{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[],"toc_visible":true,"collapsed_sections":["4zw1zRd6eJL7","T_QkeG6L3Kut","2tRxaHkXKipl"],"authorship_tag":"ABX9TyO9P8OiNQxQnajwUt9lPDN+"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["# PAL Machine Learning Workshop: Linear Regression\n","---\n","Hi all! Welcome to this workshop! Today we're going to do some really cool stuff with linear machine learning models.\n","\n","We will start by importing the necessary packages and data, then define our first linear model and try to optimize it for our task.\n","\n","Let's begin!"],"metadata":{"id":"WtrRno2HT3A7"}},{"cell_type":"code","execution_count":null,"metadata":{"id":"k7CUZtQRTbno"},"outputs":[],"source":["# Linear algebra\n","import numpy as np\n","# Nice tool for data manipulation\n","import pandas as pd\n","# Visualizing our data\n","import matplotlib.pyplot as plt"]},{"cell_type":"markdown","source":["## Data Loading"],"metadata":{"id":"ZCGCQegmT_Pf"}},{"cell_type":"markdown","source":["We will start by downloading the diabetes dataset frm `sklearn`. This dataset contains ten baseline variables: age, sex, body mass index, average blood pressure, and six blood serum measurements, that were obtained from 442 diabetes patients."],"metadata":{"id":"h_cbTj5bUbN6"}},{"cell_type":"code","source":["from sklearn import datasets\n","\n","# Load the data\n","diabetes = datasets.load_diabetes(as_frame=True)\n","\n","# Get features and targets\n","diabetes_X, diabetes_y = diabetes.data, diabetes.target\n","diabetes_X.head()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":206},"id":"yRse2z7xUBNh","executionInfo":{"status":"ok","timestamp":1677159017931,"user_tz":0,"elapsed":10,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"outputId":"f95b512f-62d8-420d-cbcf-21e831a4e630"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[" age sex bmi bp s1 s2 s3 \\\n","0 0.038076 0.050680 0.061696 0.021872 -0.044223 -0.034821 -0.043401 \n","1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163 0.074412 \n","2 0.085299 0.050680 0.044451 -0.005671 -0.045599 -0.034194 -0.032356 \n","3 -0.089063 -0.044642 -0.011595 -0.036656 0.012191 0.024991 -0.036038 \n","4 0.005383 -0.044642 -0.036385 0.021872 0.003935 0.015596 0.008142 \n","\n"," s4 s5 s6 \n","0 -0.002592 0.019908 -0.017646 \n","1 -0.039493 -0.068330 -0.092204 \n","2 -0.002592 0.002864 -0.025930 \n","3 0.034309 0.022692 -0.009362 \n","4 -0.002592 -0.031991 -0.046641 "],"text/html":["\n","
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00.0380760.0506800.0616960.021872-0.044223-0.034821-0.043401-0.0025920.019908-0.017646
1-0.001882-0.044642-0.051474-0.026328-0.008449-0.0191630.074412-0.039493-0.068330-0.092204
20.0852990.0506800.044451-0.005671-0.045599-0.034194-0.032356-0.0025920.002864-0.025930
3-0.089063-0.044642-0.011595-0.0366560.0121910.024991-0.0360380.0343090.022692-0.009362
40.005383-0.044642-0.0363850.0218720.0039350.0155960.008142-0.002592-0.031991-0.046641
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\n"," "]},"metadata":{},"execution_count":28}]},{"cell_type":"markdown","source":["Let's look at the data for a single patient"],"metadata":{"id":"k7fT-o-VV4Qg"}},{"cell_type":"code","source":["diabetes_X.iloc[0]"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Mjo_4Mq6VHXU","executionInfo":{"status":"ok","timestamp":1677159017931,"user_tz":0,"elapsed":10,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"outputId":"78373ff8-88e4-4872-ff75-8a3db3fae355"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["age 0.038076\n","sex 0.050680\n","bmi 0.061696\n","bp 0.021872\n","s1 -0.044223\n","s2 -0.034821\n","s3 -0.043401\n","s4 -0.002592\n","s5 0.019908\n","s6 -0.017646\n","Name: 0, dtype: float64"]},"metadata":{},"execution_count":29}]},{"cell_type":"code","source":["diabetes_y[0]"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"ta0P8BWVWo_h","executionInfo":{"status":"ok","timestamp":1677159017931,"user_tz":0,"elapsed":9,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"outputId":"09b70469-356e-4ac3-dd7c-321a9f8d6774"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["151.0"]},"metadata":{},"execution_count":30}]},{"cell_type":"markdown","source":["We will collect 30 data points from this dataset and use as our \"toy\" dataset"],"metadata":{"id":"2Ri5gKEHV6Qt"}},{"cell_type":"code","source":["# We will use BMI as our only feature for predicting the diabetes risk\n","X = diabetes_X.iloc[-30:]\n","X = X.loc[:, 'bmi']\n","y = np.expand_dims(diabetes_y.iloc[-30:], axis=1)\n","\n","# Add an extra column of ones to X\n","ones = np.ones_like(X)\n","X = np.stack([ones, X], axis=1)\n","\n","# Visualize our data points\n","plt.scatter(X[:, 1], y, c='green', edgecolors='black')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"Y3s5L2gCWBQt","executionInfo":{"status":"ok","timestamp":1677159017931,"user_tz":0,"elapsed":8,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"outputId":"7151838c-0750-434e-c949-6a48eef88cab"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["First, we will set random parameter values and see how well our model performs without training.\n","\n","`np.matmul()` method will return the result of matrix multiplication. Alternatively you can use `@` or `np.dot()`."],"metadata":{"id":"vkMFfHvIgZ0k"}},{"cell_type":"code","source":["# Set parameters to random values\n","w0, w1 = 100, -200\n","weights = np.expand_dims(np.array([w0, w1]), 1)\n","\n","# Compute initial prediction\n","initial_prediction = np.matmul(X, weights)\n","\n","plt.scatter(X[:, 1], y, c='green', edgecolors='black')\n","plt.plot(X[:, 1], initial_prediction, color='orange')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"GEjIXLTugVYe","executionInfo":{"status":"ok","timestamp":1677159017932,"user_tz":0,"elapsed":8,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"outputId":"c4b0c332-375b-4bc0-e9a2-67bda419be06"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Now try to implement the MSE loss function, which will give us the difference between our model prediction and the true values. Use the following formula:\n","\n","\\begin{align}\n","MSE = \\frac{1}{n}\\sum_{i=1}^n \\bigl( y - XW \\bigr)^2\n","\\end{align}\n","\n","Note: you can get the dimensions of a NumPy array using `np.shape()`."],"metadata":{"id":"ZmaqIg7GgjQN"}},{"cell_type":"code","source":["# Exercise 1\n","def mean_squared_error(X, y, weights):\n"," y_hat = None\n"," loss = None\n"," return loss\n","\n","mse = mean_squared_error(X, y, weights)\n","mse"],"metadata":{"id":"7ZHZWDZWhRF0"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["## Fitting the line using Normal Equations"],"metadata":{"id":"_H_tD2pRYAKh"}},{"cell_type":"markdown","source":["Best parameters for our linear model can be defined using the following equation:\n","\n","\\begin{align} \n","W^* = (X^TX)^{-1} X^Ty\n","\\end{align}\n","\n","Use this formula to calculate the value of $W^*$. You may find the [np.linalg.inv()](https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html) method useful."],"metadata":{"id":"6YqW_gBGbRtE"}},{"cell_type":"code","source":["# Exercise 2\n","weights_best = None\n","weights_best"],"metadata":{"id":"9H_gbty2YIXC"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Now let's try to visualize our model prediction using these parameters!"],"metadata":{"id":"ql75Ms13bx0o"}},{"cell_type":"code","source":["# Get the prediction using new parameters\n","y_hat = np.matmul(X, weights_best) \n","\n","# Visualize data points and new prediction\n","plt.scatter(X[:, 1], y, c='green', edgecolors='black')\n","plt.plot(X[:, 1], y_hat, color='orange')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"U8zEfh-Pb6R7","executionInfo":{"status":"ok","timestamp":1677159018249,"user_tz":0,"elapsed":6,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"outputId":"8a3e1baa-cf87-4e5d-874f-d3f50a635cfe"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Now let's calculate the MSE for a new prediction. Has it changed? How significant is that change?"],"metadata":{"id":"uXUPbYa6izye"}},{"cell_type":"code","source":["mean_squared_error(X, y, weights_best)"],"metadata":{"id":"tawo2WqHiy6b","executionInfo":{"status":"ok","timestamp":1677159018249,"user_tz":0,"elapsed":5,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"37564af4-7c31-4c67-e82e-e3df9fb60daa"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["2663.6342502846514"]},"metadata":{},"execution_count":36}]},{"cell_type":"markdown","source":["## Multiple Linear Regression"],"metadata":{"id":"Fxnolx-X_JYW"}},{"cell_type":"markdown","source":["Now let's try to use more features and see if our model will do a better job when given more information about the data"],"metadata":{"id":"C4xoWUgM_QBN"}},{"cell_type":"code","source":["X = diabetes_X.iloc[-30:]\n","X = X.loc[:, ['bmi', 'age', 'sex']]\n","y = np.expand_dims(diabetes_y.iloc[-30:], axis=1)\n","\n","# Add an extra column of ones to X\n","ones = np.ones((X.shape[0], 1))\n","X = np.concatenate([ones, X], axis=1)\n","\n","# Visualize data points\n","plt.scatter(X[:, 1], y, c='green', edgecolors='black')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.show()"],"metadata":{"id":"xTw1CHYW_L50","executionInfo":{"status":"ok","timestamp":1677159018443,"user_tz":0,"elapsed":198,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/","height":279},"outputId":"f20ec6c6-212b-43ff-94e8-7e0c53bf6888"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["First, let's see how our data looks like now. We still use 30 examples from our dataset and we have 3 features extracted from the dataset and 1 corresponding to the intercept term for each of them"],"metadata":{"id":"trP8XMNbEelD"}},{"cell_type":"code","source":["X.shape"],"metadata":{"id":"oKYqw6HeEeKv","executionInfo":{"status":"ok","timestamp":1677159018443,"user_tz":0,"elapsed":4,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"732df53f-5a1b-471a-a251-a87e43c4d3d9"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(30, 4)"]},"metadata":{},"execution_count":38}]},{"cell_type":"code","source":["# Then we calculate the best values for the parameters using the equation we defined earlier\n","weights_best = np.linalg.inv(np.dot(X.T, X)).dot(X.T).dot(y)\n","\n","# Get our prediction\n","prediction = np.matmul(X, weights_best)\n","\n","# Visualize data points\n","plt.scatter(X[:, 1], y, c='green', edgecolors='black', label='ground truth')\n","plt.scatter(X[:, 1], prediction, c='red', marker='x', edgecolors='black', label='prediction')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.legend()\n","plt.show()\n","\n","# Compute mean squared error loss\n","mse = mean_squared_error(X, y, weights_best)\n","print(f'MSE: {mse}')"],"metadata":{"id":"qvDg3jdPE4sb","executionInfo":{"status":"ok","timestamp":1677159018681,"user_tz":0,"elapsed":241,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/","height":296},"outputId":"798bcdc8-cd19-4471-b91b-8b4e2c28f7fe"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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TxQRUe0jEZFiYgb19cH7hQuDF8Ds2e3rE+W4WUl3CiIixSYxMcTV18O110berKSkICISoUxmWttF/GSfaM4c2Lw58mYlJQURkYhkOtNaB4kn+9mzobU1+LloUbB91qxgW58+7fvU1+esCck84k6LKE2cONGXLVtW6DBERFKqHllN84lJ8ye8AlVLq2ha15T+g7FYcPUfP9nHE8XAgTBvXpAQ4lpbu50QzGy5u09MtU0dzSIiEWnZ0BJMCJCoElruSJ6AOUks1rEDObGPIblZqbY2p3cKaj4SEYlI5fBKSD7/p5lpbRepTvKpmpUS+xhyQElBRCQiOZ1pzSxoPkrsQ6ivD5YHDlSfAqhPQUSKX+PixmCmtQ3hTGuxLGday0H5i876FJQURER6mc6SgpqPRESkjZKCiIi0UVIQkR7r0dO6UtT0nIKI9Ej8ad1tU7bBNGhuCZ7WBbLrSJWC6rKj2czMk3Yys37u/kGkkWVAHc0ihdPjp3Wl4LLtaP5x0sH2opPZ00Skd2jZ0ALJz2BVhuulZGWSFDaa2c0AZrYv8DvgzkijEpGil9XTur1ZcutMkT0W0GVScPdvAe+Z2f8QJITvu/utkUcmIkUtp0/r9hYFnGYzU2mTgpmdG38BzwAnAH8BPFwnIhEphVE9NdNraKhvoGppFTbfqFpaRUN9gzqZ0ynwNJuZStvRbGad3Q24u18aTUiZU0ezlKMOo3oqgZbgClwn3DKQmAjicjwfQiZU5kKkhGhUT5lzz3o+hGxlNfrIzL5nZnub2e5m9qiZbTKzi3IfpoiARvWUtVTTbOaw7HUuZDL66DPu/i5wFtAEHAZcHWVQIr2ZRvWUqXTTbOZ4PoRsZZIU4k89nwnc5+7vRBiPSK+nUT1lKk/zIWQrkzIXvzazNcB24AozGwzsiDYskd4r3plcF6uj5Y6wBn99ljX4pTikm2azSBICZNjRbGb7Ae+4+04zqwD2dve/RR5dF9TRLCLSfT3qaDazT4U/zwVOBc4O308GTszgS4ea2WNmtsrMXjSz2eH6/czsYTN7Kfy5b7jezGyRma03s+fMbHy3/0tFRCQrnTUfnQL8Hvhcim0O/LyLY38M/Ie7rzCzAcByM3sY+CLwqLtfb2bXANcAXwWmACPC1/HALeFPEZHi0d3pMHMwfWY+pU0K7j4v/HlJTw7s7m8Ab4Tvt5rZauAQ4GyCOw+A24E/ECSFs4GfhhVZnzazgWZ2UHgcEZHCi8WCp4/j/QDxEUUDB6YuVdHd/YtAp6OPzKyvme2fsPwJM5sZnuAzZmbVwDEE5TIOTDjR/w04MHx/CPBqwsc2huuSjzXTzJaZ2bJNmzZ1JwwRKReFKCrX3TIVJVLWYhfunvIFTAPeAV4H/gh8huBE/QtgfLrPpTjOXsBy4NxweUvS9s3hz18DJyesfxSY2NmxJ0yY4CLSy8yb5z57tntra7Dc2hosz5sX/XfHvys4pQevxFiy3T9PgGWe5rza2Z3CN4AJ7n4wUAs8CFzh7ue4+4pMEo6Z7Q7cDzS6e7wP4k0zOyjcfhDwVrj+NWBowseHhOtERAKFvvqODyFN1NmQ0u7uXwQ6Swofuvt6gDAJvOTuD2Z6YDMzggl6Vrv7DxI2PQDMCN/PAH6VsP5fw1FIJxAMgVV/goi0S3zga+HCoIZQ/AnhfJxsu1umogTKWuwi3S0EQVPR3IRXh+V0n0v4/MkEo5SeA1aGrzOAQQRNQy8BjwD7hfsbcBOwAXieLpqOXM1HIr1Xa2vHJpl8NMckNgXFm4CSl7PZP4/opPmosyGpPwIGdLLcVbJ5IjzRp3Jaiv0d+HKmxxeRXird1XfUdwrpylRA6jIV3d2/SKh0toiUjuSicvX1uy7nowmpxJ9T6OyJ5kxqH4mIFIdiuPpOdUeQy/0LTHcKIlJ6ivDqu5RkNcmOiEjRKbGr71KSycxrs8OZ18zMfmxmK8zsM/kIrlyVwqTsItI7ZXKncKkHM699BtgXuBi4PtKoylh8UvbmE5vxOqf5xGZm1s5UYhCRopBJUojfl50B3OHuL5J+qKl0oS5Wx7Yp24JJ2fsCw2DblG3UxeoKHZqISEZJYbmZ/Y4gKTwUlsFujTas8qVJ2UWkmGWSFC4jmPPgWHffBnwC6FE5bdGk7JId9UdJ1DJJCg4cAcwKl/cE+kcWUZnTpOzSU+qPknzo8jkFM7uFoLnoU+4+Opw+83fufmw+AuxMqT6n0Li4MZiUfUM4KXtMk7JL16pHVtN8YnPQHxX3ClQtraJpXVOhwpISlO1zCse7+5eBHQDuvpmgCUl6qGZ6DU3rmmjd2UrTuiYlhDKWy+Ye9Ue1UzNadDIpc/GRmfUlaEbCzAajjmaRLsWbe7ZN2QbToLklaO4BenQhUDm8kuaWpDuFXtgflevfq3SUSfNRDXABMJ5gTuXzgG+6+73Rh9e5Um0+kt4h1809HU6GlUBL0B/VUN/Qq06GakbLXlbNR+7eCHwF+C7wBvD5YkgIIsUu1809NdNraKhvoGppFTbfqFpa1esSAqgZLWpdNh+Z2R3ufjGwJsU6EUkjiuaemuk1xZUEClCYTs1o0cqko/nIxIWwf2FCNOGIlI+yH34ci3WcWjI+10EsFunXlv3vtdDSTckGfA3YCnwMvBu+3wq8DXw33efy+dJ0nFLs7my806tGVLn1Ma8aUeV3Nt5Z6JByo8BTTZbt7zVP6GQ6zkw6mr/r7l+LNDP1kDqapdcppnkEEmdBi8vX7GeSlc46mjNJCn2A6cAwd/+2mQ0FDnL3Z3MfavcoKUivEovBli3tJ934SXngwMibbNJyhz4JrdCtrUoIJSDbh9duAiYRJAaA98J1IpIv7kFCWLiwvR0/fpW+ZUt7u36+Y6qt7bgusY9BSlImD68d7+7jzewvEDzRbGZ6olkklVw176T6XHwu4oUL25tsCtVck5iU4jEkNiWpCalk6YlmkVzJVfNOZ8epr+/Yhl+ok69ZEE9iUoonrYEDlRBKWCbNR4uAXwAHmtl84AngO5FGJVJqctW809lxNm+GOXM67l/I5ppYrGNSiieGQvVvSE50eafg7o1mthw4LVz1eXdfHW1YIiUm8Uo5m+addMeZFVauX7SouJprkr9Tdwglr8vRRwBmNh44maAJ6Ul3XxF1YJnQ6CMpOrkajZPqONdeW3yjj6QkdTb6KJMyF98CzgfuJ5ib+VYzu8/dr8ttmCIlLt1onO5exXd2HNi1uUZX55JDmfQp1BBMxRlz93nACYDqHpUg1aCPUPJonNbW4Gdi30AujpNMCUFyLJPRR68TTL+5I1zuB7zW1YfM7CfAWcBb7n5UuC4GXA5sCnf7urv/Jtz2NYL5oHcCs9z9ocz/M6QrqkEfsVyNxtGoHimwtH0KZvbfBH0IlcCxwMPh8unAs+5+bqcHNvskwYNuP01KCu+5+41J+x4B3AUcBxwMPAKMdPednX2H+hQypxr0eRLVcwqFLGchZaenfQrxs+1ygiGpcX/I5Evd/U9mVp3JvsDZwN3u/gHwipmtJ0gQT2X4eelCy4YWmJa0shJa7lAN+pzqajROpid7jeqRAknbp+Dut3f2yuI7rzKz58zsJ2a2b7juEODVhH02hut2YWYzzWyZmS3btGlTql0khcrhlZB8/k+qQa8+hwgk3onHYsFzBnkuNS3SHV12NJvZCDP7mZmtMrOX468eft8twHBgHMEsbt/v7gHcvcHdJ7r7xMGDB/cwjN6nqxr08T6H5hOb8Tqn+cSgz0GJIQuJ8w24Bw+fLVoEkyYVR+0ikRQyGX10K8HJ/GPgn4GfAnf25Mvc/U133+nurcCPCJqIIOi4Hpqw6xAy6MyWzHU1lWNdrC7ohB4G9AWGwbYp26iL1RU07pKV/GRyomeeCZ5BSKwbpOYhKRKZlM5e7u4TzOx5dx+TuK7Lgwd9Cr9O6Gg+yN3fCN/XEhTbm2ZmRwKLae9ofhQYoY7m/OnTtw9e50FCiNsJNt9o3alSVz3q+E0138CsWcHdQpxKTUsBZFs6+4NwToWXzOwqMzsH2CuDL72LoKP4cDPbaGaXAd8zs+fN7DmCu45aAHd/EbgXWAUsAb7cVUKQ3Mqkz6HX6um0k4nDSdNRqWkpMpkkhdlABTCLYG7mi4EZXX3I3S9094PcfXd3H+LuP3b3i919jLsf7e5T43cN4f7z3X24ux/u7r/t6X+Q9IzmvU0jm0J3qZ5MXrQouFvo6cNtIlFLN09nKbw0R3Nuad7bNBLnH46/upqHONWcxccfHyzPmhUsx/eZNy9v/yki7j2co9nMFrj7HDN7kHAuhaRkMjXifNUl9SlI3vSk0F2qeRHmzIF9921vetJDaVIAPX147Y7w542d7CNS/npa6C4W63jSN4MFCzp+RglBikzapODuy8OffwxnW8Pd9bSY9C6ZTjuZbnSSnkyWEtNpQbywVtFVBB3SZmYfA//t7v+Zh9hECi+TAnW5moZTpAikTQpmNhc4iaBs9ivhukOBW8ys1t27GGsnkhuNixupi9XRsqGFyuGVzI/Nz29l11TNQIkJID46CWg8diIfXHUll27Zyk8GDqDfiMOoqbkof7GKZKmzO4WLgdPd/e/xFe7+spldBPwOUFKQyBVNye90zUBJ02fGI1pwHNSO2krF3H8HM5Unl5LR2eijFzx8Erk72/JJo4/KX/XIaponNcOhCStfhqqniqzkd9LoJJtHME+hypNLEerpE80f9nCbSM5c8lIz9WtoHxTtUL8mWF80UoxOql9C22wkLRtUnlxKR2fNR2PN7N0U641gJjaRaLkzdOAALn12KxjUTg5OtnOehZ8MHBDdGP/u1DlKGJ30k4EDuGzqVurXwpxngs21h6tUiJSWzoak9k23TSQvzOj3w5u56fJLmPPMx20n2pv22I2BP7w5moTQ3ZFECaOT+h07kYq5/07t5G3gsGUHVCypYH59Ly8VIiUlkzmaRQqmpuYiGgEuurht3cAf3RrNiJ6kkUQdnkmYPTv9HUM4OqkmfC6hLlbH3PXNVB5WRUN9nkdKiWSpy9LZxUwdzb1AqvLTUc5BkO/vEymAbEtnSy9V8Ok5k58mzkdl0VTlrpUQpBdR85Gk1OnzARdO7/6EMz2RydPEudbTOkciZULNR5JS9chqmk9sDqbnjHsF6h/chzkXfzG/JR1aW3etUNongpvczuocqQlJyoiaj6TbWja0QPJIyqFg/3inZxPO9FQsBnPndpz1bO7caBJQujuT2bOjuzMRKTJqPpKUKodX0tySdKfwKtQfVsnsM88JEkG8M7arq+iezG8c368no4Gy0VmdI5FeQHcKklLa6Tmv/U73OmJ7Or8xdLxSX7gwaDLKR1OOyl1LL6akICnVTK+hob6BqqVV2HyjamkVDfUNQSdzqo7YVE1H2cxvHFeA0UAFH3UlUkjp5ukshZfmaM6zVPMOJy939pnk+Y07m+M4k89H4M7GO73igApnBs43cWbgFQdU5Gy+as2DLcWATuZoLviJPZuXkkIBzJvX8aScyeTzra0dT+qZTlrfkySUpaoRVUFCiCW8ZuBVI6qyPnbUCUckU50lBQ1Jle7zbhaMmzMHFi1qXzdrVvBz0aKu+wfyPKtZn7598DqHxMpfO8HmG607W7M6drphviqtLfnW2ZBUJQVJrzsn/3Sfj/chJCaCuFmzdp3IPoo4uiHKE3eUCUekO/ScgmQm8QIhFguu8OPr4if47lydJ477X7AgeCXKJCHEj9PZcg6lHXUVy77SaeXwSkieWqFFpbWluCgpSCBx6Kg7bN4cXNVPmpTdQ2qxWPvooUxHLSXJ52igtKOuclDpNMqEI5Iz6TobSuGljuYcSdWBO2tWx87hbDp3s+gwLrfOWY0+kmKAOpqlS4l3A3GzZnXsA2ht7XnTTQ87jNU5K5J7BelTMLOfmNlbZvZCwrr9zOxhM3sp/LlvuN7MbJGZrTez58xsfFRxSRqpHhJLlk256ngzUnL5iC76KFLWYNK8xyKRibJP4TZgctK6a4BH3X0E8Gi4DDAFGBG+ZgK3RBiXpBK/ck+0aFFwt5CreQx60GGszlmR/IosKbj7n4B/JK0+G7g9fH878PmE9T8Nm7ueBgaa2UFRxdbrJZ/UW1t3nczm+OM77lOgaqHqnL6hn5sAAA7qSURBVBXJr3xXST3Q3d8I3/8NODB8fwjwasJ+G8N1b5DEzGYS3E1QWamrxW5L1bY/dy6sXNnxQbKnngqGpO67b3sSKEC10Pion7pYHS13tFA5vJL5mvdYJDIFK53t7m5m3W6HcPcGoAGCjuacB1bOvItS1D/4Qcc2//hzBPGHxeLbInx4LJWa6TVKAiJ5ku/nFN6MNwuFP98K178GDE3Yb0i4TnKpq1LUybOZmUEsxpozplA9oip4TmBEFWvOmBLdLGsiUlD5TgoPADPC9zOAXyWs/9dwFNIJwDsJzUySS90pRe3OmmeeZtSSh5izewv+dWfO7i2MWvIQa555OpqZ1kSkoKIcknoX8BRwuJltNLPLgOuB083sJeDT4TLAb4CXgfXAj4Aro4qr13MPrvQTrDljSuoTvBmT169mwWiYsxr8uuDngtEwef1qTT4jUob08FpvEiaEUUseYsFoqP0C1N8fnOjXTP4so37z211O9H369sG/7vh17evsG2DfURE3kVLV2cNrmqO5NzFjybNPs2Q01P4LYOHPe4Fnn2ZUiiv/ykOHMuf+jg8K1N8PCw4dusu+IlL6VBCvl5m75V1qvwDEz/8W3DHM3fLurju7s+Sw0W1NRvYN2pqSlhw2Wn0KImVISaGXqRxe2fGJEIBX0zwhbMao409gzeTPsuCjSuw7xoKPKoOmpuNPUJ+CSBlSUuhluv2EcCzGqN/8lqaXmmnd2UrTS81B30M3hqTms/S1iGRHfQq9TI+eEM5ikpvGxY3MrJ3JtinbYBo0tzQzs3Zmh1hEpHho9JFESqWvRYqPpuOUQPIFQB4uCFT6WqS0KCn0FonTbULP5lzuAZW+FiktSgqFkKp0dWfbc/F98UJ48cTQ0zmXu0mlr0VKTLp5OkvhVZJzNM+b13Fe4m99y33cuOCne/v8xfPm5fZ7E+dFznbO5W7SvMQixYVO5mjWnUI+JV+xt7bCAw8Ecxk88EDHyW5yfQXfnUJ4OVYzvYamdU3BkNZ1TRp1JFLENCQ1nxJPzAsXts9rMG5ckBj69g2WEye7yZVU023W1hZk4hwRKV66U4hQyoe2Ul2xL1/ecTmqhJA43WYu5lwWkbKjO4WINC5uZOacy9l2xvb2h7bmXA7u1Pw56dmKCRM6Luf6Ct4smFs58Q4knpjyPOeyiBQ3PbwWkQWDBsKB77RVI8Wh/l445eVPcMwHH7ZPfzlhQtB0NG5ccMcwd27H2dByfceQeLw8T6spIsVBD6/lmzv2j3eYsxrqlxAkhCVBddEPPvgQZs1qn/5y6tQgIUydGizHp8uM4go+i3IV0jnVd5KykW5YUim8inlIatVhlV4/OmH4J3j9aLzqsMpdh4Hu3NlxOQ/DRLOhIaYd3dl4p1ccUOHMwPkmzgy84oCKXv97keKFhqTm3/xrv0Pd3/fosK7u73sw/9rv7HqF3ifpz1DEV/DxAnfNJzbjdU7ziUGBu958ZVwXqwsK/g0D+gLDYNuUbdTF6godmki3KSlEpObC6Syf8MkO65ZP+CQ1F04vUES5kc0JsFybWFTfScqJkkIUwiGgo5Y81GEI6KglD5X8ENCengDL+Q5D9Z2knCgpRCHdENCoOpDzqKcnwHJuYlF9JyknGpIapTIcAtph0pxKoCU4ATbUN3RavqJP3z54nQcJIW4n2HyjdWdr2s+VisbFjcHERRvCiYtiXUxcJFJAnQ1JVVKQbuvJCVCT7YgUDz2nkEK5dnrmQ08K3KmJRaQ09MqkUM6dnsWqZnoNDfUNVC2twuYbVUurumxyEilG5X5B2Subj6pHVtM8qRkOTVj5MlQ9paYMEUmvp31qxUbNR0kueamZ+jVAPB861K8J1ouIpFPOo+jiel9ScGfowAHMeTapLtGzMHTggJJ+hkBEotUbHlQsSFIwsyYze97MVprZsnDdfmb2sJm9FP7cN6rv7/fDm7lpj92Y8wz4tTDnGbhpj93o98ObS37IqIhEpzc8qFjIO4V/dvdxCe1a1wCPuvsI4NFwObdiMdacMYW6WB1Xbf+4w6aBP7qVmpqLcv6VUh7KvXNRMtMrRtGlq5QX5QtoAvZPWrcWOCh8fxCwtqvjdKtKamurr5782aBa6Si8/riOFUx91qyir04qhaEqqJKoHKoE00mV1IKMPjKzV4DNBF29/8fdG8xsi7sPDLcbsDm+nPTZmcBMgMrKygnNzZl3DlePqGLObi3MWdO+bsEo2PuNAVz6ztZoJraRkqcH76TcFOPoo5PdfTwwBfiymXUoJxpmspTZyt0b3H2iu08cPHhwt7605eVXqT2v47ra8+Df3t1aFnWJJBq9oXNRJK4gczS7+2vhz7fM7BfAccCbZnaQu79hZgcBb+X6eysPHcqc+zv+j1x/PywYXqk7BEmrcnglzS1Jdwpl1rkoEpf3OwUz29PMBsTfA58BXgAeAGaEu80AfpXTL3ZnyWGjmbMaFowG+0bwc85qWHLY6Jx+VXepE7O49YrORZFQIe4UDgR+EXQbsBuw2N2XmNmfgXvN7DKgGfiXnH6rGaOOP4E1wIL1q7HvvMqCQ4cyefJoRh1/QsHuEjo8ITkNmluCkhtAST0hWc7if4e6WB0td4RFAOtVBVXKU+8rc1Fk5azViSki+VaMHc2Fk5wACtyPoE5MESkmvS8pFJne8ISkiJQOJYUCUyemiBSTggxJlXbqxBSRYtL7OppFRHo5dTSLiEhGlBRERKSNkoKIiLRRUhARkTZKCiIi0qakRx+Z2SaCOklx+wN/L1A4nSnGuIoxJijOuBRT5ooxrmKMCQobV5W7p5x7oKSTQjIzW5ZumFUhFWNcxRgTFGdciilzxRhXMcYExRuXmo9ERKSNkoKIiLQpt6TQUOgA0ijGuIoxJijOuBRT5ooxrmKMCYo0rrLqUxARkeyU252CiIhkQUlBRETalFxSMLP9zOxhM3sp/Llvmv1mhPu8ZGYzEtZfaGbPm9lzZrbEzPYvkrg+YWYNZrbOzNaY2RcKHVPC9gfM7IVs48k2JjOrMLP/F/5+XjSz63MQz2QzW2tm683smhTb+5nZPeH2Z8ysOmHb18L1a83ss9nGkm1MZna6mS0P/30vN7NPFTqmhO2VZvaemf3vXMWUbVxmdrSZPRX+W3rezPoXMiYz293Mbg9jWW1mX8tFPN3m7iX1Ar4HXBO+vwb4rxT77Ae8HP7cN3y/L8H8EW8B+yccK1bouMJt1wLXhe/7xGMsZEzh9nOBxcALhf49ARXAP4f7fAJ4HJiSRSx9gQ3AoeHx/gockbTPlcD/hO+nAfeE748I9+9HMMP2BqBvDn4/2cR0DHBw+P4o4LUc/c16HFPC9p8B9wH/Oxcx5eB3tRvwHDA2XB5UBH+/6cDd4fsKoAmoztXvK9NXyd0pAGcDt4fvbwc+n2KfzwIPu/s/3H0z8DAwGbDwtaeZGbA38HoRxAVwKfBdAHdvdfdcPOmYVUxmthcwF7guB7FkHZO7b3P3xwDc/UNgBTAki1iOA9a7+8vh8e4O40sX78+A08J/O2cT/A/8gbu/AqwPj5etHsfk7n9x9/i/5xeBPcysXyFjAjCzzxPMLfhiDmLJVVyfAZ5z978CuPvb7r6zwDE5wblpN2AP4EPg3RzE1C2lmBQOdPc3wvd/Aw5Msc8hwKsJyxuBQ9z9I+AK4HmCZHAE8ONCx2VmA8Plb5vZCjO7z8xSfT5vMcXjAb4PbMtBLLmKCYDwd/Y54NEsYunyexL3cfePgXcIrioz+Wy+Y0r0BWCFu39QyJjCC4uvEtwJ51o2v6uRgJvZQ+H/c18pgph+BrwPvEEwc/uN7v6PHMWVsaKcjtPMHgH+V4pNdYkL7u5mlvGYWjPbnSApHEPQJPHfwNfI8Eo4qrgI/g5DgKXuPtfM5gI3AhcXKiYzGwcMd/fa5PbhQsWUcPzdgLuARe7+cnc/X+7M7EjgvwiuhgstBtS7+3vhjUOx2A04GTiW4KLnUQtmI8vmIiNbxxHM1H4wQXPp42b2SL7/jRdlUnD3T6fbZmZvmtlB7v6GmR1E0EeQ7DXg1ITlIcAfgHHh8TeEx7qXoF270HG9TfAP8+fh+vuAywoc0yRgopk1Efw7OcDM/uDup9KFCGOKawBecvcFXcXShdeAoUnf81qafTaGyWgfgr9XJp/Nd0yY2RDgF8C/xv+dFzim44HzzOx7wECg1cx2uPsPCxzXRuBP8WZaM/sNMJ7s7jyzjWk6sCRs0XjLzJ4EJhJcwOZPvjsxsn0BN9Cxo/J7KfbZj6ANc9/w9Uq47mCCW7PB4X7fBr5f6LjCbXcDnwrffxG4r9AxJexTTe46mrP9PV0H3A/0yUEsuxH8DzeM9k7BI5P2+TIdOwXvDd8fSceO5pfJTUdlNjENDPc/Nxd/q1zElLRPjNx2NGfzu9qXoE+qIjzOI8CZBY7pq8Ct4fs9gVXA0bn8W2b035DvL8zBL30QQTZ/KfxDxk8WE4H/m7DfpQSdf+uBSxLWfwlYTTDy4EFgUJHEVQX8KYzrUaCy0DElbK8md0mhxzERXHV5+PdbGb7+Lct4zgDWEYwYqQvX/ScwNXzfn+DObT3wLHBowmfrws+tJYtRULmKCfgGQZv0yoTXAYWMKekYMXKYFHLw97uIoPP7BVJcnBTg77dXuP5FgoRwdS5/V5m+VOZCRETalOLoIxERiYiSgoiItFFSEBGRNkoKIiLSRklBRETaKCmI9ICZ7TSzlWb217BMwonh+mozczO7LmHf/c3sIzP7Ybgcy3W1UJFcUVIQ6Znt7j7O3ccSlEr5bsK2V4AzE5bPJ/fF4EQioaQgkr29gc0Jy9uA1WY2MVy+ALg371GJ9EBR1j4SKQF7mNlKgqdTDwKSJ7S5G5hmZm8SFDl7naDMikhRU1IQ6Znt7j4OwMwmAT81s6MSti8hqK31JnBPAeIT6RE1H4lkyd2fAvYHBies+xBYDvwHQZ18kZKgOwWRLJnZKIJpGN8mqLoZ933gj+7+jyKbS0AkLSUFkZ6J9ylAMMXrDHffmXjyd/cX0agjKTGqkioiIm3UpyAiIm2UFEREpI2SgoiItFFSEBGRNkoKIiLSRklBRETaKCmIiEib/w+GO5GrmOQwCQAAAABJRU5ErkJggg==\n"},"metadata":{"needs_background":"light"}},{"output_type":"stream","name":"stdout","text":["MSE: 2591.5581383273175\n"]}]},{"cell_type":"markdown","source":["Now let's use all features we have in our dataset and see if we can do better"],"metadata":{"id":"XYF1c-o7Mqo6"}},{"cell_type":"code","source":["X = diabetes_X.iloc[-30:]\n","X = np.concatenate([np.ones((X.shape[0], 1)), X], axis=1)\n","\n","y = np.expand_dims(diabetes_y.iloc[-30:], axis=1)\n","\n","# Get the weights\n","weights_best = np.linalg.inv(np.dot(X.T, X)).dot(X.T).dot(y)\n","\n","# Get our prediction\n","y_hat = np.matmul(X, weights_best)\n","\n","# Visualize data points\n","plt.scatter(X[:, 3], y, c='green', edgecolors='black', label='ground truth')\n","plt.scatter(X[:, 3], y_hat, c='red', marker='x', edgecolors='black', label='prediction')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.legend()\n","plt.show()\n","\n","# Compute mean squared error loss\n","mse = mean_squared_error(X, y, weights_best)\n","print(f'MSE: {mse}')"],"metadata":{"id":"hsSg0PnkMwIR","executionInfo":{"status":"ok","timestamp":1677159018988,"user_tz":0,"elapsed":309,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/","height":296},"outputId":"1aa20ba9-1407-4b8a-906b-dede55b18221"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}},{"output_type":"stream","name":"stdout","text":["MSE: 1294.3103119245802\n"]}]},{"cell_type":"markdown","source":["Let's check our results using off-the-shelf linear model from `sklearn`"],"metadata":{"id":"9USLMeozWffC"}},{"cell_type":"code","source":["from sklearn.linear_model import LinearRegression\n","\n","linear_model = LinearRegression()\n","linear_model.fit(X[:, 1:], y)\n","\n","y_hat = linear_model.predict(X[:, 1:])\n","\n","plt.scatter(X[:, 3], y, c='green', edgecolors='black', label='ground truth')\n","plt.scatter(X[:, 3], y_hat, c='red', marker='x', edgecolors='black', label='prediction')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.legend()\n","plt.show()\n","\n","# Compute mean squared error loss\n","mse = mean_squared_error(X, y, weights_best)\n","print(f'MSE: {mse}')"],"metadata":{"id":"by6FA47yV1sZ","executionInfo":{"status":"ok","timestamp":1677159020178,"user_tz":0,"elapsed":1193,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/","height":296},"outputId":"2caa6ce8-2d64-44dd-cdea-5c4c27f675b2"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}},{"output_type":"stream","name":"stdout","text":["MSE: 1294.3103119245802\n"]}]},{"cell_type":"markdown","source":["## Extension 1: Gradient Descent Optimization"],"metadata":{"id":"4zw1zRd6eJL7"}},{"cell_type":"markdown","source":["As an extension task, we will try to fit a line to our data using gradient descent algorithm\n","\n","Gradient descent is a powerful optimization algorithm that uses [backpropagation](https://en.wikipedia.org/wiki/Backpropagation) to find the minimum of a function. You can think of it as taking small steps down the hill until we reach the lowest point. The hill in this case is our loss function, which we are trying to minimize.\n","\n","![rsz_11_yasmq5kvlmbyme8edkyl6w.png](data:image/png;base64,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)\n","\n"],"metadata":{"id":"fGjbjinEeXks"}},{"cell_type":"markdown","source":["Usually evaluating our model on the data on which it has been trained is not a good decision. This is because our model must generalize to new unseen examples, rather than just doing perfectly on the data it has already seen.\n","\n","We will add some more examples to our data and store them separately until we finish training our model"],"metadata":{"id":"S8PXIoddjvrT"}},{"cell_type":"code","source":["# Training data\n","X_train = diabetes_X.iloc[-30:]\n","X_train = np.expand_dims(X_train.loc[:, 'bmi'].values, axis=1)\n","X_train = np.concatenate([np.ones_like(X_train), X_train], axis=1)\n","y_train = np.expand_dims(diabetes_y.iloc[-30:], axis=1)\n","\n","# Test data\n","X_test = diabetes_X.iloc[-50:-30]\n","X_test = np.expand_dims(X_test.loc[:, 'bmi'].values, axis=1)\n","X_test = np.concatenate([np.ones_like(X_test), X_test], axis=1)\n","y_test = np.expand_dims(diabetes_y.iloc[-50:-30], axis=1)\n","\n","plt.scatter(X_train[:, 1], y, c='green', edgecolors='black', label='train')\n","plt.scatter(X_test[:, 1], y_test, c='red', edgecolors='black', label='test')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.legend()\n","plt.show()"],"metadata":{"id":"Qi4QwlIWeWY1","executionInfo":{"status":"ok","timestamp":1677159020179,"user_tz":0,"elapsed":8,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"0334e908-1383-4370-92e4-0d7a22fc4764"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["We know that our objective function (MSE) for a linear regression problem is quadratic. Thus, we can easily derive it's gradient."],"metadata":{"id":"8UiQqxeNyVfv"}},{"cell_type":"code","source":["def compute_mse_grad(X, y, weights):\n"," \"\"\"\n"," Compute the derivative of a quadratic function\n"," \"\"\"\n"," y_hat = X.dot(weights)\n"," grad = (1/X.shape[0]) * np.sum(((y_hat - y) * X), 0)\n","\n"," return np.reshape(grad, (2, 1))"],"metadata":{"id":"5IiMlaHEkHJ0"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Now let's create a training algorithm for our linear model"],"metadata":{"id":"PdRFtTEzzJ3n"}},{"cell_type":"code","source":["# Initialize parameters randomly\n","w0, w1 = 100, 200\n","initial_weights = np.expand_dims(np.array([w0, w1]), 1)\n","\n","num_epochs = 100\n","\n","# Training loop\n","def train(alpha=0.5, num_epochs=num_epochs):\n"," weights = initial_weights\n"," epoch = 0\n"," total_loss = []\n","\n"," # Number of times our model will see our data\n"," while epoch < num_epochs:\n"," # Compute gradients and loss\n"," gradient = compute_mse_grad(X_train, y_train, weights)\n"," loss = mean_squared_error(X_train, y_train, weights)\n"," # Update model parameters\n"," weights = weights - alpha*gradient\n"," # Increase epoch counter\n"," epoch += 1\n"," # Store current loss\n"," total_loss.append(loss)\n"," \n"," return weights, total_loss\n","\n","weights_best, total_loss = train()\n","weights_best"],"metadata":{"id":"RabAre5U07rb","executionInfo":{"status":"ok","timestamp":1677159020179,"user_tz":0,"elapsed":8,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"e57ce1bc-5a0a-4c74-a344-59bc65b2b5b7"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[133.75448738],\n"," [290.95288887]])"]},"metadata":{},"execution_count":44}]},{"cell_type":"markdown","source":["Let's plot our prediction and see how well it fits to our dataset"],"metadata":{"id":"Mdeaqwtv2hO7"}},{"cell_type":"code","source":["prediction = np.dot(X_test, weights_best)\n","\n","plt.scatter(X_train[:, 1], y, c='green', edgecolors='black', label='train')\n","plt.scatter(X_test[:, 1], y_test, c='red', edgecolors='black', label='test')\n","plt.plot(X_test[:, 1], prediction, color='orange')\n","plt.xlabel('BMI')\n","plt.ylabel('Diabetes Risk')\n","plt.legend()\n","plt.show()"],"metadata":{"id":"dYrPsGmG3VJ6","executionInfo":{"status":"ok","timestamp":1677159020180,"user_tz":0,"elapsed":8,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"64164238-af39-4b3d-c903-e10469e79764"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Let's know calculate how well our model does on unseen data"],"metadata":{"id":"jw5ha_o53QIS"}},{"cell_type":"code","source":["plt.plot(list(range(num_epochs)), total_loss)\n","plt.xlabel(\"Epoch\")\n","plt.ylabel(\"Loss\")\n","plt.title(\"Training Loss\")\n","plt.show()"],"metadata":{"id":"bXNwzwmq3nfV","executionInfo":{"status":"ok","timestamp":1677159020389,"user_tz":0,"elapsed":216,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"e765cf1a-83d8-4fca-9884-a9b3d41e30dc"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["What if we try to train our model with a larger number of epochs (maybe 10000)?\n","\n","Experiment with the number of epochs and look whether our parameters get changed. Are the new parameters close to the ones we got from our normal equations? Is the resulting loss similar to the one we got from the previous method?"],"metadata":{"id":"APGJxhVA421C"}},{"cell_type":"markdown","source":["### Visualizing Gradient Descent"],"metadata":{"id":"T_QkeG6L3Kut"}},{"cell_type":"markdown","source":["In this part we will try to get a visual understanding of gradient descent optimizatin algorithm. We can keep track of our weights and gradients during training process and visualize how the weights are getting updated and where the gradients are pointing. \n","\n","Don't worry too much about the code. Instead try to get an idea of what is actually happening when we do gradient descent.\n","\n","**Note: In this part we are just using a custom quadratic function (not MSE) and try optimize it. This process is similar to how we do it in linear regression, but it's easier to visualize.**"],"metadata":{"id":"n92jxTvZ6DZl"}},{"cell_type":"code","source":["def quadratic2d(w0, w1):\n"," \"\"\"\n"," Our custom quadratic objective function J(w0, w1)\n","\n"," Args:\n"," w0: value representing first parameter\n"," w1: value representing second parameter\n"," \"\"\"\n"," w0 = np.atleast_2d(np.asarray(w0))\n"," w1 = np.atleast_2d(np.asarray(w1))\n"," return 0.5 * ((w0 - 3)**2 + (2*w1 - 2)**2)"],"metadata":{"id":"TfzHTAXu3Nzl"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["w0_grid = np.linspace(-4, 7, 100)\n","w1_grid = np.linspace(-1, 4, 100)\n","w_grid = w0_grid[np.newaxis,:], w1_grid[:, np.newaxis]\n","J_grid = quadratic2d(*w_grid)\n","\n","X, Y = np.meshgrid(*w_grid)\n","contours = plt.contour(X, Y, J_grid, 10)\n","plt.clabel(contours)\n","plt.xlabel('theta1')\n","plt.ylabel('theta0')\n","plt.title('f(theta)')\n","plt.axis('equal')\n","plt.show()"],"metadata":{"id":"nqQaXzXkFAmS","executionInfo":{"status":"ok","timestamp":1677159020927,"user_tz":0,"elapsed":540,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"09b93c65-ac55-4638-b386-43bb0ece7257"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":["def compute_quadtratic2d_grads(w0, w1):\n"," \"\"\"\n"," Compute the gradient of 0.5 * ((w0 - 3)**2 + (2*w1 - 2)**2) w.r.t w0 and w1\n"," \"\"\"\n"," grads = np.stack([w0-3, (4*w1-4)], axis=1)\n"," return grads.reshape([2, 1])"],"metadata":{"id":"c6wTQFr_GN0R"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["`alpha` defines our learning rate. Try to experiment with it and use some other values (e.g. 1e-2, 4e-1). How does it affect the optimization process?"],"metadata":{"id":"TL_qz63UGt6y"}},{"cell_type":"code","source":["# Training algorithm\n","conv_threshold = 1e-1\n","alpha = 2e-1 # try to change alpha\n","weights, weights_prev = np.array([[-2], [3]]), np.array([[0], [0]])\n","opt_pts = [weights.flatten()]\n","opt_grads = []\n","\n","while abs(quadratic2d(*weights) - quadratic2d(*weights_prev)) > conv_threshold:\n"," weights_prev = weights\n"," grads = compute_quadtratic2d_grads(*weights)\n"," weights = weights_prev - alpha*grads\n"," opt_pts += [weights.flatten()]\n"," opt_grads += [grads.flatten()]"],"metadata":{"id":"cgMSxkH4GPnR"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["opt_pts = np.array(opt_pts)\n","opt_grads = np.array(opt_grads)\n","\n","contours = plt.contour(X, Y, J_grid, 10)\n","plt.clabel(contours)\n","plt.scatter(opt_pts[:,0], opt_pts[:,1])\n","\n","for opt_pt, opt_grad in zip(opt_pts, opt_grads):\n"," plt.annotate('', xytext=(opt_pt[0], opt_pt[1]),\n"," xy=(opt_pt[0]-0.8*alpha*opt_grad[0], opt_pt[1]-0.8*alpha*opt_grad[1]),\n"," arrowprops={'arrowstyle': '->', 'lw': 2}, va='center', ha='center')\n","\n","plt.xlabel('theta1')\n","plt.ylabel('theta0')\n","plt.title('f(theta)')\n","plt.axis('equal')\n","plt.show()"],"metadata":{"id":"YP3j9K45GRQb","executionInfo":{"status":"ok","timestamp":1677159022291,"user_tz":0,"elapsed":1072,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"793ef9e5-c9d2-420b-db70-3031d2254b12"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Adapted from: https://github.com/kuleshov/cornell-cs5785-2022-applied-ml"],"metadata":{"id":"BFoBka_1sqqk"}},{"cell_type":"markdown","source":["## Extension 2: Probabilistic Linear Regression"],"metadata":{"id":"2tRxaHkXKipl"}},{"cell_type":"markdown","source":["Is there a specific reason for us to be optimizing the mean squared error to fit our linear model Why not an absolute error?\n","\n","The answer to this can be found by looking at the algorithm from probabilistic perspective\n","\n","We can make an assumption that the way our labels are generated is as follows:\n","\n","$$\n","\\begin{align}\n","y^{(i)} = \\theta^Tx^{(i)} + \\epsilon^{(i)}\n","\\end{align}\n","$$\n","\n","where $\\epsilon^{(i)}$ is *Gaussian noise*, i.e.;\n","\n","$$\n","\\begin{align}\n","\\epsilon^{(i)} \\sim N(0, \\sigma^2) \\\\\n","\\epsilon^{(i)} = y^{(i)} - \\theta^TX\n","\\end{align}\n","$$\n","\n","This assumption may or may not be true in reality, but it is useful do describe a way our data is generated\n","\n","Let's see exactly what we mean by adding noise to the straight line equation"],"metadata":{"id":"Ch8-j0XKQfGU"}},{"cell_type":"code","source":["# Create a straight line with a slope of 0.5 and an intercept of 2\n","X = np.linspace(0, 20, 30)\n","y = 0.5*X + 2\n","\n","# Add some random noise from a normal distribution\n","y_sigma = y + np.random.randn(len(y))*1.5\n","\n","# Plot the straight line on the left\n","fig = plt.figure(figsize=(10,5))\n","fig.add_subplot(121)\n","plt.scatter(X, y)\n","plt.plot(X, y, color='orange')\n","plt.title('y=0.5x + 2')\n","\n","# Plot the straight line with added noise on the right\n","fig.add_subplot(122)\n","plt.scatter(X, y_sigma)\n","plt.plot(X, y, color='orange')\n","plt.title('y=0.5x + 2 + noise')\n","plt.show()"],"metadata":{"id":"iFG8-2bvQTVN","executionInfo":{"status":"ok","timestamp":1677159023312,"user_tz":0,"elapsed":1024,"user":{"displayName":"Sergey Kuznetsov","userId":"02803571248049057958"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"fe8173fd-b593-4bfb-eb7f-9ccafc33238d"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["
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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Given the above, we can say that:\n","\n","$$\n","P(y^{(i)}|x^{(i)};\\theta) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp \\Bigl(-\\frac{(y^{(i)} - \\theta^Tx^{(i)} )^2}{2\\sigma^2}\\Bigr)\n","$$\n","\n","Note that here the mean of a Gaussian pdf for a particular data point is given by our prediction for that point"],"metadata":{"id":"YTUEdqwOdMyt"}},{"cell_type":"markdown","source":["We then make an assumption that $\\epsilon$ values for different examples are i.i.d, which gives us the joint likelihood of all examples in our dataset given the estimated parameters of our model:\n","\n","$$\n","\\begin{align} L(\\theta) &= \\prod_{i=1}^n\\frac{1}{2\\pi\\sigma^2}\\exp \\Bigl(-\\frac{(y^{(i)} - \\theta^Tx^{(i)} )^2}{2\\sigma^2}\\Bigr) \\\\ &= \\sum_{i=1}^n \\log \\Bigl[ \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp \\Bigl(-\\frac{(y^{(i)} - \\theta^Tx^{(i)})^2}{2\\sigma^2}\\Bigr) \\Bigr] \\\\ &= \\sum_{i=1}^n \\Bigl[ \\log \\frac{1}{\\sqrt{2\\pi\\sigma^2}}+ \\log \\exp \\Bigl(-\\frac{(y^{(i)} - \\theta^Tx^{(i)})^2}{2\\sigma^2}\\Bigr) \\Bigr] \\\\ &= n \\times const - \\frac{1}{\\sigma}-\\frac{(y^{(i)} - \\theta^Tx^{(i)})^2}{2\\sigma^2} \\end{align}\n","$$"],"metadata":{"id":"0-FDqQsaS17V"}},{"cell_type":"markdown","source":["Maximizing w.r.t $\\theta$ we can remove constant terms:\n","\n","$$\n","L(\\theta) = -\\frac{1}{2}\\sum^n_{i=1}(y^{(i)} - \\theta^Tx^{(i)})^2\n","$$\n","\n","This actually gives us the negative of the MSE loss!\n","\n","Note: $L(\\theta)$ here corresponds to the ***likelihood***, not the loss.\n","\n","It turns out that maximizing the likelihood $L(\\theta)$ is equivalent to minimizing the loss $J(\\theta)$:\n","\n","$$\n","\\underset{\\theta}{\\operatorname{argmax}}L(\\theta) = \\underset{\\theta}{\\operatorname{argmin}}J(\\theta)\n","$$\n","\n","This gives us a probabilistic explanation of why the mean square error is an appropriate choice of loss function for a linear regression problem\n","\n"],"metadata":{"id":"n1eZllNdTNIf"}}]}