rtbs-dev/HW3-ENME737.ipynb

## HW3-ENME737.ipynb
{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Thurston Sexton\n\nSeptember 29, 2017"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from scipy.io import loadmat\nimport numpy as np\nimport pandas as pd\nimport seaborn as sns\nimport os\n\nimport matplotlib.pyplot as plt\n%matplotlib inline",
      "execution_count": 9,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Q1 "
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# %load_ext watermark\n%watermark -v -m -p numpy,scipy,sklearn,matplotlib",
      "execution_count": 10,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "CPython 3.6.2\nIPython 6.2.0\n\nnumpy 1.13.1\nscipy 0.19.1\nsklearn 0.19.0\nmatplotlib 2.0.2\n\ncompiler   : GCC 4.8.2 20140120 (Red Hat 4.8.2-15)\nsystem     : Linux\nrelease    : 4.4.0-21-generic\nmachine    : x86_64\nprocessor  : x86_64\nCPU cores  : 8\ninterpreter: 64bit\n"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Q2\nYour task is to complete the attached Matlab code to classify three\ndifferent health states of rolling-element bearings and verify the effectiveness\nof a k-nearest neighbor classifier in terms of various classification performance\nmetrics you learned in the class.\n\n### Part a) \nK-Nearest Neighbor (kNN) is a **supervised** learning method for non-parametric classification or regression. It works by assuming (as a heuristic) that two input points that are \"close\" should be more likely to be similar that ones that are \"far\". This distance between two points, say, $x_1,x_2$, can be any number of metrics, though a common one is the Euclidean distance, or $L_2$-norm, \n$$d(x_1, x_2) = \\|x_1-x_2\\|_2$$ \nWith this metric, one can qauntify the \"closeness\" at which a given point shoul take on, say, the class-label of a nearby one. However, there are often many different class labels near a point. The kNN classification algorithm is essentially a voting or ensemble method, where we limit the points having \"influence\" over any given decision point  to the $K$-nearest ones. They then \"vote\" on the class to assign to our decision point (i.e. their own class), and the most common nearby class \"wins\". \n\nThis remarkably intuitive heuristic allows for several very desireable properties, for instance, a small $K$ will mean lots of small local variation in class decisions ($K=3$, only 2-of-3 nearby being \"A\" are needed to decide \"A\"), while a large $K$ tends to smooth-out the decision boundaries, making potentially more robust decisions if over-fitting is a problem. Not only this, but the sensitivity to noise is inherently density-dependent, since the $K$-nearest points may span a larger distance in some sparse locations, while being quite fine in others. \n\nTo calculate this, the pairwise distances between all-points must be calculated, and any given test point must be compared against the entire data-set at prediction-time. This comes at a computational cost, though techniques like Quad/KD/Ball-trees may be used to speed up the compute time. \n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Part b)"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "data_dir = os.path.join('.', 'data')\ndef load_mat(typ, i):    \n    return loadmat(os.path.join(data_dir, f'Q2/{typ}', f'{typ}{i}.mat'))['vib']\ntyps = ['bfi', 'bfo', 'dfb']\nno_files = range(1, 145)",
      "execution_count": 11,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from itertools import product\nfrom scipy.stats import kurtosis, skew\n\nrms = lambda y: np.sqrt(np.mean(y**2))\n\n#init\ndf = pd.DataFrame(columns=('rms', 'kurtosis', 'skewness', 'class'))\n\n# iter over db files\nfor n, (typ, i) in enumerate(product(typs, no_files)):\n    row = load_mat(typ, i)\n    df.loc[n] = [rms(row), kurtosis(row)[0], skew(row)[0], typ]\n\nprint(df.shape)",
      "execution_count": 12,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": "(432, 4)\n"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "df.head()",
      "execution_count": 13,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>rms</th>\n      <th>kurtosis</th>\n      <th>skewness</th>\n      <th>class</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.005514</td>\n      <td>0.051740</td>\n      <td>0.160166</td>\n      <td>bfi</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.005513</td>\n      <td>0.043504</td>\n      <td>0.155958</td>\n      <td>bfi</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.005512</td>\n      <td>0.037399</td>\n      <td>0.157612</td>\n      <td>bfi</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.005512</td>\n      <td>0.053660</td>\n      <td>0.161731</td>\n      <td>bfi</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.005511</td>\n      <td>0.055332</td>\n      <td>0.158724</td>\n      <td>bfi</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "        rms  kurtosis  skewness class\n0  0.005514  0.051740  0.160166   bfi\n1  0.005513  0.043504  0.155958   bfi\n2  0.005512  0.037399  0.157612   bfi\n3  0.005512  0.053660  0.161731   bfi\n4  0.005511  0.055332  0.158724   bfi"
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "It would be nice to see what the data looks like, so let's plot the pair-wise relationships between our three features. "
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "with sns.axes_style('ticks'):\n    sns.pairplot(data=df, hue='class')",
      "execution_count": 14,
      "outputs": [
        {
          "data": {
            "image/png": 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dcI5ZTmy79v648/m8YLZgcnSujoOqOLvgJjh/vBFLZ1xirEueasTcVRm17+aLP7t6XY27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\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fa51cab2358>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "It looks like our classifier should have little-to-no problem learning good decision boundaries, given that RMS+(kurtosis or skew) seem to be enough to separate the clusters in at least one direction. \n\nLet's try normalizing the data to try and better differentiate:"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from scipy.stats import zscore\n\ndf_norm = df[['rms', 'kurtosis', 'skewness']].apply(zscore)\ndf_norm['class'] = df['class']\nwith sns.axes_style('ticks'):\n    sns.pairplot(data=df_norm, hue='class')",
      "execution_count": 15,
      "outputs": [
        {
          "data": {
            "image/png": 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Sk8LJ5/Mxa9YsFi9ezOrVq1m1ahWfffZZ2D7PPfcc7dq147XXXuP666/nkUceiUVoIiIi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\nIiIiUkUqnERERESq6P8D21Ml7wBGUKsAAAAASUVORK5CYII=\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fa4d073e668>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Excellent, even better separation. Normalization definitely seems like it will \"help\" though perhaps not much. \n\n### Part c)"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from sklearn.neighbors import KNeighborsClassifier\nfrom sklearn.model_selection import GridSearchCV, train_test_split\nfrom sklearn.preprocessing import StandardScaler\nfrom sklearn.pipeline import Pipeline\n\ny = df['class'].values  # predicting this\nX = df[['rms', 'kurtosis', 'skewness']].values  # using this\n\nX_train, X_test, y_train, y_test = train_test_split(X, y, \n                        test_size=.2,  # save 20% data for testing\n                        stratify=y)  # we want equal class-repr.\n\n# auto-feed z-scored input to the kNN clf (for parallelization)\npipe = Pipeline([\n    ('z-score', StandardScaler()),\n    ('kNN', KNeighborsClassifier())\n])\n\n# 5-fold cross-val over (1-9)-nearest-neighbors\n# not normalized\ncv = GridSearchCV(KNeighborsClassifier(), {'n_neighbors': range(1,10)}, cv=5) \n# z-score normalized\ncv_norm = GridSearchCV(pipe, {'kNN__n_neighbors': range(1,10)}, cv=5)  \n",
      "execution_count": 16,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# fit both for later\ncv.fit(X_train, y_train)\ncv_norm.fit(X_train, y_train)",
      "execution_count": 17,
      "outputs": [
        {
          "data": {
            "text/plain": "GridSearchCV(cv=5, error_score='raise',\n       estimator=Pipeline(memory=None,\n     steps=[('z-score', StandardScaler(copy=True, with_mean=True, with_std=True)), ('kNN', KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n           metric_params=None, n_jobs=1, n_neighbors=5, p=2,\n           weights='uniform'))]),\n       fit_params=None, iid=True, n_jobs=1,\n       param_grid={'kNN__n_neighbors': range(1, 10)},\n       pre_dispatch='2*n_jobs', refit=True, return_train_score=True,\n       scoring=None, verbose=0)"
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Not Standardized "
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "pd.DataFrame(cv.cv_results_)[['mean_test_score','mean_train_score',\n                              'param_n_neighbors', 'rank_test_score']]",
      "execution_count": 18,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mean_test_score</th>\n      <th>mean_train_score</th>\n      <th>param_n_neighbors</th>\n      <th>rank_test_score</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.939130</td>\n      <td>1.000000</td>\n      <td>1</td>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.956522</td>\n      <td>0.967391</td>\n      <td>2</td>\n      <td>2</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.950725</td>\n      <td>0.969565</td>\n      <td>3</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.953623</td>\n      <td>0.965942</td>\n      <td>4</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.953623</td>\n      <td>0.963768</td>\n      <td>5</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.950725</td>\n      <td>0.963768</td>\n      <td>6</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.950725</td>\n      <td>0.961594</td>\n      <td>7</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.956522</td>\n      <td>0.962319</td>\n      <td>8</td>\n      <td>2</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.962319</td>\n      <td>0.961594</td>\n      <td>9</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "   mean_test_score  mean_train_score param_n_neighbors  rank_test_score\n0         0.939130          1.000000                 1                9\n1         0.956522          0.967391                 2                2\n2         0.950725          0.969565                 3                6\n3         0.953623          0.965942                 4                4\n4         0.953623          0.963768                 5                4\n5         0.950725          0.963768                 6                6\n6         0.950725          0.961594                 7                6\n7         0.956522          0.962319                 8                2\n8         0.962319          0.961594                 9                1"
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Let's build a confusion matrix to see where those small errors are coming from, specifically for the $K=8$ classifier that was selected via cross-valiation:"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def conf_mat(y_true, y_pred, labels=['bfi', 'bfo', 'dfb']):\n    ind = dict(zip(labels, range(len(labels))))  # convert label to int\n    mat = np.zeros((len(labels), len(labels)))  # init conf mat\n    for tru, pred in product(labels, labels):  # all combinations of true/pred\n        mat[ind[tru], ind[pred]] = np.sum((y_true==tru)&(y_pred==pred))  # how many?\n    return mat\n\n# on the test set: \nconf_mat(y_test, cv.predict(X_test))",
      "execution_count": 19,
      "outputs": [
        {
          "data": {
            "text/plain": "array([[ 29.,   0.,   0.],\n       [  5.,  24.,   0.],\n       [  0.,   0.,  29.]])"
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# overall: \nconf_mat(y, cv.predict(X))    ",
      "execution_count": 20,
      "outputs": [
        {
          "data": {
            "text/plain": "array([[ 143.,    1.,    0.],\n       [  17.,  127.,    0.],\n       [   0.,    0.,  144.]])"
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def precision(conf_mat, avg=None):\n    \"\"\"assumes NxN = True x Pred\"\"\"\n    tp = np.diag(conf_mat)  # true positives\n    pp = np.sum(conf_mat, axis=0)  # predicted positive\n    \n    if avg=='micro':  # global for all tp, cp\n        return tp.sum()/conf_mat.sum()\n    elif avg=='macro':  # label-wise avg\n        return (tp/pp).mean()\n    else:\n        return tp/pp\n\ndef recall(conf_mat, avg=None):\n    \"\"\"assumes NxN = True x Pred\"\"\"\n    tp = np.diag(conf_mat)  # true positives\n    cp = np.sum(conf_mat, axis=1)  # condition positive\n    \n    if avg=='micro':  # global for all tp, cp\n        return tp.sum()/cp.sum()\n    elif avg=='macro':  # label-wise avg\n        return (tp/cp).mean()\n    else:\n        return tp/cp\n\ndef F_β(conf_mat, β=1, avg=None):\n    \"\"\"assumes NxN = True x Pred\"\"\"\n    p = precision(conf_mat)order=3,\norder=3,\n    r = recall(conf_mat)\n    \n    if avg=='micro':  # global for all tp, cp\n        tp = np.diag(conf_mat).sum()  # diags\n        n = conf_mat.sum()-tp  # micro fn == micro fp == non-diags\n        return (1+β**2)*tp/((1+β**2)*tp+n*β**2+n)\n    elif avg=='macro':  # label-wise avg\n        return ((1+β**2)*p*r/((β**2*p)+r)).mean()\n    else:\n        return (1+β**2)*p*r/((β**2*p)+r)\n\nc = conf_mat(y, cv.predict(X))\npd.DataFrame(data={'$F_1$':F_β(c),\n                   '$R$':recall(c),\n                   '$P$':precision(c)},\n             index=['bfi', 'bfo', 'dfb'])",
      "execution_count": 21,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>$F_1$</th>\n      <th>$P$</th>\n      <th>$R$</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>bfi</th>\n      <td>0.940789</td>\n      <td>0.893750</td>\n      <td>0.993056</td>\n    </tr>\n    <tr>\n      <th>bfo</th>\n      <td>0.933824</td>\n      <td>0.992188</td>\n      <td>0.881944</td>\n    </tr>\n    <tr>\n      <th>dfb</th>\n      <td>1.000000</td>\n      <td>1.000000</td>\n      <td>1.000000</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "        $F_1$       $P$       $R$\nbfi  0.940789  0.893750  0.993056\nbfo  0.933824  0.992188  0.881944\ndfb  1.000000  1.000000  1.000000"
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "avgs=['micro', 'macro']\npd.DataFrame(data={'$F_1$':[F_β(c, avg=i) for i in avgs],\n                   '$R$':[recall(c, avg=i) for i in avgs],\n                   '$P$':[precision(c, avg=i) for i in avgs]},\n             index=avgs)",
      "execution_count": 184,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>$F_1$</th>\n      <th>$P$</th>\n      <th>$R$</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>micro</th>\n      <td>0.962963</td>\n      <td>0.962963</td>\n      <td>0.962963</td>\n    </tr>\n    <tr>\n      <th>macro</th>\n      <td>0.962848</td>\n      <td>0.966667</td>\n      <td>0.962963</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "          $F_1$       $P$       $R$\nmicro  0.962963  0.962963  0.962963\nmacro  0.962848  0.966667  0.962963"
          },
          "execution_count": 184,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "It looks like most of the problem is in differentiating BFI vs BFO. We expected this would be an issue based on the pair-wise plots, so perhaps the Z-scoring normalization will help improve our scores. "
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### z-Score kNN"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "pd.DataFrame(cv_norm.cv_results_)[['mean_test_score','mean_train_score',\n                              'param_kNN__n_neighbors', 'rank_test_score']]",
      "execution_count": 22,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>mean_test_score</th>\n      <th>mean_train_score</th>\n      <th>param_kNN__n_neighbors</th>\n      <th>rank_test_score</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>1</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>2</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>3</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>4</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>5</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>6</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>7</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>8</td>\n      <td>1</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>9</td>\n      <td>1</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "   mean_test_score  mean_train_score param_kNN__n_neighbors  rank_test_score\n0              1.0               1.0                      1                1\n1              1.0               1.0                      2                1\n2              1.0               1.0                      3                1\n3              1.0               1.0                      4                1\n4              1.0               1.0                      5                1\n5              1.0               1.0                      6                1\n6              1.0               1.0                      7                1\n7              1.0               1.0                      8                1\n8              1.0               1.0                      9                1"
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "conf_mat(y_test, cv_norm.predict(X_test))",
      "execution_count": 23,
      "outputs": [
        {
          "data": {
            "text/plain": "array([[ 29.,   0.,   0.],\n       [  0.,  29.,   0.],\n       [  0.,   0.,  29.]])"
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "c = conf_mat(y, cv_norm.predict(X))\npd.DataFrame(data={'$F_1$':F_β(c),\n                   '$R$':recall(c),\n                   '$P$':precision(c)},\n             index=['bfi', 'bfo', 'dfb'])",
      "execution_count": 24,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>$F_1$</th>\n      <th>$P$</th>\n      <th>$R$</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>bfi</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>1.0</td>\n    </tr>\n    <tr>\n      <th>bfo</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>1.0</td>\n    </tr>\n    <tr>\n      <th>dfb</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>1.0</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "     $F_1$  $P$  $R$\nbfi    1.0  1.0  1.0\nbfo    1.0  1.0  1.0\ndfb    1.0  1.0  1.0"
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "avgs=['micro', 'macro']\npd.DataFrame(data={'$F_1$':[F_β(c, avg=i) for i in avgs],\n                   '$R$':[recall(c, avg=i) for i in avgs],\n                   '$P$':[precision(c, avg=i) for i in avgs]},\n             index=avgs)",
      "execution_count": 25,
      "outputs": [
        {
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>$F_1$</th>\n      <th>$P$</th>\n      <th>$R$</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>micro</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>1.0</td>\n    </tr>\n    <tr>\n      <th>macro</th>\n      <td>1.0</td>\n      <td>1.0</td>\n      <td>1.0</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
            "text/plain": "       $F_1$  $P$  $R$\nmicro    1.0  1.0  1.0\nmacro    1.0  1.0  1.0"
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Perfect (literally)."
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Q3\n\n Let's assume our data has some $n$ feature inputs (columns) each having multiple observations (rows), represented as a matrix of observation vectors ${\\bf X}=\\{{\\bf x}_1, {\\bf x}_2, \\dots {\\bf x}_n\\}$. Each of the $m$ observations has a corresponding observed output (a *target*), which we call ${\\bf y} = \\{y_1, y_2, \\dots y_m\\}$\n \n Simple Linear Regression, or Ordinary Least Squares (OLS) is a model that assumes the target can be predicted by a linear combination of the features, represented as \n $${\\bf y} = {\\bf X}\\beta +\\varepsilon $$\n where $\\beta$ is a vector of feature-weights (like the *slope* on each ${\\bf x_i}$), and $\\varepsilon$ is the bias vector (*intercept*)\n \n The data probably does not lie perfecty on this hyperplane, so a typical approach is to minimise the **residual** between the points and the nearest point on the hyperplane (the distance from a point to its orthogonal projection onto the plane...although technically we minimise the sum of the square residual over all points). \n \n This can be solved for an \"optimal\" $\\beta$ as \n $$\\hat{\\beta} = \\left({\\bf X}^T{\\bf X}\\right)^{-1}{\\bf X}^T{\\bf y}$$\n \nThis $\\hat{\\beta}$ can then be used to predict the output for new input points. \n \n Obviously one could simply use the original data as input features, leading to true \"linear\" regression, though columns can also be transformations of the original data, leading to the possiblility for regression of arbitrary polynomial degree, etc. "
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Q4"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "p2_dir = os.path.join(data_dir, 'Q4')\ndat = loadmat(os.path.join(p2_dir, 'libdata.mat'))['libdata'][:,0]\noldat = loadmat(os.path.join(p2_dir, 'outlierlibdata.mat'))['outlierlibdata'][:,0]\nnadat = loadmat(os.path.join(p2_dir, 'nanlibdata.mat'))['nanlibdata'][:,0]",
      "execution_count": 27,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Part 1"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "from scipy.special import erfcinv\n\ndef detect_outliers(X, kind='median', window=None, plot=False):\n    def MAD(x):\n        mad = -1/(np.sqrt(2)*erfcinv(3/2))*np.median(np.abs(x.T-np.median(x, axis=-1)), \n                                                     axis=0)\n        med = np.median(x, axis=-1)\n        return (med+3*mad, med-3*mad)\n    def IQR(x):\n        upper, lower = np.percentile(x, [75, 25],axis=-1)\n        iqr = np.subtract(upper, lower)\n        return (1.5*iqr + upper, lower - 1.5*iqr)\n \n    \n    behavior = {'median':MAD, 'quartile':IQR}\n    \n    def rolling_window(a, window):\n        \"\"\"credit: http://www.rigtorp.se/2011/01/01/rolling-statistics-numpy.html\n        Trick to vectorize windowing, rather than using loops (way faster in numpy)\n        \"\"\"\n        shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)\n        strides = a.strides + (a.strides[-1],)\n        return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)\n        \n    if window is None:\n        high, low = behavior[kind](X)\n        mask = (X < high) & (X > low)\n        return np.where(mask, X, np.nan)\n    else:\n        assert type(window)==int, 'please pass window size as an int!'\n        pad = [(window-1)//2, (window-1)//2+(window-1)%2]\n        high, low =  behavior[kind](rolling_window(np.pad(X, pad, 'edge'), window))\n        if plot:\n            plt.gca().fill_between(np.arange(high.shape[0]), low, high, alpha=.5, \n                                   label=f'{kind}, window:{window}')\n        mask = (X < high) & (X > low)\n        return np.where(mask, X, np.nan)\n\ndetect_outliers(oldat, window=50)",
      "execution_count": 35,
      "outputs": [
        {
          "data": {
            "text/plain": "array([ 1.35493904,  1.35456296,  1.35042162, ...,  0.59402564,\n        0.57370956,         nan])"
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "scrolled": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "df_ol = pd.DataFrame({'MAD':detect_outliers(oldat, kind='median', window=200), \n                      'IQR':detect_outliers(oldat, kind='quartile', window=200)})\n\ndf_ol['nearest+MAD']=df_ol[\"MAD\"].interpolate(method='nearest', \n                                              limit_direction='both', limit=100)\ndf_ol['nearest+IQR']=df_ol[\"IQR\"].interpolate(method='nearest', \n                                              limit_direction='both', limit=100)\ndf_ol['linear+MAD']=df_ol[\"MAD\"].interpolate(method='linear', \n                                             limit_direction='both', limit=100)\ndf_ol['linear+IQR']=df_ol[\"IQR\"].interpolate(method='linear', \n                                             limit_direction='both', limit=100)\ndf_ol['spline+MAD']=df_ol[\"MAD\"].interpolate(method='spline', \n                                             limit_direction='both', limit=100,\n                                             order=3)\ndf_ol['spline+IQR']=df_ol[\"IQR\"].interpolate(method='spline', \n                                             limit_direction='both', limit=100,\n                                             order=3)\n\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.metrics import r2_score, mean_squared_error\n\nplt.figure(figsize=(10,6))\nplt.plot(oldat, '.', markersize=2, label='Responses')\n\nfor col in df_ol.columns.tolist()[2:]:\n    y = df_ol[col].values[:-1]\n    x = np.arange(y.shape[0]).reshape(-1,1)\n    ols=LinearRegression().fit(x,y)\n    y_pred = ols.predict(x)\n    rmse=np.sqrt(mean_squared_error(y, y_pred))\n    r2 = r2_score(y, y_pred)\n    plt.plot(x, y_pred, linewidth=1, label=f'{col} - RMSE:{rmse:.4f}, R^2:{r2:.4f}')\n\ndetect_outliers(oldat, window=200, plot=True, kind='median')\ndetect_outliers(oldat, window=200, plot=True, kind='quartile')\n\nplt.title('Robust Regression - Windowed at n=200')\nplt.legend()\n\n",
      "execution_count": 46,
      "outputs": [
        {
          "data": {
            "text/plain": "<matplotlib.legend.Legend at 0x7fa4cc0b1358>"
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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+y4YNG4x9sBq3OXOsOnToQJ06dXB2dmbAgAHMmDHDGCOnZ+yVV16hfv36PP30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82u8/cSTZHwhxNIbfdxtqBimQaTkftpj/l5z8Euzk+WeGkoR81y8KsKuzuiOK5HwKfQGfdj2i6m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\nQmCC\n",
            "text/plain": "<matplotlib.figure.Figure at 0x7fa4cc230080>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Part 2"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "df_na = pd.DataFrame({'dat':nadat})\n\ndf_na['nearest']=df_na[\"dat\"].interpolate(method='nearest')\ndf_na['linear']=df_na[\"dat\"].interpolate(method='linear')\ndf_na['spline']=df_na[\"dat\"].interpolate(method='spline', order=3)\n\nplt.figure(figsize=(10,6))\nplt.plot(nadat, '.', markersize=2, label='Responses')\n\nfor col in df_na.columns.tolist()[1:]:\n    y = df_na[col].dropna().values\n    x = np.arange(y.shape[0]).reshape(-1,1)\n    \n    ols=LinearRegression().fit(x,y)\n    y_pred = ols.predict(x)\n    rmse=np.sqrt(mean_squared_error(y, y_pred))\n    r2 = r2_score(y, y_pred)\n    plt.plot(x, y_pred, linewidth=1, label=f'{col} - R^2:{r2:.4f}, RMSE:{rmse:.4f}')\n#     sns.regplot(x, df_ol[col], scatter=False)\nplt.legend()\n",
      "execution_count": 43,
      "outputs": [
        {
          "data": {
            "text/plain": "<matplotlib.legend.Legend at 0x7fa4d06ce780>"
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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mx44d+Pj4cPz4cUaPHk3FihWzHO/RowezZ8/mxo0bfPLJJ1n2tH311VccOnSITZs2MW3a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\n1t1/W40xLxljBtibjQHuMcZsBr4C7iwsqBIRkaqhvJQlcMwoORtUAbR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            "text/plain": "<matplotlib.figure.Figure at 0x7fa4cc44c5f8>"
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "hide_input": false,
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3",
      "language": "python"
    },
    "language_info": {
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      "version": "3.6.2",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "latex_envs": {
      "eqNumInitial": 1,
      "eqLabelWithNumbers": true,
      "current_citInitial": 1,
      "cite_by": "apalike",
      "bibliofile": "biblio.bib",
      "LaTeX_envs_menu_present": true,
      "labels_anchors": false,
      "latex_user_defs": false,
      "user_envs_cfg": false,
      "report_style_numbering": false,
      "autocomplete": true,
      "hotkeys": {
        "equation": "Ctrl-E",
        "itemize": "Ctrl-I"
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    },
    "gist": {
      "id": "",
      "data": {
        "description": "kNN_robustOLS.ipynb",
        "public": true
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}