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   "source": [
    "# Assignment 8: Supervised Learning\n",
    "\n",
    "This should be a straightforward assignment and is here just to provide a concrete example of supervised learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the titanic data set from `seaborn`. We will try to predict survival from the other variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "titanic = sns.load_dataset('titanic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 1**. (10 points)\n",
    "\n",
    "Is the data set balanced or imbalanced? If it is badly imbalanced (say minority class under 20% of total), use down-sampling of the majority class to generate a balanced data set. Drop columns with any missing values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data set is not too imbalanced, so no action taken."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 2**. (10 points)\n",
    "\n",
    "Convert the categorical values into dummy encoded variables , dropping the first value to avoid collinearity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 3**. (10 points)\n",
    "\n",
    "Split the data into 70% training and 30% test data sets using stratified sampling on the sex."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 4**. 20 points)\n",
    "\n",
    "Construct an `sklearn` `Pipeline` with the components `StandardScaler`, `RidgeClassifier`, and `GridSearchCV`. Train the Pipeline classifier, choosing a value for $\\lambda$ from one of $\\lambda = \\{0, 0.1, 1, 10\\}$ using grid search with 5-fold cross-validation. Note that the $\\lambda$ parameter we use in the lecture is named `alpha` in `RidgeClassifier`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 5**. (10 points)\n",
    "\n",
    "Using the trained classifier, construct a confusion matrix for the test and predicted values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 6**. (10 points)\n",
    "\n",
    "Using the confusion matrix, calculate accuracy, sensitivity, specificity, PPV, NPV and F1 score "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Routine"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex 7**.  (10 points)\n",
    "\n",
    "Plot an ROC curve for the classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ex. 8** (20 points)\n",
    "\n",
    "- Fit polynomial curves of order 0,1,2,3,4 and 5 to the values of $X$, $y$ given below \n",
    "- Using LOOCV, what is the degree of the best-fitting polynomial model? If this is not the true degree, explain why."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(23)\n",
    "\n",
    "n = 10\n",
    "k = 3\n",
    "x = np.random.normal(0,1,n)\n",
    "X = np.c_[np.ones(n), x, x**2, x**3]\n",
    "beta = np.random.normal(0, 1, (k+1,1))\n",
    "s = 0.5\n",
    "y = X@beta\n",
    "y += np.random.normal(0, s, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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