LogisticRegression.ipynb

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   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
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   "id": "60bc0b20",
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   "source": [
    "class LogisticRegression:\n",
    "    def __init__(self,\n",
    "                 epochs=100,\n",
    "                 lr=0.1,\n",
    "                 use_bias=True):\n",
    "        \"\"\"Logistic Regression\n",
    "\n",
    "        Args:\n",
    "            epochs (int, optional): Epochs. Defaults to 100.\n",
    "            lr (float, optional): Learning Rate. Defaults to 0.1.\n",
    "            use_bias (bool, optional): Bias Term. Defaults to True.\n",
    "        \"\"\"\n",
    "        self.epochs = epochs\n",
    "        self.weights = None\n",
    "        self.bias = 0\n",
    "        self.lr = lr\n",
    "        self.use_bias = use_bias\n",
    "        self.n_features = 0\n",
    "    \n",
    "    def _sigmoid_function(self, x):\n",
    "        # To avoid overflow issue\n",
    "        if x >= 0:\n",
    "            z = np.exp(-x)\n",
    "            return 1 / (1 + z)\n",
    "        else:\n",
    "            z = np.exp(x)\n",
    "            return z / (1 + z)\n",
    "        \n",
    "    def _sigmoid(self, x):\n",
    "        return np.array([self._sigmoid_function(value) for value in x])\n",
    "        \n",
    "    def _compute_loss(self, y_true, y_pred):\n",
    "        # loss = -y_true*log(y_pred)-(1-y_true)*log(1-y_pred)\n",
    "        # Added 1e-9 to avoid log(0)\n",
    "        loss = y_true * np.log(y_pred + 1e-9)\n",
    "        loss += (1-y_true) * np.log(1 - y_pred + 1e-9)\n",
    "        return -1*np.mean(loss)\n",
    "    \n",
    "    def _compute_derivate_w(self, X, y_true, y_pred):\n",
    "        # derivative w.r.t w using chain rule X^T * (y_true - y_pred)\n",
    "        #\n",
    "        #     h = w^T * X\n",
    "        #     z = σ(h) = 1/(1+e^−h)\n",
    "        #     J(w) = −(y * log(z) + (1−y) * log(1−z))\n",
    "        #\n",
    "        #     ∂J(w)/∂w = (∂J(w)/∂z)*(∂z/∂h) * (∂h/∂w)\n",
    "        #     ∂J(w)/∂z = −((y/z) − ((1−y)/(1−z))) = (z−y)/(z(1−z))\n",
    "        #     ∂z/∂h = z(1−z)\n",
    "        #     ∂h/∂w = X\n",
    "        #     ∂J(w)/∂w = X^T * (z−y)\n",
    "        derivative = (np.dot(X.T, (y_true-y_pred)))/len(y_true)\n",
    "        return derivative\n",
    "        \n",
    "    def _compute_derivative_b(self, y_true, y_pred):\n",
    "        # derivative w.r.t to b = (1/n) * (y_true - y_pred)\n",
    "        return np.mean(y_true-y_pred)\n",
    "    \n",
    "    def _plot_loss(self, losses):\n",
    "        plt.xlabel('Epochs')\n",
    "        plt.ylabel('Loss')\n",
    "        plt.plot(range(self.epochs), losses, 'm', linewidth=\"5\")\n",
    "        plt.show()\n",
    "\n",
    "    def fit(self, X, y, verbose=False, plot_loss=False):\n",
    "        \"\"\"Fit\n",
    "\n",
    "        Args:\n",
    "            X : Features\n",
    "            y : Target\n",
    "            verbose (bool, optional): controls logging. Defaults to False.\n",
    "            plot_loss (bool, optional): Plots loss vs epochs if true. Defaults to False.\n",
    "        \"\"\"\n",
    "        assert X.shape[0] == len(y), \"Number of rows in X, y doesn't match\"\n",
    "        \n",
    "        self.n_features = X.shape[1]\n",
    "        self.weights = np.random.randn(self.n_features)\n",
    "        losses = []\n",
    "        \n",
    "        for epoch in range(self.epochs):\n",
    "            y_pred = self._sigmoid(np.dot(X, self.weights) + self.bias)\n",
    "            loss = self._compute_loss(y, y_pred)\n",
    "            losses.append(loss)\n",
    "            grad_w = self._compute_derivate_w(X, y, y_pred)\n",
    "            self.weights += self.lr*grad_w\n",
    "            if self.use_bias:\n",
    "                grad_b = self._compute_derivative_b(y, y_pred)\n",
    "                self.bias += self.lr*grad_b\n",
    "            if verbose:\n",
    "                print(f\"Epoch: {epoch} Loss: {loss}\")\n",
    "            \n",
    "        if plot_loss:\n",
    "            self._plot_loss(losses)\n",
    "    \n",
    "    def predict_proba(self, X):\n",
    "        \"\"\"Predict\n",
    "\n",
    "        Args:\n",
    "            X : Features\n",
    "\n",
    "        Returns:\n",
    "            np.array : Predictions probabilities\n",
    "        \"\"\"\n",
    "        assert X.shape[1] == self.n_features, \\\n",
    "                f\"Expected {self.n_features} features but got {X.shape[1]}\"\n",
    "        \n",
    "        return self._sigmoid(np.dot(X, self.weights)+self.bias)\n",
    "    \n",
    "    def predict(self, X, thresh=0.5):\n",
    "        \"\"\"Predict\n",
    "\n",
    "        Args:\n",
    "            X : Features\n",
    "            thresh : Threshold. Defaults to 0.5.\n",
    "        Returns:\n",
    "            np.array : Predictions \n",
    "        \"\"\"\n",
    "        assert X.shape[1] == self.n_features, \\\n",
    "                f\"Expected {self.n_features} features but got {X.shape[1]}\"\n",
    "        \n",
    "        probabilities = self._sigmoid(np.dot(X, self.weights)+self.bias)\n",
    "        return [1 if p > thresh else 0 for p in probabilities]"
   ]
  },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 2) (200,)\n"
     ]
    }
   ],
   "source": [
    "#Generate data\n",
    "X, y = make_blobs(n_samples=200, centers=2, n_features=2, cluster_std=5, random_state=11)\n",
    "print(X.shape, y.shape)"
   ]
  },
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hsFccDnuRTLiyM5FY1IuR+DOr2lOTbsDCYW1tRs7fDH7iMPghmTQ0RK8qtdTXcyoskd14MeIu5vwQ+QSnwsrNirwQEofeujyNjc61iRKTaqo7EcXy+lRYL3f119VFq/f2P1kGg9EEV6/lcXj5c+yPFyPyYM8PkcTUVa6TLV8XCABFRXKu7OzlGWx+SlL38ucYz+sXI17C4IdIYl6dCuvl4EBrvSYAqKryxhCYlz/HRLx8MeI1DH6IJOe1qbBeDw78khfi9c8xEa9ejHgRgx8iDwiFgObm6Kyumprov01N8gU+gPeDA7/khXj9c0zGaxcjXsWEZyKP8MpK1rIHB1rJvX7JC5H9czQjFALKy/2R5C0rBj9EZJids3dkCw7674v33wd+8YvUM7jUvBCt9ZqM5oWINqNKts/RakYuRkT77HxBoRhdXV0KAKWrq8vtphAJaft2RQkGFSV66o7egsHo/Vb44ovo8wUCsa+h3gIBRSkqim7ntkT7IlF7A4HY/bN9++n7tbZNtx1WfibpkOlzdJOIn52sjJy/mfNDrmBxNzk5MXtHlqTRZPsiXqLkXivzQurqgLlzxZtR5fbnKMN3jN9mwwnFgWBMKuz5sR+vdOSkXsmn6uGw8ko+0XFSVCTGcaK1L5Ld6usHPk99vaLU1ET/NbrvvvhCUUaMcO4zSYcbn6MM3zFO/z35gZHzN9f2isO1vexl16J/ZD831hETNRdC776IV1MDLFxoXTvWrwfWrNHezorPxMxn4eTnKMt3DNfls56R8zcTnskxWnU/AoHo0EB5uRgnOIrlxuwdUWewpfserUzujURODytpMfuZmF2Kw8znaCRwkuk7xs+z4UTAnB9yjF/rfniF32fv9Gf0PdpR2bexEejs1Letmc/EzbwUo0tjyPQdo/czOecce9vhVwx+yDG80hGXnuRQlu4/TWtf9GdXcq/ev5O8vPQ/EzerNKcTdMn0HVNSAowYob3d4sVMfLYDgx9yDHsOxKT36trt2TsiSbUv4tlV2Vfv38ny5el/Jm71pKQbdMn0HbNjB3D8uPZ2nPllDwY/5Bj2HIjH6NU1S/eflmpfrFtn/zIjenqfRowAVq9O/zXc6klJN+iS5TtGDe708Oo6aG5jwjM5Rr1arqiIfgn1v6rzW8+BCNJNDmXp/tPc3Bep/p6A6H2PPGKuLW71pKQbdMnyHaMV3MXrH+yJOAFARuz5IUdp9RyUl4tfmMwrzAxpqLN3Fi6M/uv2ycTNgnZG9oXV7Uz291RUZE1PnFs9KWaCLhl6J9PtKRMhV8kr2PNDjkt2tbxjRzTXJN3ptGSMTMmhqRiZhu1m3SCz08WTsbP3ya2eFLPrnznVI5fu8ZRuT1mi3xO1FpbwbC+5KBlWeHaHutaRnnWRyBr19elVJRaJkePGzaq/sh/fblVptnL9Mzval+7xpLXumd5qz3Yc02arjrvJyPmbwU8cBj/OY5l3d8i+8KSR48bN4MMrx7cbJ0VRlzix4nhKFtzpfU47jmkZlgVJhcGPCQx+nOeFHghZiX51Ha//Cfjee/UdNy++6G7wwePbHNF6IqwMZhMFGxkZ2sGeHQG17L2TimLs/M2cH3KdV3JPZKQmhybKRamuFiPXSs1p2LED+PWvgWPHjP1+Q4P+xG47ZtLw+DZHtCVOjEwU0Gp3otykadOA3btT5/BY2QZArmVBrMLgh1wnU2EyLxJ56nqiJGG72BV88Pj2FquD2UTBnVbAYnUbrA6mZMDgh1xndmYHmSfa1TWQfHVuvdTjprQUuPNO7e3tCj54fHtLOsGs1TOyrA6o/dg7yTo/5DoumyA/q+vXpOqG16P/cVNa6m7VXx7f1nKzphNgvPaR0cVZ7WiDFl/2TjqQgyQVJjy7R9SZHZSaHTNE9CYJJ7vFHzciJHbz+DZPlNlIeo8nO5OIrTymZZ/5qeJsLxMY/LhLtJkdlJpdX+41NcYDnnvvTX3ciBB88PhOn2izkbSOJydKHFh5TItwgWCWkfN3QFHS7Vj2pnA4jNzcXHR1dSEnJ8ft5hAJKxIZWJG7PzWXpanJ+JBOQ0N0eEAPI6/DarhysvNYM9uuZMeT3mO4vt5cvp2Vx3SiCQZFReLM/NRi5PztuYTntWvXYt26dTH3FRQUoKOjw6UWEXmTnTNEtJKE4+nNmRExsZu0iTobKdXx5FQSsZXHtMgzP63mueAHAL7yla/gxRdf7Ps5w4ufHJHL7Pxy11qxXDViRHTlchmuSs1wo8dKpF4yGWcjiTArLB1+uUDwZPBzxhlnoLCw0O1mEHma3TNE1AKMN98MHD+eeJtk93uJXQuiivKaek74Ms5GMlriwI3P2ddsz0By2Jo1a5QhQ4Yoo0aNUoqLi5Xrr79e+ctf/pJ0+88++0zp6urqu7W2tjLhmUgHJ2aIfPGFoowZY2/SqMiSJfmqt2eece417Uh81Tt7S9bZSCLMCkuHrIn5vp7t9dxzzynbtm1T3n77bWXXrl3K1VdfrRQUFCjHjh1LuP2aNWsUAANuDH6ItNk9Q8TP62JpzRYCoutAbd3q3GtaGWQYPeHLOhtJhFlhZtsry+Kmvg5+4p08eVIpKChQ7r777oSPs+eHyBw7p5DrnfJeU2P+tURjpNaRVScmp4LNdE/4IpQrSEeqnhSRAnzReqCM4sKm/Zx11lm4+OKL8f777yd8PCsrC1lZWQ63imQhQgKi6OycISJjrodVjCTvWrXopFOJxenO3pJ1NpIIs8K0+G1xU88HP93d3Th48CBKuHAOGcQERP3smiHi53WxjAR0Vk3zdirYNHPCl2k2kkzJ3KKWE7CL59b2uu222/Dyyy+jqakJr7/+OioqKhAOh1FZWel200gi6qKa8V8GbW3R+82sy0P6+XldLDXw08uKngGr14xKRpQTvp30runl1D7XIkoPlFM8F/wcPnwYCxcuxIUXXohQKITMzEy89tprGDdunNtNI0lodf8C0e5fpxdU9Ct1yvuYMbH3B4PR+73aC9c/8NPDikDBqWBTlBO+XYxcPIkS4PshIO2Py1vE4fIW5FRZejLGr/lX27YBCxYkD7btWNrBiWUO1AABiL3QUE/4sga26S7F4fbSEmq7tYaYnV5CxAhfL29BZJbfun9lIVOuh5UqKoDaWmD+/IGP2dUz4ERisdqjlyivTpa1pBKRNZk7VVV1Lw4xM/ghiuO37l8S37x5wPbt1gcKqXrTnAg23T7h20HmZG6vBqSJcNgrDoe9yAvdv+RNdq/gzdmM5nlh2FzWIWYj528GP3EY/BDg3XwE8q/+J7T33wfWrBm4DY9v83jx5B4j52/PzfYisoJfZxiRN8VPu04U+ADmZzNGItGej9ra6L9+nBHp1uwt7ntj2PMThz0/1J+s3b9EKrUX0+g3vdFhGRmH0ez8+3Zy9paM+94OHPYygcEPEYnAihOz1rTrVGpqgIUL9W2bLMASeRjNiYDBiYsnGfe9XRj8mMDgh8gd7GU7zaoTs97k20T09vykW9fGSfHH1rFj0dIBsgcMMux7JzHnh4ikoncpAD+wcmmVdGpRGa2ubKSujRsSHVsLFnijgrvo+15kDH6IJODlZEauo3aa1tIqihJ9XO/nb7QWVToJuSIXBU12bKXafzIFDCLve9Ex+CESnJd7RbiOWiytK3kg+viGDfqeT2sNrXjpzGYUtShoqmNLDycCBrMXNaLuexkw+CESmNd7RdhtH0vvCXfNGn2fvda060AAWLcumtxcXx/NDTGa6yLqIqV6AslU7A4YrLioEXXfy4DBD5Gg/NArwm77WEZOuHo/e62aVXfcEZ3VVVqaXlKsKKuSx0v3mHEiYLDqokbUfZ+KKEP4DH6IBOWHXhF228dSr+T1MPLZh0JAc3O0d8dML0+q5xetKGg6x4wTAYPVFzUi7vtkRBrC51T3OJzqTqKorY1+QWgxUo/FLulOU09nKQCvT4mvqwPmztW3rdOfvda+F+mz0Tq2gGjb+gcZdhUh7M+utb9E2veJOFGPyMj5m6u6EwlKll4RMzVp1G77iorol2D8F6OiAEuWWPNasgiFonk4yZag6M/Jz17Pvnd7VfL+Uh1b6gm3thYYOdLZgMGuoV6R9n08rd6uQCDa21Ve7mDAplCMrq4uBYDS1dXldlPI5774QlGCQUUJBNRJzrG3QEBRioqi27ll+/bE7QsEorft2/U/TzCY+H0C0cd+8ANrXksG6mefbH84/dlb9Tm7IdGxVVTkXpvr65N/rv1v9fXutM8OTr1nI+dvDnvF4bAXiUTk1eWtri4biUSncCdbbTzVN5UXK9mK8tl7oYqwSENCflz13akhfFZ4JvIIkZMZ7UjI/sUvkj9XKl5I/o4nymfvhcR7dUjIzKw2K9si2wwts0QcwmfOD5HgQqHoWLgoV64qq3MXzNZlMfJashDhs2c5AuupgW2iHCq7E67doM5i1OrtcrIeEYMfIgmImMxo9dWcFSdPt5O/7eD2Zy/iVbsXiBDYOkVP8rnTvV3M+YnDnB8ifazOXTCzArkX8yT6czNnxY85KmSPRDMGrSwvwJwfIrKdlbkLkUj0lpdnvB1ezZNQuV0Yzo85KmQPu4ttGsHgh4jSZkVSrnpy/9rXgM7OxNuo61D94AcDKyCLkPxtF1HWdhMl+ZrkJ0ryOYe94nDYi8i4dIdlklV9jde/a1ykact2EnGKuV/2PVnD6ePFyPmbwU8cBj9EztA6uQPRYbCtW92fnuwGu5ZBSAeDHjLKjWrszPkhIuHpmdre2Rk9yfrxRCvKFHO3c45IPqIM16bC4IeIXCHKyV1UIkwx13sSi0SiPVW1tdF/9a5ITnJK9XlbvWq9XRj8EJEr9J60zznH3naISi0MFz/DShUIRHOh7CoMp/ck9swz7BnyE62eQFkqgjP4ISJXaJ3cVZWV/jyRuj3FXO9JbP58sYc3yDp6egJl6dFl8ENErkh1cu/vyBH/nkjdnGJu5uQk0vAGWUNvT6Denlq3K4Iz+CEi1yQ7uffn9xOpW4XhzJ6cRBneIGvo7QkE3B2u1YtrexGRq0IhIDc3WuQwmf4nUtHWONPLzHRxN9b30lqMUi+3hzfIGno/x6NHxVvHKxFP9vw88MADGD9+PAYPHowpU6agkZceREI7elTfdrKeSGWcLq4n50gPt4c3yBpGZh/KUBHcc8HP008/jaqqKqxevRr79u1DSUkJZs2ahZaWFrebRkRJiDCt2y4y1DxJJtVJ7Jln5BjeIGsYnX0o0jpeiXiuwvMVV1yByZMn48EHH+y7b8KECfjWt76FjRs3av4+KzwTGWe2ArBXVw4XcYmKdCT7fNXADkg8vCHKVT5ZQ/TP27cVnnt6erB3715Mnz495v7p06dj9+7dCX+nu7sb4XA45kZE+lkxpBM7xBIb/ag/i5AnYJTRmieR3ggamhtQ+04tGpobEOkVI8M72WKUMgxvkHW89Hl7KuH52LFjiEQiKCgoiLm/oKAAHR0dCX9n48aNWLdunRPNI/KcZAuTqkM6Rr4QQyHgturXcM8dYxHpGt13/6DcI1i5rhWh0JW62yXKWlRGap7UHazD8ueX43D4dLQUzAli88zNCE1w9qxiZP+FQkB5uRj7m+znlc/bU8GPKhA3KKkoyoD7VKtWrcLKlSv7fg6HwygqKrK1fUReEK37ofw98In/m4t2hVdVRb8oda3wfrAOd31cAWV5APigBDg5Chjajsi4V3HXx7248uA2XUGAUwsqRnojaGxpRPuJdowaNgolY0uQMSj2jerNUXq/5xWs3VoBBbFRZFu4DRVbK7Btvr73boV09p8bs9HIPV74vD017JWfn4+MjIwBvTxHjx4d0BukysrKQk5OTsyNiLRt+PUrOHw4gPjAR2WkzkukN4Llzy+PnvwH9QLjXwYufir676Do0E/V81Waw0BOJRfXHaxD8eZilG0pw6K6RSjbUobizcWoOxj7AnqSRINFCh45dsOAwAdA33163rsVZE7OJjLCU8FPZmYmpkyZgl27dsXcv2vXLkybNs2lVhF5T93BOqz5/UO6ttUz9NPY0hgz3BNPgYLWcCsaW5JHUk4tqFh3sA4VWysGtFftpekfAOmZLn7TvxxA28nks1H1vHcryLIgJZEVPBX8AMDKlSvx6KOP4vHHH8fBgwexYsUKtLS04JZbbnG7aUSeoPbSYOgRXdvrGfppP6EvOSbVdk4sqBjTQxX//El6abSSRM+/6h1dr613H6VLlgUptXCFedLDczk/119/PY4fP47169ejvb0dEydOxHPPPYdx48a53TQiT+jrpRl3BMhpBcJjkPA6KqCgKBjQVedl1DB9yTGptnNiQUUjPVSlxaV996dKEm1oNv/erSDKgpR6cqmScSrfi+TnueAHAJYuXYqlS5e63QwioaU7I6qvB2JQLzBzObB1G4BexAZAvQACuqenl4wtQTAniLZwW8JelQACCOYEUTI2eSTlRKFEMz1UyZJErXjvVhCh0KSZGW9Wzjwk7/PcsBcRaTNTmyemB+Ki3wLzK4CcttiNcg5j3QMHdJ9sMgZlYPPMaHJMIC6BWv25emZ1yh4AoxVo02FFD1U8K967FZzYf6kYyaWKx3wlMorBD9mGY+9iMjujR+2p6DtRX/RboKoYqCwF5i4EKssQvON/Y/XNEwy1KzQhhG3zt2FMTmxyTDAnqGuqt57kYrOFEge89zgBBFCUU2S4l8bse7eCE/svmXRyqfrzSr4SOcdzy1uYxeUtrMGxdzFZtdyCepUOIOaEpQYFZk7YZnI+gMTHXlFR9MRtxbEn8nu3gt37L16kN4L7/us+rHhhhea29ZX1MblUqtraaA+mlpqaaJVq8iYj528GP3EY/JiXbOxdlPVf/KyhITrEpaW+XruIWaL8jKKcIlTPrHa8InE8uys8i/zereBUhexE+zGVmlANFl48MHqx8rgmeTH4MYHBjzleWcjRLXZf+Vt9hSxCT4VbtN67n/eNHmoPWqKhrmSS9fx4dWFcMsbI+duTs73IPUbG3nkFFiudmS5GT7DnFEQAaH/7653RkzEoI+HJyA9SvfdtB7Zh6XNL8dEnH/Xd59Y6XSJKleOTiNaMNzVfqaIiGugkWnFcxoVxyT5MeCZLiVIrRDbpzHTRu8RC/+0r930pWpsHvQm3sXtGjxGyJsz/cNcPMW/bvJjABwAOhw9rzlryC616Sf3pnfHmpRXHyX4MfshSItQKkU06M12MBkvq9m0nW6K1eQDEB0AiXSGbmYrvpmcOPINNuzclfVyB4tg6XSIzUq3ayIy3UAhobo7m9tTURP9tamLgQwMx+CHTIr0RNDQ3oPadWkSKGhAMKq7VCpGR0XWtjAZLA7ZPUptnTFAR4gpZ1sU1I70RLH1Ou7iqE+t0iU5vHaR7Z9yLpuVNhoYK1WKSCxdG/3U7kCcxMeeHTEmUpzLia0ugbHkEgUCAY+86GK0abHSJhYTbX/Rb4Ms7gA9KgJOjgKHtePJf1+Kac0vTfRuW0CpWFwhEi9V985vA7t32z0YyorGlEcc+OaZrW6PrdDk1+8opeqtaf+9/fY9J4jp57RixG4MfSluy2RqdxY8B8zqR9/KvcPzDIX33B4P21QqRmdGqwUaDpaTbD+oFxr/c9+PRT9xPxNKbMB8MAh/1S6kRoYaUkYDGSAVoL9bMUqtaV2ytQACBhPWSnKhqLaJ0gphUx0iyNeX8jsNelBatoZfARb9F9g8uwosvRTj2rsFo1WCjwZIdSzLYRW8i/EexucQ43KagokJxdUhM7/4bOWSk7grQsg4B6iFCVWvRpJPrluoYmTsXKCiQL3fOCazzE4d1fvRpaG5A2RbtqmLJ6nJQLCNVgyO9ERRvLtYcMmha3oSMQRmGt3eT3mJ1ifViROFn+PDwEFeubNX9rDWL6ZmKZ1DxlQrt5/NJzSzWQ4pKpzis1jGSiJeLzRo5f7Pnh9JiZnVrGsjIVbDRhTBFWThTD63FNVMbhOMdQ7Dh169Y3Sxd1P2crAcPAH4w7Qe6Ah/AP+tVqfWSFl68EKXFpUIch05Ld2FWrWMkES70GsXgh9Ii01CKLEITQmhe3oz6ynrUhGpQX1mfdKaL0SEDWYYYUi2uqdfmF7e6NpVc3c/BnGDM/SOHjMTWiq34+dd/rvu5WDPLP9INdNP97L0SOJvBhGeKobcLWu9sDaOrW/udkYrJoQkhlF9YrnvIwOj2blGL1cUncI4cOTDXJ5HOjD/1zXRzg1X7mTWz/CPdQNfsZ+/nwJnBD/VJNG195JCR+D8X/x+Uf7k85gucszXEYHR5CVmWowiFBs5SmTYNGDX2FDo/zEbiTuteIOcwMK7R9eFWK/azOgSotV4Va2bJL91AV+sYsep1vYjDXgQgecXgjz75CNWvVydcOkGWoRSSU3yxusxMYPnapr8/Gr88x99/nvwL4MB8fHhggvT5DKmGAFkzy1u0ct2SFYdNd5iYxWY522sAP8720jtLBYj26sQHNpytQU6J9EZQcOMtOF53BxAuOv1A9kcAAsCn+X13yV4LR5WohktREWtmeY062wtIvDBrqtlZiY6RESOA48eTL/Tq99leDH7i+DH40TttHRBrWjT5U93BOsx9av7fq1MXAsfPAxrW/f3R053ZXvqSZ/VefzAT6CY6Rnbs8FfgzODHBD8GP7Xv1GJR3SJDv8P6PeSmvvy0vx0BqpuB8BgkGsWXpRYOgxtSWX0s+OnYMnL+ZsIzpTUd3e2EUvI3dUbVfVvfwYr+w19x+k/pLS11rn1GeHH5Ckqfmusm2vN5LYhiwjNpLq+QCOv3kNsyBmWgQJmka1tRp/R6efkK8o50lt0QXVrBz6effoq2trYB9x84cMB0g8h5qSoAx4tfZ4rITaLUwolEoktz1NZG/9Uz0yzdqr5ETvJqgG44+Nm2bRsuuOACfOMb38All1yC119/ve+xG264wdLGkXOSTVvvj/V7SDTpThG2UrpXxX5ZvoLk5eUA3XDwc+edd+Ktt97Cf//3f+Pxxx/Ht7/9bdTU1AAAmDstt/7LK1RdWYX8Ifkxj7N+D4nG7Vo4Zq6KuXwFic7LAbrhhOfPP/8cI0eOBABcdtlleOWVVxAKhXDo0CEE0l2Mh4ShVqYtLS7FXV+/i/V7SHjJlsMIBu2d0qt1VRwIRK+Ky8sTB1+iDNkRJePlAN1w8HPOOefg7bffxiWXXAIAGDFiBHbt2oXKykq8/fbbljeQ3CPLUghEiZbDsHs2ipGr4kSzbbh8BYnOywG67uDnxIkTGDZsGH71q1/hjDNify0zMxO1tbVYtmyZ5Q0kItLD6inCWsxeFatDdhUVyavwphqyc3PqMau6+4OXA3TdOT8lJSXo6OhAMBhEYWFhwm2uuuoqyxpGRCQyK66K1SG7MXHzDIJB7eUM3Jp6XHewDsWbi1G2pQyL6hYlXPePvMHtnDo76Q5+LrvsMlxxxRV47733Yu7ft28fvvGNb1jeMCIikVk10ywUApqbgfp6oKYm+u+hQ0BeXuKp825OPU62AHJbuA0VWysYAHlQugG66HQHP48++ii+/e1v4x/+4R/w6quv4s9//jPmz5+Pyy67DFlZWXa2kYhIOFZeFfdfwb6zEzj33MS9Om5OPY70RrD8+eVQMPDF1fuqnq9CpFfCec+UUqIAvalJ3sAHMJjwvGbNGmRmZuLrX/86IpEIZsyYgTfeeAOTJ0+2q33kIo7rE6Vm9UwztVcnPrhRe3XWrjWXZG1GY0vjgB6fmNeGgtZwKxpbGjlRQjJ68seczqmzm+7gp729HRs3bsSjjz6Kiy66CO+99x4WLFggVOBTXFyMDz74IOa+H/3oR/i3f/s3l1okr76FI/t92QVzgtg8czPr/AhI9EBV9PaZYdVMMz1T59WeJi12TD3Wu54f1/2Ti1/XltMd/HzpS1/Cl7/8ZTzzzDOYPXs2XnjhBcyfPx+HDx/Gj370IzvbaMj69etx00039f08dOhQF1sjJ3VcP757Wx3XZ6FDsYgeqIrePitYcVWsZ+p8Z6e+57Jj6rHe9fy47p88tHoaZc7p0aI75+eJJ57Avn37MHv2bADAjBkzUF9fj82bN2Pp0qW2NdCoYcOGobCwsO8mSvAT6Y2gobkBte/UoqG5QdhxcY7ry0X0BFTR2ycSvb01eXnuLOehtQAy1/2Ti5eXrtBDd/CzYMGCAfdNnjwZu3fvRkNDg5VtMuVnP/sZRowYgUmTJmHDhg3o6elxu0lSTQ01Mq5P7hI9UBW9faLR21uzfHn0X6enHqdaAJnr/snHy0tX6JHWqu79FRcX4z//8z+taItpy5cvx1NPPYX6+nosW7YM1dXVmr1S3d3dCIfDMTcryXbly3F98STrNRQ9UBW9faLRO3V+9Wr3ph4nWwCZ6/7Jx8tLV+hheHmLRIYPH27F0yS0du1arFu3LuU2b7zxBi677DKsWLGi775LLrkEw4cPR0VFRV9vUCIbN27UfP50aV35BhBA1fNVKL+wXJirJZHH9b2cNJtMqnyZ7i+6dT2HW4EqA2ljjFR8dmM5D1VoQgjlF5b77m/Ra7y8dIUeAUXwpdiPHTuGY8eOpdymuLgYgwcPHnB/W1sbgsEgXnvtNVxxxRUJf7e7uxvd3adPIuFwGEVFRejq6kJOTo6ptjc0N6BsS5nmdvWV9cJMDY30RlC8uRht4baEQVsAAQRzgmha3uTol50fkmbjJUs8V4cY1pauxZqGNZrP49bxJePxL4JEs2+KiuxdpJX8JxKJ1o/SWrqiqUmeCs7hcBi5ubm6zt+W9PzYKT8/H/n5+Wn97r59+wAAo1KErllZWbYVaZTxylcd16/YWoEAAjEnXrfG9f04+0xPr+Ev9v4CwWFBtJ1IHai6lYCqJshqBdJMkI3lZq+O09xcn8zvzK4tJzvTOT+i2LNnD+69917s378fTU1N2Lp1K77zne/g2muvxdixY11pk8hDSKmINK7v16RZPfkyh08cxk1TomUdRExAZYJs+vpXfC4t9eYJyM31ySjKq0tX6CH8sJdeb731FpYuXYr33nsP3d3dGDduHBYsWIAf/vCHGDJkiO7nMdJtpkXUISS9RMix8evQSe07tVhUt0hzu5pQDbLOyBowJFiUU4TqmdVC9IglGrIUqX3kvGT1ZdQeB6+feEXjlR44Tw176TV58mS89tprbjcjhohDSEZkDMpwPaCQcegwXjpBpJFew9LiUqETUL2SICvCxYAX6KlkXVUVHfqT8QQsI68tXaGHZ4IfUalDSImSdXnlq03WoUNVuonaRvNlRAhUUxG9fVr8mHBvFyP1Zfx2QibneCbnR2ShCSE0L29GfWU9akI1qK+sR9PyJn5p6iBzVVkzNZ6YLyMO2Wp1ic7v9WVIDAx+HKJe+S68eCFKi0t50tJJ1iDAikRtkRLP/cqvCfd28nt9GRKDZxKerWJlwjNZR7akWSsTtZlr4h6/JtzbyYv1ZUgMvkx4Jm+TLWnWykRtK/NlGEgZ44WEe9H4vb4MiYHBD0lDpqRZERO1mbRrnJHPkYGlfmp9mfhK1sEgK1mTMxj8ENlAtOrGfqySbQW9n+NHpz5C8eZioQJL0YMxP1WyJvEw5ycOc37IKmrAASBhjSetgMOqk5dabDNZxWjRi226TetzvG3abbhr911J12BzI7BkLx/5kZHzN2d7EdnEzGytuoN1KN5cjLItZVhUtwhlW8pQvLk4rWnVepbKaA23orGl0fBz+0Gqz3FrxVbU/qlWqNlgnJpPpI09P3HY80NWM9qDo7Wau9GeBCNLZSy8eKHu5/Uarc8p0eONLY1CzQZjLx/5GWd7EQnESKK2ntXcq56vQvmF5bpPXiImX4tGzzBRos9RtNlgRnr5ZJk8QGQHDnsRCcSOISqZq2Q7wcwwkWiBpd4ga8d7O2xuCZHYGPwQCcSOnoR0q2RHeiNoaG5A7Tu1aGhu8GQVY7MVnEULLPUGWdWvVzP3h3yNwQ+RQOzqSTCafG1lwrXI9Pa0NTQ3JAwERVt+RQ3GtKjDpzIFtH4Ixsk5THiOw4RncpOasKpVVybdhFU9ydfbDmzDvG3zEr424M7UbbvoTQbPy85D56edfT/H5wOJtPxK3cE6zN06V9e2sizLwan7pIeR8zeDnzgMfshtZusDmfHMgWewcPtCRJTEV9Vemy2kd+2ueIk+C5GKCq54YQWqX6vW3E6GGX5Wz34k72KdHyIJqd363V90Y23pWowZ5uxq7nUH6zB/2/ykgQ/gvZpAJWNLMCJ7hOHfS5QPpM4GW3jxQpQWl7oaHJZfWK5rO9Fn+JnNySJKhlPdiQSQqFt/zLAxWFe6DufnnW97T4J6ktHLKwt57vifHTj+6fG0flfkaeOiLa+SLk7dJ7uw54fIZcmmWh85cQRrG9Yi64ws23sStE4y8Yz2GIiYrGo04EtGxEBQtETsdIlWR4m8g8EPkYtE6dY3cvIwOnVb1JljRgO+ZEQdOjKzvIooRKujRN7BYS/SJFIip9eI0q1v5ORhpMdA5NXkzfYWyDB0FJoQQvmF5dL+/Xpl+I7Ew+CHUuIUU3uJ0q2vdZIBgEGBQagN1er+3O1YqkN9XitO5kYCvgACCWfeyTB0ZGR5FdGow3cVWyuk/gxIPBz2oqS4OrT9ROnWT5UjoupVenHrrlt1f+52LNVh5RBaydgSjBwyUte2+UPyY36WaehIdl4YviPxsM5PHNb5iRJ1dWivDcHpLWp46HuHsPvwbtvfd6Kevvj2APpqq1i9mrxWvZenK57GyLNGGtpHK55fgerXqzVf+9fX/RpjcsYYWvFd5uNSRNzHpIWrupNpouSi9OfFITg93foLJi7Aufed68j7Dk0I4ZvnfxNj7h2DY58cG/C4keEqK3q11BNeW7gNVS9UpUwMjy/OGMwJ4p7p96QMiMq/XK4r+BmTMybpce7F41JEMg/fkXg47EUJiZKLovLyEFyqbv3bpt2Gu3bf5ej73n14d8LAR6V3uMrsop/9h7j+6bf/lLJNAAYUZzwcPoz52+anHCLTWgtLTxu9elwSeRmDH0pIlFwUQJzp4HYKTQiheXkz6ivrUROqQX1lPQ597xBq/1Tr6PuO9Ebw0l9f0rWtVuBrptZMsqDCrPigRG1j4O//6WmjWrPoN2//Bt/5f9+x7PMRsRYSkVcx+KGEzF61W8mOxFkRxS+PsPvwbkfft9rTcmfjnbq21xP4JuvVGp49HGtL1yZchiFVsGtWoqDESEKtkd4oI5+PqLWQiLyKwQ8lJFKFWNGG4Jzi5Ps20tNiNPBVe7XWla5DXnYeAKDz006saViT8ARvVfHBZBIFJYl63pqWNw0IfNLpjUr0+fTv5Vn/8noOnRE5jAnPlJR6RZwombN6ZrVjyZwiDcE5yan3baSnJd3Ad8f/7MDahrW6ih06FcTGv06qhFozvVHxn4/WjDqVmVpIRJQagx9KSYQKsXoK8I3IHuG5Kq9OVbc10tOSTuBrtNih0WAuI5CRciX6ZIy8Tjq9UYk+n2TT9ZPhwp1E9uCwF2mKz0XRG/hYlcCpDsGlOmEc//Q4dvzPjrSeX1RODT3q7Wm5veT2AUNBehjN2dKTbzZyyEj8+rpfo76yHk/NfSphwnIy6eSrGe2NSvT5mOk98tqQrl8xqV0c7PkhW1hd+6T8wnKMyB6B458eT/i4KMMDVhdiSzX0ePf0u5GXnYfad2odWebhmi9dk9bzG81d0lP76KFvPhRzHG0bNHAfJZJu0Gi0NypRD5mZXCavDen6EetBiYUVnuOwwrN5WpV40ylJ39DcgLItZZrb1VfW2zo8kCq4sfPLLf51j506hhU7V1jyWnqrTKdbzTvdzy7R/izKKUo67KZnH6X6/VT07KP8Ifm4d8a9GJMzJmEgqrfidfzzulFJnaxlx3ciDWTk/C1N8LNhwwY8++yz2L9/PzIzM/G3v/1twDYtLS347ne/iz/+8Y/Izs7GokWLcNdddyEzM1P36zD4MceuZTGsXiohHamCGwCOfbnZ8UWqPieAhD0tZtpvJrgy25Nm5Pe1tjW7j/QGgfG2z9/OE6PERF0qyIuMnL+lyfnp6enBvHnz8M///M8JH49EIpg9ezZOnTqFV199FU899RS2b9+OW2+91eGW+ptdNXmcnPGVaFxeq5Lvzb+/2ZFihHYVfLRz8UgzuUvp5psZ/X09dXbM7iOtXKZERmSPSFgLieThlzplspEm52fdunUAgCeffDLh4zt37sS7776L1tZWjB49GgBw9913Y/HixdiwYQN7cRxiV20ap2Y+JezdGRbEp198mjLgSJaLpG5jZsZO/x6JD099aNuaa3bO7BOlbEIiyXrSEk3DN7OPUuUyJXP80+Oc6SU5v9YpE500wY+WPXv2YOLEiX2BDwDMmDED3d3d2Lt3L8rKEnc3d3d3o7u7u+/ncDhse1u9zK4eGj1JsGZnPiU7CR4+YU3BvXS+3PTWhLHitQB7F48UoWxCPKPT8AFz+yhZEJgKT4py82udMtFJM+ylpaOjAwUFBTH3DR8+HJmZmejo6Ej6exs3bkRubm7fraioyO6mepqdy2LYOTRj55IKKqNfbmbWtxL1i9TsMJbV3BiSUKtJ3zvjXl3bi/pZkj4iLRVEp7ka/KxduxaBQCDl7c0339T9fIHAwINLUZSE96tWrVqFrq6uvltra2ta74Wi7K5No2cZgnTYuaRCOl9u6QZj/CI1xq0hiYxBGfje//oeT4o+INJSQXSaq8Ney5Ytw4IFC1JuU1xcrOu5CgsL8frrr8fc9/HHH+Pzzz8f0CPUX1ZWFrKysnS9Buljd36HHUMzZk5uAQSQl52H458et2xILt1gTIHCL1ID3ByScGIol8Qgcs6bX7ka/OTn5yM/P9+S55o6dSo2bNiA9vZ2jBoV/aLauXMnsrKyMGXKFEteg/QTMb8jlXRPbupJ6pE5jwCA6S83Nbl5+7vb02pP1RVV/CI1wKlE+mR4UvQP2b4TvU6aOj8tLS3o7OzEf/zHf2DTpk1obIyOwZ933nkYOnQoIpEIJk2ahIKCAmzatAmdnZ1YvHgxvvWtb+G+++7T/Tqs8+NPemrR5GXnYfAZg9F2oq3v/viieWbq0qSb3Nyf3UUevcjOGkd6WV0ZnMiPPFnkcPHixdiyZcuA++vr61FaWgogGiAtXbp0QJFDI8NaDH78S89J0K4rN6MLXsZjoTRzjFaTlgWDKvITTwY/TmHw429unAS1KsBqEaVEvuwnWtnbH49rSZHfMPgxgcEPOX0SNLrsQUYgAxHldAVnEXooeKIVC9eSIj9i8GMCgx9ymt51y5ZdvgxzL5qLacFp2H14tzA9FDzRioVrSZFfGTl/e6bCM5Gs9M40m3vR3L5kZjuSmtPp8UqnQjLZy0jhRibHk18x+CFymdvTrQHjw1ZqoPTSX1/iiVYwXEuKSBuDH/IEmZNV3S52Z2RhT3V7o1PyeaJ1DteSItLmmbW9yL/qDtaheHMxyraUYVHdIpRtKUPx5mLUHaxzu2m62bluWSpaw1YAUPV8FSK90QTrdNcb44nWOVxLikgbE57jMOFZLlYm24rQe5RuG9L9Pb0zzeor61EytsTwlHwm17pDhMKNRE5jwjP5gpXJtqJM1U5n3TIzbd/x3g5dr9F+ot3wemNcn8o9XDaDKDX2/MRhz488jPRapAooZJ6qbabtdQfrMHfrXF2vU19Zj/YT7bqm5KtEqD/kdyL0ZhI5hT0/5AtWzGqReaq2mbarv6uHmh/S2NKoa/vbS27HNV+6hidaAaTTk0jkB0x4JmlZMavFSE0U0Zhpu5EhLHXYSm8i7drStSgtLmXgQ0TCYvBD0rJiVovMNVHMtF3v7w49c2jf/6tT8gEM2OfM7yEimTD4IWlZcTKWuSaKmbbr/d2Tn59ExdaKvrIBbk3JJyKyEhOe4/gp4dkryZBmVmJX10HSqq4s4lRtM23X+l2t5/HKsWMn7iMiZ3FhUxP8EvyIMrXbKmZONDLXRDHT9mQzxZLRmjVHp3nt74tIBkbO3xz28qFkVXrV5QxkqoysUhNyRw0b1VeTRq1KrEXmoRwzbVd/Ny87T9drJcsTivRG0NDcgNp3atHQ3KB7v8vEyHu0+u/LD/uXyGns+Ynj9Z4fdbgj2Uwfp4Z5rB4SsOJKW+ZhCjNtf+mvL+Frv/qa5naJen7M7HdZ9reR92j13xd7kIj047CXCV4PfqwqDGiG1V/oMhcpFEG6uUNmCyzKcFI3+h6t/PvicU1kDIe9KCm3p3bbMSRgZGFOGiidWXNm9rssw67pvEer/r54XBPZi8GPz7g5tduOL3SZixSKxGjuULr7XaaTejrv0aq/Lx7XRPbi8hY+oxYG1BriSFUYMF1GvtD1Drm53ZPlJaEJIZRfWK4rDyfd/W7HMWCXdN6jVX9fPK6J7MWeH59xs0qvHV/oMhcpFJG6FtTCixemXKIi3f0u00k9nfdo1d8Xj2tv4Ew9cTH48SG3pnbb8YVuxRIXZFy6+12mk3q679GKvy+nj2uepK1Xd7AOxZuLUbalDIvqFqFsSxmKNxcLk9Pmd5ztFcfrs736c3qqsV3VlGUuUhhPlunfQHr7XbaK2maOLbOfpVPHtSwz72TCmXru4FR3E/wU/LjBri90M0tciELGk1A6+122YNXNY8vu1+ZJ2nqi1FLzIwY/JjD4sZ9dX+gy9ZrEk/kklM5+ly1YdfPYsuu1eZK2hwi11PyKwY8JDH6cIXOgYjW/noR4DLiLJ2l71L5Ti0V1izS3qwnVYOHFCx1okX8YOX9zqju5Qp1VRHJN/7YSjwF36Z1R1xZuQ0NzA4NUnWRK6vczBj9ELpNp+jd5h96T74oXVuCjTz7q+1n0PDS3uVlLjfTjVHcil/FK0ftEnEquNZ1e1T/wAcRbhkQ0btZSI/0Y/BC5jLWKvE3Uei+pTtKpiLYMiYjcqqVG+jHhOQ4TnsXjh8RY2aZ/kz4yzOJLNPNu5JCRA3p8EmEydGp++O4SCWd7mcDgRywy1r5Jl2zTv2XixknIrVl86bzX+N9pC7fhn377T5qvxRlLJBJPzvbasGEDnn32Wezfvx+ZmZn429/+NmCbQGBg1+2DDz6IW265xYEWktWSXTWrOQciXDVbycjCoqSfWwG0G7P40n2v8TPvGpobdL0e89BIVtIEPz09PZg3bx6mTp2Kxx57LOl2TzzxBGbOnNn3c25urhPNIwP0XJlGeiNY/vzyhLMlFCgIIICq56tQfmG5p4IDTv+2lpsBtNOz+Kx8r3bNWOIwEIlCmuBn3bp1AIAnn3wy5XZnn302CgsLHWgRpUPvlalfa9+QddwOoJ2cxWf1e1WToSu2ViCAQMI8NKMzlvw0hE3i89xsr2XLliE/Px+XX345HnroIfT29rrdJPo79co0PqhJNHWWtW/ILCMBtB2cnMVnx3u1csaSkb99IidI0/Ojx09+8hNcc801yM7OxksvvYRbb70Vx44dw+233570d7q7u9Hd3d33czgcdqKprnB7fSIjV6asfUNmuR1A29F7koxd79WKPDS3e+CIEnG152ft2rUIBAIpb2+++abu57v99tsxdepUTJo0CbfeeivWr1+PTZs2pfydjRs3Ijc3t+9WVFRk9m0Jye1aI0avTFn7hswSIYB2qt6Lne9VzUNbePFClBaXGg5Q3O6BI0rE1Z6fZcuWYcGCBSm3KS4uTvv5r7zySoTDYXz44YcoKChIuM2qVauwcuXKvp/D4bDnAiARZk0ZvTJ18qrZj/yQeCrKMgNOzOIT5b0m4nYPHFEirgY/+fn5yM/Pt+359+3bh8GDB+Pss89Ouk1WVhaysrJsa4PbROlyTufKVL1qTpQkydo36fNL4qlIAbTds/hEeq/xROiBI4onTc5PS0sLOjs70dLSgkgkgv379wMAzjvvPAwdOhS///3v0dHRgalTpyI7Oxv19fVYvXo1br75Zk8HN1pEmTWV7pUpa99YS4ReQCfJEkBb0RMn6nsVuVeK/EuaCs+LFy/Gli1bBtxfX1+P0tJSPP/881i1ahUOHTqE3t5efOlLX8KSJUvw3e9+F2ecoT/G81qF59p3arGobpHmdk5UauUSDu5yq+KwCEQe5rO6J07E98q/fXICl7cwwWvBT0NzA8q2lGlu59QaPVzCwT2iHQskx9pfVuHfPtnNk8tbUHpE63LmMJZ7mHgqFlHy8ZzCv30SCYMfjxMxEZJLOLiDiadiESUfz0n82ydReK7CMw3kVK0REhtrJ4mFPXFE7mHPj0+wy5lE7AX0M/bEEbmHCc9xvJbwTBSPiadiUGffaeXjeXH2HZEdmPBMREmxF1AM7Ikjcg97fuKw54eInMSeOCJrsM6PCQx+iMhpIhYmJJINh72IiCTCKeBEzuJUdyIiIvIVBj9ERETkKxz2IiJNzEkhIi9h8ENEKVm96jgRkds47EVESamrjsevQdUWbkPF1grUHaxzqWVEROlj8ENECWmtOg4AVc9XIdIbcbppRESmMPghooSMrDpORCQT5vz4CJNWyQiuOk5EXsXgxyeYtEpGcdVxIvIqDnv5AJNWKR0lY0sQzAn2LbIZL4AAinKKUDK2xOGWERGZw+DH45i0SulSVx0HMCAA4qrjRCQzBj8ex6RVMiM0IYRt87dhTM6YmPuDOUFsm7+NQ6ZEJCXm/Hgck1bJrNCEEMovLGeyPBF5BoMfj2PSKlmBq46nxpmURHJh8ONxatJqW7gtYd5PAAEEc4JMWiVKE2dSEsmHOT8ex6RVIvtwJiWRnBj8+ACTVp0R6Y2gobkBte/UoqG5gTPoPI4zKYnkxWEvn2DSqr049OE/RmZSMl+KSCwMfnyESav2UIc+4nsA1KEP9q55E2dSEsmLw15EJnDow784k5JIXgx+iExgEUn/4vIf3sO8Pf/gsBeRCRz68C91JmXF1goEEIjp/eNMSvkwb89f2PNDZAKHPvyNMym9gSUL/CegKMrAZAUfC4fDyM3NRVdXF3JyctxuDgku0htB8eZizSKSTcub2APgYazwLC/1bzjZ8DX/huVh5PzNnh8iE1hEkoDTMykXXrwQpcWl/Lwlwrw9f5Ii+GlubsaNN96I8ePHIzs7G+eeey7WrFmDnp6emO1aWlowZ84cnHXWWcjPz8f3v//9AdsQWY1DH0TyYt6eP0mR8Pzee++ht7cXDz/8MM477zz86U9/wk033YRTp07hrrvuAgBEIhHMnj0bI0eOxKuvvorjx4+jsrISiqLgvvvuc/kdkNexiCSRnJi350/S5vxs2rQJDz74IP76178CAP7whz/gm9/8JlpbWzF69GgAwFNPPYXFixfj6NGjuvN3mPNDROQfzNvzDl/k/HR1dSEvL6/v5z179mDixIl9gQ8AzJgxA93d3di7d2/S5+nu7kY4HI65ERGRPzBvz5+kDH7+8pe/4L777sMtt9zSd19HRwcKCgpiths+fDgyMzPR0dGR9Lk2btyI3NzcvltRUZFt7SYiIvEwb89/XA1+1q5di0AgkPL25ptvxvzOkSNHMHPmTMybNw9LliyJeSwQGFhpVVGUhPerVq1aha6urr5ba2urNW+OiIikEZoQQvPyZtRX1qMmVIP6yno0LW9i4ONRriY8L1u2DAsWLEi5TXFxcd//HzlyBGVlZZg6dSoeeeSRmO0KCwvx+uuvx9z38ccf4/PPPx/QI9RfVlYWsrKyjDeeiIg8hYs/+4erwU9+fj7y8/N1bdvW1oaysjJMmTIFTzzxBAYNiu20mjp1KjZs2ID29naMGhXNyt+5cyeysrIwZcoUy9tOREREcpJitteRI0dw9dVXY+zYsfjlL3+JjIzTiWeFhYUAolPdJ02ahIKCAmzatAmdnZ1YvHgxvvWtbxma6s7ZXkRERPIxcv6Wos7Pzp07cejQIRw6dAjBYDDmMTV2y8jIwLPPPoulS5fiqquuQnZ2NhYtWtRXB4iIiIgIkKTnx0ns+SEiIpKPL+r8EBEREaWDwQ8RERH5CoMfIiIi8hUGP0REROQrDH6IiIjIVxj8EBERka8w+CEiIiJfYfBDREREvsLgh4iIiHyFwQ8RERH5CoMfIiIi8hUGP0REROQrDH6IiIjIVxj8EBERka+c4XYDiCi5SG8EjS2NaD/RjlHDRqFkbAkyBmW43SwiIqkx+CESVN3BOix/fjkOhw/33RfMCWLzzM0ITQi52DIiIrlx2ItIQHUH61CxtSIm8AGAtnAbKrZWoO5gnUstIyKSH4MfIsFEeiNY/vxyKFAGPKbeV/V8FSK9EaebRkTkCQx+iATT2NI4oMenPwUKWsOtaGxpdLBVRETeweCHSDDtJ9ot3Y6IiGIx+CESzKhhoyzdjoiIYjH4IRJMydgSBHOCCCCQ8PEAAijKKULJ2BKHW0ZE5A0MfogEkzEoA5tnbgaAAQGQ+nP1zGrW+yEiShODHyIBhSaEsG3+NozJGRNzfzAniG3zt7HODxGRCQFFUQbOp/WxcDiM3NxcdHV1IScnx+3mkM+xwjMRkT5Gzt+s8EwksIxBGSgtLnW7GUREnsJhLyIiIvIVBj9ERETkKwx+iIiIyFcY/BAREZGvMPghIiIiX2HwQ0RERL7C4IeIiIh8hcEPERER+QqLHMZRC16Hw2GXW0JERER6qedtPQtXMPiJc+LECQBAUVGRyy0hIiIio06cOIHc3NyU23Btrzi9vb04cuQIhg0bhkAgoP0LgguHwygqKkJrayvXKrMZ97VzuK+dw33tHO5rcxRFwYkTJzB69GgMGpQ6q4c9P3EGDRqEYDDodjMsl5OTwz8mh3BfO4f72jnc187hvk6fVo+PignPRERE5CsMfoiIiMhXGPx4XFZWFtasWYOsrCy3m+J53NfO4b52Dve1c7ivncOEZyIiIvIV9vwQERGRrzD4ISIiIl9h8ENERES+wuCHiIiIfIXBj4dt2LAB06ZNw5AhQ3D22Wcn3CYQCAy4PfTQQ8421AP07OuWlhbMmTMHZ511FvLz8/H9738fPT09zjbUo4qLiwccxz/+8Y/dbpYnPPDAAxg/fjwGDx6MKVOmoLGx0e0mec7atWsHHL+FhYVuN8vTWOHZw3p6ejBv3jxMnToVjz32WNLtnnjiCcycObPvZ70VMuk0rX0diUQwe/ZsjBw5Eq+++iqOHz+OyspKKIqC++67z4UWe8/69etx00039f08dOhQF1vjDU8//TSqqqrwwAMP4KqrrsLDDz+MWbNm4d1338XYsWPdbp6nfOUrX8GLL77Y93NGRoaLrfE+Bj8etm7dOgDAk08+mXK7s88+m1cZJmnt6507d+Ldd99Fa2srRo8eDQC4++67sXjxYmzYsIGl7C0wbNgwHscWu+eee3DjjTdiyZIlAIDq6mq88MILePDBB7Fx40aXW+ctZ5xxBo9fB3HYi7Bs2TLk5+fj8ssvx0MPPYTe3l63m+Q5e/bswcSJE/sCHwCYMWMGuru7sXfvXhdb5h0/+9nPMGLECEyaNAkbNmzgkKJJPT092Lt3L6ZPnx5z//Tp07F7926XWuVd77//PkaPHo3x48djwYIF+Otf/+p2kzyNPT8+95Of/ATXXHMNsrOz8dJLL+HWW2/FsWPHcPvtt7vdNE/p6OhAQUFBzH3Dhw9HZmYmOjo6XGqVdyxfvhyTJ0/G8OHD8V//9V9YtWoVmpqa8Oijj7rdNGkdO3YMkUhkwHFbUFDAY9ZiV1xxBX75y1/iggsuwIcffog777wT06ZNw4EDBzBixAi3m+dJ7PmRTKLEuPjbm2++qfv5br/9dkydOhWTJk3CrbfeivXr12PTpk02vgN5WL2vA4HAgPsURUl4Pxnb/ytWrMDVV1+NSy65BEuWLMFDDz2Exx57DMePH3f5Xcgv/vjkMWu9WbNmYe7cubj44ovxta99Dc8++ywAYMuWLS63zLvY8yOZZcuWYcGCBSm3KS4uTvv5r7zySoTDYXz44YcDrvj8xsp9XVhYiNdffz3mvo8//hiff/657/dzMmb2/5VXXgkAOHToEK+c05Sfn4+MjIwBvTxHjx7lMWuzs846CxdffDHef/99t5viWQx+JJOfn4/8/Hzbnn/fvn0YPHhw0unafmLlvp46dSo2bNiA9vZ2jBo1CkA0CTorKwtTpkyx5DW8xsz+37dvHwD07WsyLjMzE1OmTMGuXbtw3XXX9d2/a9culJeXu9gy7+vu7sbBgwdRUlLidlM8i8GPh7W0tKCzsxMtLS2IRCLYv38/AOC8887D0KFD8fvf/x4dHR2YOnUqsrOzUV9fj9WrV+Pmm2/mqsIGae3r6dOn46KLLsINN9yATZs2obOzE7fddhtuuukmzvQyac+ePXjttddQVlaG3NxcvPHGG1ixYgWuvfZaTsc2aeXKlbjhhhtw2WWXYerUqXjkkUfQ0tKCW265xe2mecptt92GOXPmYOzYsTh69CjuvPNOhMNhVFZWut0071LIsyorKxUAA2719fWKoijKH/7wB2XSpEnK0KFDlSFDhigTJ05Uqqurlc8//9zdhktIa18riqJ88MEHyuzZs5Xs7GwlLy9PWbZsmfLZZ5+512iP2Lt3r3LFFVcoubm5yuDBg5ULL7xQWbNmjXLq1Cm3m+YJ//7v/66MGzdOyczMVCZPnqy8/PLLbjfJc66//npl1KhRyplnnqmMHj1aCYVCyoEDB9xulqcFFEVR3Aq8iIiIiJzG2V5ERETkKwx+iIiIyFcY/BAREZGvMPghIiIiX2HwQ0RERL7C4IeIiIh8hcEPERER+QqDHyIiIvIVBj9ERETkKwx+iMiTamtrMXjwYLS1tfXdt2TJElxyySXo6upysWVE5DYub0FEnqQoCiZNmoSSkhLcf//9WLduHR599FG89tprGDNmjNvNIyIXcVV3IvKkQCCADRs2oKKiAqNHj8bmzZvR2NjYF/hcd911aGhowDXXXINt27a53FoichJ7fojI0yZPnowDBw5g586duPrqq/vur6+vx8mTJ7FlyxYGP0Q+w5wfIvKsF154Ae+99x4ikQgKCgpiHisrK8OwYcNcahkRuYnBDxF50ltvvYV58+bh4YcfxowZM/Cv//qvbjeJiATBnB8i8pzm5mbMnj0bP/7xj3HDDTfgoosuwuWXX469e/diypQpbjePiFzGnh8i8pTOzk7MmjUL1157Lf7lX/4FADBlyhTMmTMHq1evdrl1RCQC9vwQkafk5eXh4MGDA+7fsWOHC60hIhFxthcR+dKMGTPw1ltv4dSpU8jLy8Nvf/tbXH755W43i4gcwOCHiIiIfIU5P0REROQrDH6IiIjIVxj8EBERka8w+CEiIiJfYfBDREREvsLgh4iIiHyFwQ8RERH5CoMfIiIi8hUGP0REROQrDH6IiIjIVxj8EBERka8w+CEiIiJf+f+QLWIlj2h6lQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*X[y==0].T, color='g', label='0')\n",
    "plt.scatter(*X[y==1].T, color='b', label='1')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2bf75204",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:15.248031Z",
     "iopub.status.busy": "2023-08-13T12:36:15.247698Z",
     "iopub.status.idle": "2023-08-13T12:36:15.256230Z",
     "shell.execute_reply": "2023-08-13T12:36:15.255079Z"
    },
    "papermill": {
     "duration": 0.017115,
     "end_time": "2023-08-13T12:36:15.258383",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.241268",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(160, 2) (40, 2)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_val, y_train, y_val = train_test_split(X, y,\n",
    "                                                test_size=0.2,\n",
    "                                                shuffle=True,\n",
    "                                                stratify=y,\n",
    "                                                random_state=35)\n",
    "print(X_train.shape, X_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d292589",
   "metadata": {
    "papermill": {
     "duration": 0.005326,
     "end_time": "2023-08-13T12:36:15.269157",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.263831",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "04c15288",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:15.281130Z",
     "iopub.status.busy": "2023-08-13T12:36:15.280817Z",
     "iopub.status.idle": "2023-08-13T12:36:15.576228Z",
     "shell.execute_reply": "2023-08-13T12:36:15.575473Z"
    },
    "papermill": {
     "duration": 0.303638,
     "end_time": "2023-08-13T12:36:15.578329",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.274691",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = LogisticRegression(epochs=100)\n",
    "model.fit(X_train, y_train, verbose=False, plot_loss=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b03f025c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:15.590927Z",
     "iopub.status.busy": "2023-08-13T12:36:15.590626Z",
     "iopub.status.idle": "2023-08-13T12:36:15.599204Z",
     "shell.execute_reply": "2023-08-13T12:36:15.598344Z"
    },
    "papermill": {
     "duration": 0.016905,
     "end_time": "2023-08-13T12:36:15.601170",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.584265",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def plot_decision_boundary(weights, bias):\n",
    "    # Retrieve model parameters.\n",
    "    b = bias\n",
    "    w1, w2 = weights\n",
    "\n",
    "    # Calculate the intercept and gradient of the decision boundary.\n",
    "    c = -b/w2\n",
    "    m = -w1/w2\n",
    "\n",
    "    # Plot the data and the classification with the decision boundary.\n",
    "    xmin, xmax = X[0].min()-10, X[0].max()+3\n",
    "    ymin, ymax = X[1].min()-10, X[1].max()+3\n",
    "\n",
    "    xd = np.array([xmin, xmax])\n",
    "    yd = m*xd + c\n",
    "\n",
    "    plt.plot(xd, yd, 'k', lw=1, ls='--')\n",
    "    plt.fill_between(xd, yd, ymin, color='tab:blue', alpha=0.5)\n",
    "    plt.fill_between(xd, yd, ymax, color='tab:orange', alpha=0.5)\n",
    "\n",
    "    plt.scatter(*X[y==0].T, alpha=0.9)\n",
    "    plt.scatter(*X[y==1].T, alpha=0.9)\n",
    "    plt.xlim(xmin, xmax)\n",
    "    plt.ylim(ymin, ymax)\n",
    "    plt.ylabel(r'$x_2$')\n",
    "    plt.xlabel(r'$x_1$')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3183bee3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:15.615038Z",
     "iopub.status.busy": "2023-08-13T12:36:15.613259Z",
     "iopub.status.idle": "2023-08-13T12:36:15.880733Z",
     "shell.execute_reply": "2023-08-13T12:36:15.879742Z"
    },
    "papermill": {
     "duration": 0.276275,
     "end_time": "2023-08-13T12:36:15.883087",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.606812",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(model.weights, model.bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5ae68cbc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:15.897367Z",
     "iopub.status.busy": "2023-08-13T12:36:15.897045Z",
     "iopub.status.idle": "2023-08-13T12:36:15.905155Z",
     "shell.execute_reply": "2023-08-13T12:36:15.904137Z"
    },
    "papermill": {
     "duration": 0.01762,
     "end_time": "2023-08-13T12:36:15.907114",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.889494",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy:  0.90625\n",
      "Validation accuracy:  0.9\n"
     ]
    }
   ],
   "source": [
    "print('Train accuracy: ', accuracy_score(y_train, model.predict(X_train)))\n",
    "print('Validation accuracy: ', accuracy_score(y_val, model.predict(X_val)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b5c52cd",
   "metadata": {
    "papermill": {
     "duration": 0.00627,
     "end_time": "2023-08-13T12:36:15.919453",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.913183",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Scikit-Learn API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8b07b451",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:15.935153Z",
     "iopub.status.busy": "2023-08-13T12:36:15.934274Z",
     "iopub.status.idle": "2023-08-13T12:36:16.032585Z",
     "shell.execute_reply": "2023-08-13T12:36:16.031475Z"
    },
    "papermill": {
     "duration": 0.109105,
     "end_time": "2023-08-13T12:36:16.034967",
     "exception": false,
     "start_time": "2023-08-13T12:36:15.925862",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#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>LogisticRegression()</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\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "model = LogisticRegression()\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "180f4240",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:16.049836Z",
     "iopub.status.busy": "2023-08-13T12:36:16.049479Z",
     "iopub.status.idle": "2023-08-13T12:36:16.314877Z",
     "shell.execute_reply": "2023-08-13T12:36:16.313736Z"
    },
    "papermill": {
     "duration": 0.275683,
     "end_time": "2023-08-13T12:36:16.317328",
     "exception": false,
     "start_time": "2023-08-13T12:36:16.041645",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(model.coef_.T, model.intercept_[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cb842142",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-13T12:36:16.333252Z",
     "iopub.status.busy": "2023-08-13T12:36:16.332911Z",
     "iopub.status.idle": "2023-08-13T12:36:16.341774Z",
     "shell.execute_reply": "2023-08-13T12:36:16.340971Z"
    },
    "papermill": {
     "duration": 0.018828,
     "end_time": "2023-08-13T12:36:16.343808",
     "exception": false,
     "start_time": "2023-08-13T12:36:16.324980",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy:  0.91875\n",
      "Validation accuracy:  0.875\n"
     ]
    }
   ],
   "source": [
    "print('Train accuracy: ', accuracy_score(y_train, model.predict(X_train)))\n",
    "print('Validation accuracy: ', accuracy_score(y_val, model.predict(X_val)))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  },
  "papermill": {
   "default_parameters": {},
   "duration": 12.987012,
   "end_time": "2023-08-13T12:36:17.070311",
   "environment_variables": {},
   "exception": null,
   "input_path": "__notebook__.ipynb",
   "output_path": "__notebook__.ipynb",
   "parameters": {},
   "start_time": "2023-08-13T12:36:04.083299",
   "version": "2.4.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}