notebooks/Lec19/Lecture 19 - Model Validation and Bias-Variance Tradeoff.ipynb

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   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "# AMAT 502: Modern Computing for Mathematicians\n",
    "## Lecture 19 - Model Validation and the Bias-Variance Tradeoff\n",
    "### University at Albany SUNY"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Topics for Today\n",
    "\n",
    "- Recommended Reading from Vanderplas\n",
    "- Recap of the Data Science Pipeline\n",
    "- Model Validation\n",
    "    - Physics versus Data Science\n",
    "    - Under and Overfitting Data\n",
    "    - $R^2$---The Coefficient of Determination\n",
    "    - The Bias-Variance Tradeoff\n",
    "- Case Study in Polynomial Regression\n",
    "- Case Study in KNN and the Iris Data Set\n",
    "    - k-Fold Cross Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Recommended Reading: VanderPlas\n",
    "\n",
    "I recommend that everyone read Jake VanderPlas's [Data Science Handbook](https://github.com/jakevdp/PythonDataScienceHandbook) especially, Chapter 5 on Machine learning. Chaper 4 contains lots of instructions on plotting that will be useful for your final projects. Today's lecture will mostly follow [Secton 5.03 on Hyperparameters and Model Validation](https://jakevdp.github.io/PythonDataScienceHandbook/05.03-hyperparameters-and-model-validation.html).\n",
    "\n",
    "I *highly* recommend that everyone read VanderPlas's [Introduction to Scikit-learn](https://jakevdp.github.io/PythonDataScienceHandbook/05.02-introducing-scikit-learn.html) so that you have a more formal understanding of the Scikit-Learn API (API=Application Programming Interface). We'll go through a salient portion of that section to start. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Scikit-Learn Data Science Pipeline\n",
    "\n",
    "1. **Choose a class of model**\n",
    "2. **Instantiate this class**\n",
    "3. **Shape your data into a features matrix and target vector**. For example, `X` is a matrix (Pandas dataFrame) with `m_samples` rows and `n_features` columns. The target vector `y` is just a length `m_samples` array/column vector.\n",
    "4. **Fit the model to your data** by calling the `fit()` method of the model instance, e.g. call `model.fit(X,y)`\n",
    "5. **Apply the model to new/reserved data**:\n",
    "    - For supervised learning, often we predict labels for unknown data using the `predict()` method, e.g. `xfit = np.linspace(-1, 11)`  and then `yfit = model.predict(Xfit)`\n",
    "    - For unsupervised learning, we often transform or infer properties of the data using the `transform()` or `predict()` method.\n",
    "\n",
    "### Quick Recall Question \n",
    "\n",
    "- **Give 2 examples of a supervised learning and 2 examples of an unsupervised learning method.**\n",
    "\n",
    "- **Did they use the `predict()` or the `transform()` method respectively?**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simple Linear Regression Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "rng = np.random.RandomState(42)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 1 + rng.randn(50)\n",
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 1: Choose a class of model by importing the appropriate estimator class from Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 2: Choose model hyperparameters by instantiating this class with desired attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# here we create an instance of the class LinearRegression (think back to OOP)\n",
    "model = LinearRegression(fit_intercept=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 3: Arrange data into a features matrix and target vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 1)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = x[:, np.newaxis]\n",
    "X.shape\n",
    "#x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 4: Fit the model to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.9776566])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9033107255311164"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comment on Underscore Notation\n",
    "\n",
    "See [this article](https://dbader.org/blog/meaning-of-underscores-in-python) on the different ways the `_` notation is used in Python.\n",
    "\n",
    "I extracted this summary from the above article:\n",
    "\n",
    "![Underscore Summary](underscore_summary.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 5: Make Predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sqSOv4IhX4Q16yCi+0UNMkWYCsQnmH9sOkLEol92HKr3+Hj1kFF9oBC7SqGnZX0FpFZZ/boLxdn76SFUtGVk5fP/lL4ky8ObMc0n1Ipj1kFF8dcoAN8b8wRhTbIzJa3athzFmpTFma+Ofp7VvmSLtz59NMCs37ueqBR/zVvYefnrxGbx/30Wce0ZPt6tCYqMMp3WO1UNG8Zs3Uyh/An4N/LnZtQxglbU20xiT0fj5nMCXJxI8vmyCOXD0GPOWbmBZThEj+nTlpdvSGXt60vGvt2UTjkhbnTLArbWrjTEDW1yeBlzS+PErwN9RgIvDtWUTjLWWJesKeOydjVQcq+M/rhzGXRc3NJ9qydtNOCJt5esceG9rbRFA45+9AleSSGi4m+4wwKUjUk64VlBaxY/+9DX3/3U9g5ITWX7vhdx7+VC34S3Sntp9FYoxZiYwEyAtLa29byfis+kTUsnedYjXvthN0+4IC2StKSB9QA+uG9eP177aTebyTbgsPHrtKG47byDRUYHbSSnSFr4G+H5jTF9rbZExpi9Q7OmF1toXgRehYSOPj/cTCYqP8kto+Ze0qraep5Zv4vUvd/PVzkNcMCSZ+TPG0L9H6/1LRNqbr7/zLQVub/z4duDtwJQjElqeHlgWlx8jf18ZN5/Tn+0lR7nomY/cnqgjEkynHIEbY96g4YFlsjFmL/AokAm8ZYy5A9gN3NSeRYq0B3ebdjw9yAS4YlRv3l5XqMMSJGyoF4p0SO5OyUmIjeaGs1NZmL33pDMooeGBprv/W9THRNqbeqGINONp0877efvo3jnW7fd4Guqoj4mEinqhSMTxpp+Jp9A9cLTGq+3vzamPiYSKRuASUbztZ+IpdBPjollx/0UeQ7zlgkH1MZFQUoBLRPG2n8msKcOJb7HxJi46iv+6fgxdOsV4PNnmB+em6bAECRuaQpGI4m0/k/jYaOJioo4/rOzXPZ7Z3xlxPIzVw0ScQAEuEeVU/UyKy6uZt3QDy3P3MapvN565cSyjU7u7/VnqYSLhTlMoElE8TX3851XDyFqzlyufX80Hm4qZNWU4b98z2WN4iziBRuASUdxNfdxxwSAWrytk9ZYSzh5wGk/fMJYhvbqEuFIR/ynAJeI0TX24XJZXv9zF0+/lY4HHrjuTW88dQJSaT0mEUICLY7W23vvbkqNkZOXw9c7DXDg0maeuV/MpiTwKcHGkllvhm9Z717ss+8qqeWHVVhJio3nupnHccFYqxmjULZFHAS6O5Gm9d8aiHGrrLd8d04d5151Jr67xIapQpP0pwMWRPK33rq23/PZfz+I7o/sGuSKR4NMyQnEkT1vh+3aLV3hLh6EAF0f62WVDTjrKLCE2mjlTR4SoIpHg0xSKhJw33QOb+3hLCb/6cBsulyUxLpqKmnpStdVdOiAFuISUp9UkcPIpN6WVNTyxbBNZ3+xlcEoiC+8+j7MH9Ah6zSLhQgEuIdVa98DmAb48t4hH3s6jtLKWn102hHsuG0KnmOiWP06kQ1GAS0idqntgcVk1j7y9gfc37GNManf+/ONJjOrXLZglioQtBbiElKfugX27x/NW9h6eXLaRY3UuMqaO4CcXDCImWs/dRZro/wYJKXfdAzvFRNE1PpbZC3MY0acb7/38Qu66eLDCW6QFjcAlpJp3DyworaJ7QixVNfXsPVzJE9NH84OJaWo+JeKBAlxCbvqEVEandmP2why+2V3KJcNT+K/rx7T5cGGRjkYBLiFVW+/idx9/yy9XbSOxUzQLvjeO6ePVfErEGwpw8VtbN+I0yd17hFkL15O/r5xrxvZl3nVnktylUxAqFokMCnDxS1s24jSprq1nwQdbeGn1dpK7dOLFW8/mqjP7BK1mkUihABe/eLsRp8kX2w8yd1EuOw5UcPM5/Zn73ZF0T4j1qwZffwMQcToFuHjNXVCeaiNOk/LqWjLfy+e1L3fTv0cCr/1kEpOHJAekprb+BiASKRTg4hVPQZnUOZbDlbUnvb55u9eP8ot5cHEu+8qqueOCQTxw1TA6xwXmr15bfwMQiSQKcPGKp6DsFBNFQmz0CV9LiI1m1pThHKqo4fF3NrBkXSFDe3Uh6+7zOSvttIDW5e1vACKRSFvbxCueAvFIVS3zZzSs2TZAalICT10/mugow5XPf8yynCLuvXwoy+69IODhDZ4PdvB0XSSSaAQuXvHUs6RfUgLTJ6Qen67YX1bNQ4vz+GDTfsae3p3X7pzEiD7t13xq1pThJ0ztwD9/AxCJdApw8Yq7oIyNMlTW1DEo4136do/nwqEpLM8roqbOxUPfHcmPJg/02L8kUCtHmm/F1yoU6WiMtdb3bzZmJ1AO1AN11tr01l6fnp5us7Ozfb6fhFbz0O2eEEtFTR219Sf+/Rmcksjvbz+HgcmJrf4cd6Pm+TPGKHhF3DDGrHGXr4GYA7/UWjv+VOEtzjd9QiqfZVzGjsyrSewUc1J4A1TV1Lca3tD6yhER8Z4eYopP3M2HAxQdqT7l92rliEhg+BvgFvibMWaNMWamuxcYY2YaY7KNMdklJSV+3k5CrabOxQsfbPX4dW9Wf2jliEhg+Bvgk621ZwFTgX83xlzU8gXW2hettenW2vSUlBQ/byehtH5PKdf+6lMWfLCFs9KSiI858a+Pt6s/3B3ioJUjIm3n1yoUa21h45/FxpjFwERgdSAKk/BRVVPP8ys38/tPd9Crazwv35bOFaN6+7ySRCtHRALD51UoxphEIMpaW9748UrgcWvt+56+R6tQnOcf3x5g7qJcdh2s5PuT0siYOoJu8f41nxKRtvG0CsWfEXhvYHFj4/0Y4PXWwlucpay6lvnL83njq90M6NmZ1++cxPmDT2w+pS6AIqHlc4Bba7cD4wJYi4SJVZv289DiPIrLq5l50Rncf8UwEuJOnLNWF0CR0NNOTAdqr5HvwaPHeOydjSxdX8jw3l357a1nM75/ktvXqgugSOgpwB2mLSNfb4PeWsvS9YU89s5Gyqtruf+KYdx9yWDiYjwvUtJabpHQU4A7jKeR731/XcezKzYfD2lvg77oSBUPL85jVX4x4/sn8cyNYxnWu6vH+zf9o+Dp0bfWcosEjwLcYVob4RaUVjHr/9YDp57icLksb369h/nLN1HrcvHw1SP50eRBREd5Pg3eXQ+T5rSWWyS4FOAO46mta5Nal2Xe0g0cqTr5lBxo+Adg54EKMhbl8MX2Q5w/uCfzZ4xhQM/W+5eA+38UmqRqFYpI0CnAHcZdW9eWSqtqSfUQ9F3jY5jyi9XERUeROWMM3zunP41LQU85Z+5p9G+AzzIu8++NiUibqZmVw0yfkHr8BJzWuNuubgyUVddx4dAUVv7Hxdw8Me2E8J67KJeC0ios/5wzX7K24Pj3q4eJSHhRgDtQU1vXzrHu//N1jo06HvT9uscfv54YF8Ovvz+Bl247mz7NroN3LV7Vw0QkvGgKxcE6xUZTWetyex1gQM/OdImPgSNw/YRUHrlmFKclxrn9Wd4sC1QPE5HwogB3sNJK9w8qD1fWMjDjXQCSEmL54w/P4dIRvVr9Wa2dedlc8/MvRSS0NIXiYN7MPVfX1ntckdKcpkdEnEcB7mDuQrel6jqXV0eVNX84amhYFqgzKkXCm6ZQHKwpXB9/ZyOHKms8vs7b7e2aHhFxFo3AHayk/BgrN+7nUGUNI/t2I6VLJ7ev0zI/kcikEbgDWWtZvLaAx5dtpPJYPQ9cOYy7LhnMuzlFJ23y0Ty2SORSgDtMQWkVDy3O5e+bSzgrraH51JBeDc2ntMxPpGNRgDuEy2V57ctdZL6Xj8vCo9eO4rbzBp7UfErz2CIdhwLcAbaXHCUjK5evdh7iwqHJPHX9GPr36BzqskQkxBTgYayu3sVLn+xgwQdbiI+J4tkbx3Lj2acf718iIh2bAjxMbSwsY3bWevIKyphyZm+emDaaXt3iT/2NItJhKMDDTHVtPT97Yy0rN+4HoEfnOKaO7qvwFpGTGGs9HY4VeOnp6TY7Ozto93OaNbsOcfer31BcfuyE67HRhsS4GI5U1WpliUgHZIxZY61Nb3ldI/AwUHGsjmdXbOaVz3cSxcnz27X1ltLGfiatHWIsIh2LAtxL3p7w3laZ723ipdU7qLeWxLhoKmo8n7TTpPnZliLScSnAveDtCe9tcaSyljv/ks1XOw4dv1ZRU48Bjye+N+dtfxMRiVzqheIFb06raYv384q4YsHHJ4R3EwtuJlFOpv4mIqIA94I3p9V4o7i8mrtfXcNdr37jsfEUNIR4U1vX0zrHEttit6X6m4gIaArFK96eVuOJtZaHFufxxte7sRa6xcdwxwWDeH7lFrc/NzUp4YRT3ttr/l1EnE0jcC/4c1rN3sOVTH3hE17/qiG8oeFk+IeX5HHpiBSdgiMiPlOAe8GX02pcLssr/9jJVQtWs3lf+Ulfr6qt56P8klP+3KYHqAWlVVj++QB1ydqCwL9REXEUbeRpB9uKj5KRlUP2rsNcNCyF1VtK3L7OADsyr271Z03O/NCraRYRiVzayNPOlqwt4Jn38yk8Ug1A57honrtpHDeclcoFT3/k8xx6oB6gikjk0RRKACxZW8CcrJzj4Q0NUygxUQZjjF9z6J5CXssIRcSvADfGfMcYs9kYs80YkxGoopykuraeh5fkcazOdeL1ZqfB+3Piuz/hLyKRzecpFGNMNPAb4EpgL/C1MWaptXZjoIoLd1/vPMSchTkcPVbn9uvNpzl8PSlHx6SJiCf+zIFPBLZZa7cDGGPeBKYBERPgntZfHz1Wx7Pv5/PK57vokRhHFOBy8/2BmubQMWki4o4/AZ4K7Gn2+V5gUssXGWNmAjMB0tLS/LhdcHnqf7KpqIxlOUUUHqnioqHJfLXjkNvw1jSHiLQ3f+bA3bXsOGlNorX2RWtturU2PSUlxY/bBZen/ie/W72dhLhoFt51Pt+WVFBdd3J8Rxvj9Ry3iIiv/BmB7wX6N/v8dKDQv3LCR2vL9N699wI6xUR7fI3LWoW3iLQ7f0bgXwNDjTGDjDFxwM3A0sCUFXqe5q9TkxJ4L3cfkzM/9Nj2VUv8RCQYfA5wa20dcA+wAtgEvGWt3RCowkLJWsuFQ5NPup4QG82lI1KOb213R3PfIhIsfu3EtNYuB5YHqJawsOdQJXMX5fLptgMMTkmkvLqOkvJjx1ehuJsbb5KqJX4iEkTaSt+ovrH51LMrNhMdZXhy+mi+PzGNqBa9uO//6zq3329AvUlEJKgU4MDW/eXMzsph7e5SLhmewlPXj2l1C7s/vcFFRAKlQ/dCqalz8ctVW7n6l5+y80AFC743jj/+8JxWw1hb20UkXHTYEXjO3lJmL8whf185147rx6PXjiK5lWPOmmhru4iEiw4X4NW19SxYuYWXPtlOStdOvHRbOleO6t2mn6Gt7SISDjpUgH+x/SAZWTnsPFjJLRP7kzF1JN0TYkNdloiITzpEgJdX15L5Xj6vfbmbtB6def0nkzh/yMnrvEVEnCTiA/yj/GIeXJzL/rJqfnLBIB64ajgJcdGn/kYRkTAXsQF+qKKGx9/ZwJJ1hQzr3YX/+cH5TEg7LdRliYgETMQFuLWWZTlFzFu6gbLqWn5++VD+/dIhxMV06BWTIhKBIirA9x2p5uEleXywaT/jTu/O0zdOYkSfbqEuS0SkXUREgFtrefPrPTz17iZqXS4e+u5IfnzBIKKj3LUsFxGJDI4P8F0HK8jIyuXz7Qc594weZM4Yy8DkxFCXJSLS7hwb4PUuyx8/28Fzf9tMbFQUT10/hpvP6X9S8ykRkUjlyADfvK+h+dT6PaVcPqIXT14/mr7d1UxKRDoWRwV4TZ2L//n7Nn7z0Ta6xsfyws3juW5cP4zRqFtEOh7HBPi6PaXMWZjD5v3lTBvfj0euGUVPL5pPiYhEKkcE+K9WbWXBB1vo1TWe39+ezuUj29Z8SkQkEjkiwNN6dubmiWlkTB1Bt3g1nxIRAYcE+LTxqUwbr/atIiLNaX+5iIhDKcBFRBxKAS4i4lAKcBERh1KAi4g4lAJcRMShFOAiIg6lABcRcShjrQ3ezYwpAXYF7Ya+SQYOhLqIAIiU9wF6L+EoUt4HOOO9DLDWprS8GNQAdwJjTLa1Nj3UdS60AAMAAANRSURBVPgrUt4H6L2Eo0h5H+Ds96IpFBERh1KAi4g4lAL8ZC+GuoAAiZT3AXov4ShS3gc4+L1oDlxExKE0AhcRcSgFuIiIQynAGxljvmOM2WyM2WaMyQh1Pb4yxvQ3xnxkjNlkjNlgjPl5qGvyhzEm2hiz1hizLNS1+MMYk2SMWWiMyW/8b3NeqGvylTHm/sa/W3nGmDeMMfGhrslbxpg/GGOKjTF5za71MMasNMZsbfzztFDW2BYKcBpCAvgNMBUYBdxijBkV2qp8Vgc8YK0dCZwL/LuD3wvAz4FNoS4iAF4A3rfWjgDG4dD3ZIxJBe4F0q21o4Fo4ObQVtUmfwK+0+JaBrDKWjsUWNX4uSMowBtMBLZZa7dba2uAN4FpIa7JJ9baImvtN40fl9MQFI48j84YczpwNfByqGvxhzGmG3AR8HsAa22NtbY0tFX5JQZIMMbEAJ2BwhDX4zVr7WrgUIvL04BXGj9+BZge1KL8oABvkArsafb5Xhwaes0ZYwYCE4AvQ1uJz34BzAZcoS7ET2cAJcAfG6eDXjbGJIa6KF9YawuA54DdQBFwxFr7t9BW5bfe1toiaBgAAb1CXI/XFOANjJtrjl5faYzpAmQB91lry0JdT1sZY64Biq21a0JdSwDEAGcB/2utnQBU4KBf05trnB+eBgwC+gGJxph/DW1VHZcCvMFeoH+zz0/HQb8WtmSMiaUhvF+z1i4KdT0+mgxcZ4zZScOU1mXGmFdDW5LP9gJ7rbVNvwktpCHQnegKYIe1tsRaWwssAs4PcU3+2m+M6QvQ+GdxiOvxmgK8wdfAUGPMIGNMHA0PZZaGuCafGGMMDXOtm6y1z4e6Hl9Za+daa0+31g6k4b/Hh9ZaR470rLX7gD3GmOGNly4HNoawJH/sBs41xnRu/Lt2OQ59INvMUuD2xo9vB94OYS1tEhPqAsKBtbbOGHMPsIKGp+p/sNZuCHFZvpoM3ArkGmPWNV570Fq7PIQ1CfwMeK1xgLAd+FGI6/GJtfZLY8xC4BsaVjytxUFb0Y0xbwCXAMnGmL3Ao0Am8JYx5g4a/oG6KXQVto220ouIOJSmUEREHEoBLiLiUApwERGHUoCLiDiUAlxExKEU4CIiDqUAFxFxqP8P8ZQgrMj1e9MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xfit = np.linspace(-1, 11)\n",
    "Xfit = xfit[:, np.newaxis]\n",
    "yfit = model.predict(Xfit)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model Validation: Physics versus Data Science\n",
    "\n",
    "### Key Question: Causation vs. Correlation\n",
    "\n",
    "**How do we know when a chosen model is a good (correct) one?**\n",
    "\n",
    "I propose two possible answers.\n",
    "\n",
    "1. If there is an underlying **causal explanation** that when modeled mathematically produces the choice of model, then we are likely to believe in the model.\n",
    "2. Alternatively, if we can come up with a model that **fits the data** better than any other model, then we are likely to believe in the model.\n",
    "\n",
    "Notice that **Reason 1** described above lies within the tradition of physics. One uses basic physical laws to model a problem and solving the appropriate equations (Newton's equations, Schrödinger's wave equations, et al) gives the specifically chosen model. However **Reason 1** is totally useless in most data science applications today, such as this one: \n",
    "\n",
    "> In predictive political science, one might want to know how living in a rural or urban area predicts ones choice of presidential candidate. \n",
    "\n",
    "**Is it the case that one can write down physical laws that causally determine one's voting preference?** \n",
    "\n",
    "The answer to the above question is clearly **NO.** This would contradict the widely held belief of *free will.*\n",
    "Nevertheless, it has [been observed empirically](https://www.pewsocialtrends.org/2018/05/22/urban-suburban-and-rural-residents-views-on-key-social-and-political-issues/) that where you live does have a strong correlation with political preference. \n",
    "\n",
    "Consequently, there are areas where non-causal models are the best we can hope for, such as K-nearest neighbors (KNN).\n",
    "\n",
    "**Question:** Do you think KNN is actually a non-causal model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Under and Over Fitting Data\n",
    "\n",
    "### A Word of Caution\n",
    "\n",
    "Of course just fitting the data without some broader principles or heuristics is not wise either.\n",
    "\n",
    "For example, we know by [Lagrange's Interpolation Formula](https://en.wikipedia.org/wiki/Lagrange_polynomial#targetText=In%20numerical%20analysis%2C%20Lagrange%20polynomials,functions%20coincide%20at%20each%20point) that we can find a polynomial that passes through every point in our *training* data set. This is the canonical example of **over-fitting** that I gave in my first lecture on regression.\n",
    "\n",
    "**Question:** What are the approximate degrees of each of these polynomials?\n",
    "\n",
    "<center>\n",
    "    <img src=\"bias-variance.png\" alt=\"The Bias Variance Tradeoff\" width=\"1000\" height=\"800\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Testing the Quality of the Model\n",
    "\n",
    "Recall that we can either **split the data** into training and test samples `X_train` and `X_test` or we can just generate new samples and predict their targets using the training model. Usually we do the former.\n",
    "\n",
    "Luckily, just because an over-fitted model can (near) perfectly predict the targets values of the training data set, that doesn't mean it will do well on the test data set. Consequently, *this gives us a way of validating a model without physical laws!* \n",
    "\n",
    "### Quick summary of $R^2$\n",
    "\n",
    "The $R^2$ value is the coefficient of determination, which is\n",
    "$$R^{2}=1-{SS_{\\rm {res}} \\over SS_{\\rm {tot}}}$$\n",
    "where\n",
    "$$SS_{\\text{tot}}=\\sum _{i}(y_{i}-{\\bar {y}})^{2}$$\n",
    "is the **variance in the in the data** and\n",
    "$$SS_{\\text{res}}=\\sum _{i}(y_{i}-f_{i})^{2}=\\sum _{i}e_{i}^{2}$$\n",
    "is the **sum of the squared errors** between the prediction and the actual value.\n",
    "\n",
    "<center>\n",
    "    <img src=\"bias-variance-2.png\" alt=\"Testing the Bias-Variance Tradeoff\" width=\"1000\" height=\"800\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Bias-Variance Tradeoff\n",
    "\n",
    "- For **high-bias models** the performance of the model on the validation set **is similar** to the performance on the training set.\n",
    "- For **high-variance models** the performance of the model on the validation set **is far worse** than the performance on the training set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Validation Curve\n",
    "\n",
    "For example, if we consider the *degree of the polynomial* as a measure of *model complexity* then we obtain the following curve. \n",
    "\n",
    "*Note that the best model is one that maximizes the validation score*\n",
    "\n",
    "<center>\n",
    "    <img src=\"validation-curve.png\" alt=\"Validation Curve\" width=\"600\" height=\"400\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Validation Curve: Polynomial Regression Example\n",
    "\n",
    "To consider an actual example, we follow VanderPlas's subsection of 5.03 on Validation Curves in Scikit-Learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "#**kwargs is like *args in that they allow a variable number of arguments to be passed\n",
    "def PolynomialRegression(degree=2, **kwargs):\n",
    "    return make_pipeline(PolynomialFeatures(degree),\n",
    "                         LinearRegression(**kwargs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Generating Synethetic Data\n",
    "\n",
    "**Question:** In the following code block, what is the actual function describing $y=f(x)$?\n",
    "\n",
    "$$y= 10 - \\frac{1}{x+.1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def make_data(N, err=1.0, rseed=1):\n",
    "    # randomly sample the data\n",
    "    rng = np.random.RandomState(rseed)\n",
    "    X = rng.rand(N, 1) ** 2\n",
    "    y = 10 - 1. / (X.ravel() + 0.1)\n",
    "    if err > 0:\n",
    "        y += err * rng.randn(N)\n",
    "    return X, y\n",
    "\n",
    "X, y = make_data(40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set()  # plot formatting\n",
    "\n",
    "X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n",
    "\n",
    "plt.scatter(X.ravel(), y, color='black')\n",
    "axis = plt.axis()\n",
    "for degree in [1, 3, 5]:\n",
    "    y_test = PolynomialRegression(degree).fit(X, y).predict(X_test)\n",
    "    plt.plot(X_test.ravel(), y_test, label='degree={0}'.format(degree))\n",
    "plt.xlim(-0.1, 1.0)\n",
    "plt.ylim(-2, 12)\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Scikit-learn's Validation Curve Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#N.B. VanderPlas is out of date, sklearn.learning_curve has been replaced with sklearn.model_selection\n",
    "from sklearn.model_selection import validation_curve\n",
    "degree = np.arange(0, 21)\n",
    "train_score, val_score = validation_curve(PolynomialRegression(), X, y,\n",
    "                                          'polynomialfeatures__degree', degree, cv=7)\n",
    "\n",
    "plt.plot(degree, np.median(train_score, 1), color='blue', label='training score')\n",
    "plt.plot(degree, np.median(val_score, 1), color='red', label='validation score')\n",
    "plt.legend(loc='best')\n",
    "plt.ylim(0, 1)\n",
    "plt.xlabel('degree')\n",
    "plt.ylabel('score');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## More Data Isn't Always Better\n",
    "\n",
    "Unfortunately as the size of the training set increases, the validation curve tends to approach the training score curve. This yields **the learning curve**.\n",
    "\n",
    "<center>\n",
    "    <img src=\"learning-curve2.png\" alt=\"Validation Curve\" width=\"600\" height=\"400\">\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Returning to our Regression Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X2, y2 = make_data(200)\n",
    "plt.scatter(X2.ravel(), y2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### More Data Means No Clear Model Winner\n",
    "\n",
    "Notice that the validation and training curve are plotted with respect to model complexity (degree of the polynomial) there is no clear local maximum, like it had with just 40 points and a third degree polynomial.\n",
    "\n",
    "Below the plot for 40 points is dashed, and the plot for 200 points is bold.\n",
    "\n",
    "**Question: Is VanderPlas's example a good one? For this example, is a degree 3 polynomial somehow more correct than a degree 20 polynomial?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree = np.arange(21)\n",
    "train_score2, val_score2 = validation_curve(PolynomialRegression(), X2, y2,\n",
    "                                            'polynomialfeatures__degree', degree, cv=7)\n",
    "\n",
    "plt.plot(degree, np.median(train_score2, 1), color='blue', label='training score')\n",
    "plt.plot(degree, np.median(val_score2, 1), color='red', label='validation score')\n",
    "plt.plot(degree, np.median(train_score, 1), color='blue', alpha=0.3, linestyle='dashed')\n",
    "plt.plot(degree, np.median(val_score, 1), color='red', alpha=0.3, linestyle='dashed')\n",
    "plt.legend(loc='lower center')\n",
    "plt.ylim(0, 1)\n",
    "plt.xlabel('degree')\n",
    "plt.ylabel('score');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Cross-Validation and Holdout Sets\n",
    "\n",
    "We already considered a practical example, on the MNIST data set, where setting the training set to be 100% of the available data gave the result that our predictions were right 100% of the time.\n",
    "\n",
    "This is why we use **holdout sets**, which is built into the `train_test_split` function.\n",
    "\n",
    "Let's run through the Iris Data set with KNN again as an example.\n",
    "\n",
    "### First Example: The Wrong Way --- No Holdout Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "model = KNeighborsClassifier(n_neighbors=1)\n",
    "\n",
    "model.fit(X, y)\n",
    "y_model = model.predict(X)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(y, y_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Using Train_Test_Split\n",
    "\n",
    "Here we use a 50-50 split of the Iris data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9066666666666666"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split #had to change VdP from cross_validation to model_selection\n",
    "# split the data with 50% in each set\n",
    "X1, X2, y1, y2 = train_test_split(X, y, random_state=0,\n",
    "                                  train_size=0.5)\n",
    "\n",
    "# fit the model on one set of data\n",
    "model.fit(X1, y1)\n",
    "\n",
    "# evaluate the model on the second set of data\n",
    "y2_model = model.predict(X2)\n",
    "accuracy_score(y2, y2_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Train on the Test and Test on the Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.96, 0.9066666666666666)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y2_model = model.fit(X1, y1).predict(X2)\n",
    "y1_model = model.fit(X2, y2).predict(X1)\n",
    "accuracy_score(y1, y1_model), accuracy_score(y2, y2_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### K-Fold Cross Validation\n",
    "\n",
    "Luckily, there is a `cross_validation` function that automates this process.\n",
    "\n",
    "The simplest form of cross validation uses what's called **$k$-fold cross validation.** Here you divide your training data into $k$ subsets of equal size.\n",
    "\n",
    "- A model is trained using $k-1$ of the folds as training data\n",
    "\n",
    "- the resulting model is validated on the one remaining fold\n",
    "\n",
    "![Cross Validation](cross_validation.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.93333333, 1.        , 0.93333333, 0.86666667,\n",
       "       1.        , 0.86666667, 1.        , 1.        , 1.        ])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "cross_val_score(model, X, y, cv=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "pygments_lexer": "ipython3",
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 },
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