updating book

doc/LectureNotes/chapter1.ipynb

@@ -1963,7 +1963,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\frac{\\partial \\log{\\vert\\boldsymbol{A}\\vert}}{\\partial \\boldsymbol{A}} = (\\boldsymbol{A}^{-1})^T.\n",
+    "\\frac{\\partial\\log{\\vert\\boldsymbol{A}\\vert}}{\\partial \\boldsymbol{A}}=(\\boldsymbol{A}^{-1})^T.\n",
     "$$"
    ]
   },
@@ -3359,66 +3359,6 @@
     "You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions. \n",
     "Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.\n",
     "\n",
-    "!bsol\n",
-    "The code here is an example of where we define our own design matrix and fit parameters $\\beta$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": false,
-    "editable": true
-   },
-   "outputs": [],
-   "source": [
-    "import os\n",
-    "import numpy as np\n",
-    "import pandas as pd\n",
-    "import matplotlib.pyplot as plt\n",
-    "from sklearn.model_selection import train_test_split\n",
-    "\n",
-    "def save_fig(fig_id):\n",
-    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
-    "\n",
-    "def R2(y_data, y_model):\n",
-    "    return 1 - np.sum((y_data - y_model) ** 2) / np.sum((y_data - np.mean(y_data)) ** 2)\n",
-    "def MSE(y_data,y_model):\n",
-    "    n = np.size(y_model)\n",
-    "    return np.sum((y_data-y_model)**2)/n\n",
-    "\n",
-    "x = np.random.rand(100)\n",
-    "y = 2.0+5*x*x+0.1*np.random.randn(100)\n",
-    "\n",
-    "\n",
-    "#  The design matrix now as function of a given polynomial\n",
-    "X = np.zeros((len(x),3))\n",
-    "X[:,0] = 1.0\n",
-    "X[:,1] = x\n",
-    "X[:,2] = x**2\n",
-    "# We split the data in test and training data\n",
-    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
-    "# matrix inversion to find beta\n",
-    "beta = np.linalg.inv(X_train.T @ X_train) @ X_train.T @ y_train\n",
-    "print(beta)\n",
-    "# and then make the prediction\n",
-    "ytilde = X_train @ beta\n",
-    "print(\"Training R2\")\n",
-    "print(R2(y_train,ytilde))\n",
-    "print(\"Training MSE\")\n",
-    "print(MSE(y_train,ytilde))\n",
-    "ypredict = X_test @ beta\n",
-    "print(\"Test R2\")\n",
-    "print(R2(y_test,ypredict))\n",
-    "print(\"Test MSE\")\n",
-    "print(MSE(y_test,ypredict))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "!esol\n",
     "\n",
     "\n",
     "\n",
@@ -3545,9 +3485,7 @@
     "\n",
     "!bsubex\n",
     "Add now a model which allows you to make polynomials up to degree $15$.  Perform a standard OLS fitting of the training data and compute the MSE and $R2$ for the training and test data and plot both test and training data MSE and $R2$ as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?\n",
-    "!bsol\n",
-    "Here you simply need to change the degree of the polynomial in the above code to $n=15$.\n",
-    "!esol\n",
+    "\n",
     "!esubex"
    ]
   }