to divide the\n",
    "predictor space into high-dimensional rectangles, or boxes, for\n",
    "simplicity and for ease of interpretation of the resulting predictive\n",
    "model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
    "MSE, given by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\overline{y}_{R_j}$  is the mean response for the training observations \n",
    "within box $j$. \n",
    "\n",
    "\n",
    "Unfortunately, it is computationally infeasible to consider every\n",
    "possible partition of the feature space into $J$ boxes.  The common\n",
    "strategy is to take a top-down approach\n",
    "\n",
    "The approach is top-down because it begins at the top of the tree (all\n",
    "observations belong to a single region) and then successively splits\n",
    "the predictor space; each split is indicated via two new branches\n",
    "further down on the tree. It is greedy because at each step of the\n",
    "tree-building process, the best split is made at that particular step,\n",
    "rather than looking ahead and picking a split that will lead to a\n",
    "better tree in some future step.\n",
    "\n",
    "\n",
    "### Making a tree\n",
    "\n",
    "In order to implement the recursive binary splitting we start by selecting\n",
    "the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j < s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j \\geq s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so that we obtain the lowest MSE, that is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which we want to minimize by considering all predictors\n",
    "$x_1,x_2,\\dots,x_p$.  We consider also all possible values of $s$ for\n",
    "each predictor. These values could be determined by randomly assigned\n",
    "numbers or by starting at the midpoint and then proceed till we find\n",
    "an optimal value.\n",
    "\n",
    "For any $j$ and $s$, we define the pair of half-planes where\n",
    "$\\overline{y}_{R_1}$ is the mean response for the training\n",
    "observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
    "response for the training observations in $R_2(j,s)$.\n",
    "\n",
    "Finding the values of $j$ and $s$ that minimize the above equation can be\n",
    "done quite quickly, especially when the number of features $p$ is not\n",
    "too large.\n",
    "\n",
    "Next, we repeat the process, looking\n",
    "for the best predictor and best cutpoint in order to split the data\n",
    "further so as to minimize the MSE within each of the resulting\n",
    "regions. However, this time, instead of splitting the entire predictor\n",
    "space, we split one of the two previously identified regions. We now\n",
    "have three regions. Again, we look to split one of these three regions\n",
    "further, so as to minimize the MSE. The process continues until a\n",
    "stopping criterion is reached; for instance, we may continue until no\n",
    "region contains more than five observations.\n",
    "\n",
    "\n",
    "The above procedure is rather straightforward, but leads often to\n",
    "overfitting and unnecessarily large and complicated trees. The basic\n",
    "idea is to grow a large tree $T_0$ and then prune it back in order to\n",
    "obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
    "lead to smaller variance and better interpretation at the cost of a\n",
    "little more bias.\n",
    "\n",
    "The so-called Cost complexity pruning algorithm gives us a\n",
    "way to do just this. Rather than considering every possible subtree,\n",
    "we consider a sequence of trees indexed by a nonnegative tuning\n",
    "parameter $\\alpha$.\n",
    "\n",
    "Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py).\n",
    "\n",
    "\n",
    "For each value of $\\alpha$  there corresponds a subtree $T \\in T_0$ such that"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "is as small as possible. Here $\\overline{T}$ is \n",
    "the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
    "rectangle (i.e. the subset of predictor space)  corresponding to the $m$-th terminal node.\n",
    "\n",
    "The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
    "complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
    "subtree $T$ will simply equal $T_0$, \n",
    "because then the above equation just measures the\n",
    "training error. \n",
    "However, as $\\alpha$ increases, there is a price to pay for\n",
    "having a tree with many terminal nodes. The above equation will\n",
    "tend to be minimized for a smaller subtree. \n",
    "\n",
    "\n",
    "It turns out that as we increase $\\alpha$ from zero\n",
    "branches get pruned from the tree in a nested and predictable fashion,\n",
    "so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
    "easy. We can select a value of $\\alpha$ using a validation set or using\n",
    "cross-validation. We then return to the full data set and obtain the\n",
    "subtree corresponding to $\\alpha$. \n",
    "\n",
    "\n",
    "### Schematic Regression Procedure\n",
    "\n",
    "Building a Regression Tree\n",
    "\n",
    "1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
    "\n",
    "2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
    "\n",
    "3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
    "\n",
    "  * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
    "\n",
    "  * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
    "\n",
    "  * Finally  we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
    "\n",
    "\n",
    "4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
    "\n",
    "!eblock\n",
    "\n",
    "\n",
    "\n",
    "## A Classification Tree\n",
    "\n",
    "A classification tree is very similar to a regression tree, except\n",
    "that it is used to predict a qualitative response rather than a\n",
    "quantitative one. Recall that for a regression tree, the predicted\n",
    "response for an observation is given by the mean response of the\n",
    "training observations that belong to the same terminal node. In\n",
    "contrast, for a classification tree, we predict that each observation\n",
    "belongs to the most commonly occurring class of training observations\n",
    "in the region to which it belongs. In interpreting the results of a\n",
    "classification tree, we are often interested not only in the class\n",
    "prediction corresponding to a particular terminal node region, but\n",
    "also in the class proportions among the training observations that\n",
    "fall into that region.  \n",
    "\n",
    "\n",
    "\n",
    "The task of growing a\n",
    "classification tree is quite similar to the task of growing a\n",
    "regression tree. Just as in the regression setting, we use recursive\n",
    "binary splitting to grow a classification tree. However, in the\n",
    "classification setting, the MSE cannot be used as a criterion for making\n",
    "the binary splits.  A natural alternative to MSE is the **classification\n",
    "error rate**. Since we plan to assign an observation in a given region\n",
    "to the most commonly occurring error rate class of training\n",
    "observations in that region, the classification error rate is simply\n",
    "the fraction of the training observations in that region that do not\n",
    "belong to the most common class. \n",
    "\n",
    "When building a classification tree, either the Gini index or the\n",
    "entropy are typically used to evaluate the quality of a particular\n",
    "split, since these two approaches are more sensitive to node purity\n",
    "than is the classification error rate. \n",
    "\n",
    "\n",
    "\n",
    "If our targets are the outcome of a classification process that takes\n",
    "for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
    "is to set up the splitting criteria for each node.\n",
    "\n",
    "We define a PDF $p_{mk}$ that represents the number of observations of\n",
    "a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
    "this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
    "observations of this class in the region $R_m$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We let $p_{mk}$ represent the majority class of observations in region\n",
    "$m$. The three most common ways of splitting a node are given by\n",
    "\n",
    "* Misclassification error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Gini index $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Information entropy or just entropy $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the Tree, Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
      "0          17.99         10.38          122.80     1001.0          0.11840   \n",
      "1          20.57         17.77          132.90     1326.0          0.08474   \n",
      "2          19.69         21.25          130.00     1203.0          0.10960   \n",
      "3          11.42         20.38           77.58      386.1          0.14250   \n",
      "4          20.29         14.34          135.10     1297.0          0.10030   \n",
      "..           ...           ...             ...        ...              ...   \n",
      "564        21.56         22.39          142.00     1479.0          0.11100   \n",
      "565        20.13         28.25          131.20     1261.0          0.09780   \n",
      "566        16.60         28.08          108.30      858.1          0.08455   \n",
      "567        20.60         29.33          140.10     1265.0          0.11780   \n",
      "568         7.76         24.54           47.92      181.0          0.05263   \n",
      "\n",
      "     mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
      "0             0.27760         0.30010              0.14710         0.2419   \n",
      "1             0.07864         0.08690              0.07017         0.1812   \n",
      "2             0.15990         0.19740              0.12790         0.2069   \n",
      "3             0.28390         0.24140              0.10520         0.2597   \n",
      "4             0.13280         0.19800              0.10430         0.1809   \n",
      "..                ...             ...                  ...            ...   \n",
      "564           0.11590         0.24390              0.13890         0.1726   \n",
      "565           0.10340         0.14400              0.09791         0.1752   \n",
      "566           0.10230         0.09251              0.05302         0.1590   \n",
      "567           0.27700         0.35140              0.15200         0.2397   \n",
      "568           0.04362         0.00000              0.00000         0.1587   \n",
      "\n",
      "     mean fractal dimension  ...  worst radius  worst texture  \\\n",
      "0                   0.07871  ...        25.380          17.33   \n",
      "1                   0.05667  ...        24.990          23.41   \n",
      "2                   0.05999  ...        23.570          25.53   \n",
      "3                   0.09744  ...        14.910          26.50   \n",
      "4                   0.05883  ...        22.540          16.67   \n",
      "..                      ...  ...           ...            ...   \n",
      "564                 0.05623  ...        25.450          26.40   \n",
      "565                 0.05533  ...        23.690          38.25   \n",
      "566                 0.05648  ...        18.980          34.12   \n",
      "567                 0.07016  ...        25.740          39.42   \n",
      "568                 0.05884  ...         9.456          30.37   \n",
      "\n",
      "     worst perimeter  worst area  worst smoothness  worst compactness  \\\n",
      "0             184.60      2019.0           0.16220            0.66560   \n",
      "1             158.80      1956.0           0.12380            0.18660   \n",
      "2             152.50      1709.0           0.14440            0.42450   \n",
      "3              98.87       567.7           0.20980            0.86630   \n",
      "4             152.20      1575.0           0.13740            0.20500   \n",
      "..               ...         ...               ...                ...   \n",
      "564           166.10      2027.0           0.14100            0.21130   \n",
      "565           155.00      1731.0           0.11660            0.19220   \n",
      "566           126.70      1124.0           0.11390            0.30940   \n",
      "567           184.60      1821.0           0.16500            0.86810   \n",
      "568            59.16       268.6           0.08996            0.06444   \n",
      "\n",
      "     worst concavity  worst concave points  worst symmetry  \\\n",
      "0             0.7119                0.2654          0.4601   \n",
      "1             0.2416                0.1860          0.2750   \n",
      "2             0.4504                0.2430          0.3613   \n",
      "3             0.6869                0.2575          0.6638   \n",
      "4             0.4000                0.1625          0.2364   \n",
      "..               ...                   ...             ...   \n",
      "564           0.4107                0.2216          0.2060   \n",
      "565           0.3215                0.1628          0.2572   \n",
      "566           0.3403                0.1418          0.2218   \n",
      "567           0.9387                0.2650          0.4087   \n",
      "568           0.0000                0.0000          0.2871   \n",
      "\n",
      "     worst fractal dimension  \n",
      "0                    0.11890  \n",
      "1                    0.08902  \n",
      "2                    0.08758  \n",
      "3                    0.17300  \n",
      "4                    0.07678  \n",
      "..                       ...  \n",
      "564                  0.07115  \n",
      "565                  0.06637  \n",
      "566                  0.07820  \n",
      "567                  0.12400  \n",
      "568                  0.07039  \n",
      "\n",
      "[569 rows x 30 columns]\n",
      "     malignant  benign\n",
      "0         True   False\n",
      "1         True   False\n",
      "2         True   False\n",
      "3         True   False\n",
      "4         True   False\n",
      "..         ...     ...\n",
      "564       True   False\n",
      "565       True   False\n",
      "566       True   False\n",
      "567       True   False\n",
      "568      False    True\n",
      "\n",
      "[569 rows x 2 columns]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "cancer = load_breast_cancer()\n",
    "X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
    "print(X)\n",
    "y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
    "y = pd.get_dummies(y)\n",
    "print(y)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/cancer.dot\",\n",
    "    feature_names=cancer.feature_names,\n",
    "    class_names=cancer.target_names,\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import os\n",
    "\n",
    "np.random.seed(42)\n",
    "X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/moons.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other ways of visualizing the trees\n",
    "\n",
    "**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
       " Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
       " Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
       " Text(0.3076923076923077, 0.5833333333333334, 'x[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
       " Text(0.15384615384615385, 0.4166666666666667, 'x[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
       " Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
       " Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.46153846153846156, 0.4166666666666667, 'x[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
       " Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
       " Text(0.5384615384615384, 0.25, 'x[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
       " Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
       " Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.8461538461538461, 0.5833333333333334, 'x[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
       " Text(0.7692307692307693, 0.4166666666666667, 'x[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
       " Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
       " Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
       " Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
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     },
     "execution_count": 4,
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     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_24_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn import tree\n",
    "X, y = load_iris(return_X_y=True)\n",
    "tree_clf = tree.DecisionTreeClassifier()\n",
    "tree_clf = tree_clf.fit(X, y)\n",
    "# and then plot the tree\n",
    "tree.plot_tree(tree_clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
    "This method doesn’t require the installation of external libraries and is more compact:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|--- petal width (cm) <= 0.80\n",
      "|   |--- class: 0\n",
      "|--- petal width (cm) >  0.80\n",
      "|   |--- petal width (cm) <= 1.75\n",
      "|   |   |--- class: 1\n",
      "|   |--- petal width (cm) >  1.75\n",
      "|   |   |--- class: 2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.tree import export_text\n",
    "iris = load_iris()\n",
    "decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
    "decision_tree = decision_tree.fit(iris.data, iris.target)\n",
    "r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithms for Setting up Decision Trees\n",
    "\n",
    "Two algorithms stand out in the set up of decision trees:\n",
    "1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
    "\n",
    "2. The ID3 algorithm based on the computation of the information gain for classification\n",
    "\n",
    "We discuss both algorithms with applications here. The popular library\n",
    "**Scikit-Learn** uses the CART algorithm. For classification problems\n",
    "you can use either the **gini** index or the **entropy** to split a tree\n",
    "in two branches.\n",
    "\n",
    "### The CART algorithm for Classification\n",
    "\n",
    "For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
    "This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
    "\n",
    "How do we find these two quantities?\n",
    "We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
    "The cost function it tries to minimize is then"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset  and $m_{\\mathrm{left/right}}$\n",
    " is the number of instances in the left/right subset\n",
    "\n",
    "Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
    "and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
    "$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
    "hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
    "$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$.\n",
    "\n",
    "\n",
    "### The CART algorithm for Regression\n",
    "\n",
    "The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
    "training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the MSE for a specific node is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the mean value of all observations in a specific node.\n",
    "\n",
    "Without any regularization, the regression task for decision trees, \n",
    "just like for classification tasks, is  prone to overfitting.\n",
    "\n",
    "\n",
    "\n",
    "### Computing the Gini index\n",
    "\n",
    "The example we will look at is a classical one in many Machine\n",
    "Learning applications. Based on various meteorological features, we\n",
    "have several so-called attributes which decide whether we at the end\n",
    "will do some outdoor activity like skiing, going for a bike ride etc\n",
    "etc.  The table here contains the feautures **outlook**, **temperature**,\n",
    "**humidity** and **wind**.  The target or output is whether we ride\n",
    "(True=1) or whether we do something else that day (False=0). The\n",
    "attributes for each feature are then sunny, overcast and rain for the\n",
    "outlook, hot, cold and mild for temperature, high and normal for\n",
    "humidity and weak and strong for wind.\n",
    "\n",
    "The table here summarizes the various attributes and\n",
    "<table border=\"1\">\n",
    "<thead>\n",
    "<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr><td align=\"center\">   1      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   2      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   3      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   4      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   5      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   6      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   7      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   8      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   9      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   10     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   11     </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   12     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   13     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   14     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "</tbody>\n",
    "</table>\n",
    "\n",
    "### Simple Python Code to read in Data and perform Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  (0, 0)\t1.0\n",
      "  (0, 7)\t1.0\n",
      "  (0, 9)\t1.0\n",
      "  (0, 13)\t1.0\n",
      "  (1, 3)\t1.0\n",
      "  (1, 5)\t1.0\n",
      "  (1, 8)\t1.0\n",
      "  (1, 12)\t1.0\n",
      "  (2, 3)\t1.0\n",
      "  (2, 5)\t1.0\n",
      "  (2, 8)\t1.0\n",
      "  (2, 11)\t1.0\n",
      "  (3, 1)\t1.0\n",
      "  (3, 5)\t1.0\n",
      "  (3, 8)\t1.0\n",
      "  (3, 12)\t1.0\n",
      "  (4, 2)\t1.0\n",
      "  (4, 6)\t1.0\n",
      "  (4, 8)\t1.0\n",
      "  (4, 12)\t1.0\n",
      "  (5, 2)\t1.0\n",
      "  (5, 4)\t1.0\n",
      "  (5, 10)\t1.0\n",
      "  (5, 12)\t1.0\n",
      "  (6, 2)\t1.0\n",
      "  :\t:\n",
      "  (8, 12)\t1.0\n",
      "  (9, 3)\t1.0\n",
      "  (9, 4)\t1.0\n",
      "  (9, 10)\t1.0\n",
      "  (9, 12)\t1.0\n",
      "  (10, 2)\t1.0\n",
      "  (10, 6)\t1.0\n",
      "  (10, 10)\t1.0\n",
      "  (10, 12)\t1.0\n",
      "  (11, 3)\t1.0\n",
      "  (11, 6)\t1.0\n",
      "  (11, 10)\t1.0\n",
      "  (11, 11)\t1.0\n",
      "  (12, 1)\t1.0\n",
      "  (12, 6)\t1.0\n",
      "  (12, 8)\t1.0\n",
      "  (12, 11)\t1.0\n",
      "  (13, 1)\t1.0\n",
      "  (13, 5)\t1.0\n",
      "  (13, 10)\t1.0\n",
      "  (13, 12)\t1.0\n",
      "  (14, 2)\t1.0\n",
      "  (14, 6)\t1.0\n",
      "  (14, 8)\t1.0\n",
      "  (14, 11)\t1.0\n",
      "Train set accuracy with Decision Tree: 0.73\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "infile = open(data_path(\"rideclass.csv\"),'r')\n",
    "\n",
    "# Read the experimental data with Pandas\n",
    "from IPython.display import display\n",
    "ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
    "ridedata = pd.DataFrame(ridedata)\n",
    "\n",
    "# Features and targets\n",
    "X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
    "y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
    "\n",
    "# Create the encoder.\n",
    "encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
    "# Assume for simplicity all features are categorical.\n",
    "encoder.fit(X)    \n",
    "# Apply the encoder.\n",
    "X = encoder.transform(X)\n",
    "print(X)\n",
    "# Then do a Classification tree\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X, y)\n",
    "print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
    "#transfer to a decision tree graph\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/ride.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above functions (gini, entropy and misclassification error) are\n",
    "important components of the so-called CART algorithm. We will discuss\n",
    "this algorithm below after we have discussed the information gain\n",
    "algorithm ID3.\n",
    "\n",
    "In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "Split: [X3 < 1.000]\n"
     ]
    }
   ],
   "source": [
    "# Split a dataset based on an attribute and an attribute value\n",
    "def test_split(index, value, dataset):\n",
    "\tleft, right = list(), list()\n",
    "\tfor row in dataset:\n",
    "\t\tif row[index] < value:\n",
    "\t\t\tleft.append(row)\n",
    "\t\telse:\n",
    "\t\t\tright.append(row)\n",
    "\treturn left, right\n",
    " \n",
    "# Calculate the Gini index for a split dataset\n",
    "def gini_index(groups, classes):\n",
    "\t# count all samples at split point\n",
    "\tn_instances = float(sum([len(group) for group in groups]))\n",
    "\t# sum weighted Gini index for each group\n",
    "\tgini = 0.0\n",
    "\tfor group in groups:\n",
    "\t\tsize = float(len(group))\n",
    "\t\t# avoid divide by zero\n",
    "\t\tif size == 0:\n",
    "\t\t\tcontinue\n",
    "\t\tscore = 0.0\n",
    "\t\t# score the group based on the score for each class\n",
    "\t\tfor class_val in classes:\n",
    "\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
    "\t\t\tscore += p * p\n",
    "\t\t# weight the group score by its relative size\n",
    "\t\tgini += (1.0 - score) * (size / n_instances)\n",
    "\treturn gini\n",
    "\n",
    "# Select the best split point for a dataset\n",
    "def get_split(dataset):\n",
    "\tclass_values = list(set(row[-1] for row in dataset))\n",
    "\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
    "\tfor index in range(len(dataset[0])-1):\n",
    "\t\tfor row in dataset:\n",
    "\t\t\tgroups = test_split(index, row[index], dataset)\n",
    "\t\t\tgini = gini_index(groups, class_values)\n",
    "\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
    "\t\t\tif gini < b_score:\n",
    "\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
    "\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
    " \n",
    "dataset = [[0,0,0,0,0],\n",
    "            [0,0,0,1,1],\n",
    "            [1,0,0,0,1],\n",
    "            [2,1,0,0,1],\n",
    "            [2,2,1,0,1],\n",
    "            [2,2,1,1,0],\n",
    "            [1,2,1,1,1],\n",
    "            [0,1,0,0,0],\n",
    "            [0,2,1,0,1],\n",
    "            [2,1,1,0,1],\n",
    "            [0,1,1,1,1],\n",
    "            [1,1,0,1,1],\n",
    "            [1,0,1,0,1],\n",
    "            [2,1,0,1,0]]\n",
    "\n",
    "split = get_split(dataset)\n",
    "print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropy and the ID3 algorithm\n",
    "\n",
    "The ID3 algorithm  learns decision trees by constructing\n",
    "them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
    "\n",
    "1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
    "\n",
    "2. The best attribute is selected and used as the test at the root node of the tree.\n",
    "\n",
    "3. A descendant of the root node is then created for each possible value of this attribute.\n",
    "\n",
    "4. Training examples are sorted to the appropriate descendant node.\n",
    "\n",
    "5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
    "\n",
    "6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
    "\n",
    "The ID3 algorithm selects which attribute to test at each node in the\n",
    "tree.\n",
    "\n",
    "We would like to select the attribute that is most useful for classifying\n",
    "examples.\n",
    "\n",
    "What is a good quantitative measure of the worth of an attribute?\n",
    "\n",
    "Information gain measures how well a given attribute separates the\n",
    "training examples according to their target classification.\n",
    "\n",
    "The ID3 algorithm uses this information gain measure to select among the candidate\n",
    "attributes at each step while growing the tree.\n",
    "\n",
    "\n",
    "### Cancer Data again now with Decision Trees and other Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(426, 30)\n",
      "(143, 30)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy with Logistic Regression: 0.94\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy with SVM: 0.63\n",
      "Test set accuracy with Decision Trees: 0.90\n",
      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
      "Test set accuracy SVM with scaled data: 0.96\n",
      "Test set accuracy with Decision Trees and scaled data: 0.89\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "# Load the data\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "# Logistic Regression\n",
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "logreg.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
    "# Support vector machine\n",
    "svm = SVC(gamma='auto', C=100)\n",
    "svm.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
    "deep_tree_clf.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
    "#now scale the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "# Logistic Regression\n",
    "logreg.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Support Vector Machine\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Another example, the moons again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_42_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "\n",
    "from sklearn.svm import SVC\n",
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "\n",
    "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
    "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
    "deep_tree_clf1.fit(Xm, ym)\n",
    "deep_tree_clf2.fit(Xm, ym)\n",
    "\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"No restrictions\", fontsize=16)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_43_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(6)\n",
    "Xs = np.random.rand(100, 2) - 0.5\n",
    "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
    "\n",
    "angle = np.pi/4\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xsr = Xs.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_s.fit(Xs, ys)\n",
    "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_sr.fit(Xsr, ys)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Quadratic training set + noise\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m, 1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.randn(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeRegressor</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2, random_state=42)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_46_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_47_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
    "y_pred1 = tree_reg1.predict(x1)\n",
    "y_pred2 = tree_reg2.predict(x1)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"No restrictions\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pros and cons of trees, pros\n",
    "\n",
    "* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
    "\n",
    "* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
    "\n",
    "* No feature normalization needed\n",
    "\n",
    "* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
    "\n",
    "* Can model nonlinear relationships\n",
    "\n",
    "* Can model interactions between the different descriptive features\n",
    "\n",
    "* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)\n",
    "\n",
    "### Disadvantages\n",
    "\n",
    "* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
    "\n",
    "* If continuous features are used the tree may become quite large and hence less interpretable\n",
    "\n",
    "* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
    "\n",
    "* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
    "\n",
    "* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
    "\n",
    "* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
    "\n",
    "* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
    "\n",
    "However, by aggregating many decision trees, using methods like\n",
    "bagging, random forests, and boosting, the predictive performance of\n",
    "trees can be substantially improved."
   ]
  }
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