Chapter 03 - Linear Methods For Regression.ipynb

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   "source": [
    "# Chapter 3 - Linear Methods For Regression"
   ]
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   "source": [
    "## Section 3.1"
   ]
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    "* Largely developed in pre-computer age, but still useful, especially in cases of small training set or sparse data.\n",
    "* Easy to interpret.\n",
    "* Can be expanded in scope by applying transformation to features."
   ]
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   "source": [
    "## Section 3.2"
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    "$f(X) = \\beta_{0} + \\sum_{j = 1}^{p} X_{j}*\\beta_{j}$\n",
    "\n",
    "Features can be\n",
    "\n",
    "* Quantitative inputs\n",
    "* Transformations of quantitative inputs (e.g. log)\n",
    "* Basis expansion (e.g. $X_{2} = X_{1}^{2}, \\ X_{3} = X{1}^3$)\n",
    "* One-hot or dummy encoding of qualitative variables\n",
    "* Interactions between variables (e.g. $X_{3} = X_{1}*X_{2}$)\n",
    "\n",
    "While these new interaction or basis terms can be non-linear, the model is still linear in the parameters $\\beta_{j}$.  However, these new terms can create a richer model than what is otherwise possible.\n",
    "\n",
    "**Least squares** - method in which we pick the coefficients $\\beta_{j}$ in order to minimize the RSS where $RSS = \\sum_{i=1}^{N}(y_{i} - f(x_{i}))^2$ for N training points.\n",
    "\n",
    "The coefficients $\\beta_{j}$ are selected by minimizing the RSS function using calculus. The first derivative is taken and set = 0 and then the corresponding linear algebra is solved to obtain $\\vec{\\beta}$.\n",
    "\n",
    "Residual vector $\\hat{y} - y = (y-X\\beta)$. Because $X^T(y-X\\beta)=0$ from our minimization, the residual vector can be said to be orthogonal to the subspace spanned by $X$.  Thus $\\hat{y}$ is the orthogonal projection of $y$ onto this subspace.\n",
    "\n",
    "Redundant columns (e.g. those that are linearly dependent, i.e. a scalar multiple of others) can cause issues because then $X$ is not full rank and the math will not work out as expected.  There will be more than 1 solution to the equation.  Near linear independence can also cause difficulties with the optimization algorithms.\n",
    "\n",
    "Rank deficiencies can also occur if the number of features is > number of training samples. "
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   "source": [
    "import pandas\n",
    "X = pandas.read_csv('./data/Chapter3/lung_cancer_features.csv', index_col=0)\n",
    "y = pandas.read_csv('./data/Chapter3/lung_cancer_response.csv', index_col=0)"
   ]
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     "text": [
      "Feature shape: (181, 12533)\n",
      "Response shape: (181, 1)\n"
     ]
    }
   ],
   "source": [
    "print('Feature shape: {0}'.format(X.shape))\n",
    "print('Response shape: {0}'.format(y.shape))\n",
    "\n",
    "# as you can see we have high dimensional data where # features > # training samples"
   ]
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       "0.9995559173435511"
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     "execution_count": 3,
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   "source": [
    "# Curse of dimensionality formula\n",
    "(1-0.5**(1.0/181))**(1.0/12533)"
   ]
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    "# Correlation matrix on features\n",
    "correlations = X.corr()"
   ]
  },
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       "           response\n",
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       "4      mesothelioma\n",
       "5      mesothelioma\n",
       "..              ...\n",
       "177  adenocarcinoma\n",
       "178  adenocarcinoma\n",
       "179  adenocarcinoma\n",
       "180  adenocarcinoma\n",
       "181  adenocarcinoma\n",
       "\n",
       "[181 rows x 1 columns]"
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    "y"
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       "      <td>-0.281355</td>\n",
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       "            1000_at   1001_at  1002_f_at  1003_s_at   1004_at   1005_at  \\\n",
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       "1001_at   -0.043401  1.000000   0.079289   0.037468  0.140561  0.283577   \n",
       "1002_f_at -0.106262  0.079289   1.000000   0.084790  0.160398 -0.044737   \n",
       "1003_s_at -0.187240  0.037468   0.084790   1.000000 -0.320351  0.100152   \n",
       "1004_at   -0.051083  0.140561   0.160398  -0.320351  1.000000  0.048034   \n",
       "...             ...       ...        ...        ...       ...       ...   \n",
       "994_at    -0.015864  0.247879   0.101355  -0.051440  0.158331  0.056327   \n",
       "995_g_at   0.045199  0.274741   0.007600  -0.140417  0.128278  0.179719   \n",
       "996_at     0.021438 -0.144453   0.050601   0.049930 -0.145383 -0.041597   \n",
       "998_s_at   0.038466 -0.186025   0.097334  -0.506415  0.246493 -0.043764   \n",
       "999_at    -0.094613 -0.105916  -0.069340  -0.098000 -0.010224  0.114019   \n",
       "\n",
       "            1006_at  1007_s_at  1008_f_at   1009_at  ...    989_at    990_at  \\\n",
       "1000_at    0.026196   0.150805  -0.019221 -0.093804  ... -0.158659  0.055587   \n",
       "1001_at    0.157358  -0.113356   0.258841 -0.184640  ... -0.281355  0.287193   \n",
       "1002_f_at -0.034900   0.073034   0.068408  0.040655  ... -0.080264  0.075682   \n",
       "1003_s_at -0.059123  -0.237124   0.285958  0.129374  ... -0.009194 -0.077167   \n",
       "1004_at    0.148798   0.151428  -0.257692 -0.096516  ... -0.201821  0.074393   \n",
       "...             ...        ...        ...       ...  ...       ...       ...   \n",
       "994_at     0.054608   0.016592   0.101494 -0.150710  ... -0.097280  0.178722   \n",
       "995_g_at   0.036542  -0.012366  -0.123745 -0.315493  ... -0.087849  0.034695   \n",
       "996_at    -0.090716   0.011012  -0.035910  0.012591  ...  0.060109 -0.018147   \n",
       "998_s_at   0.047183   0.077264  -0.265170 -0.001199  ...  0.100336 -0.082022   \n",
       "999_at    -0.000507  -0.063247  -0.218883 -0.127193  ...  0.282566 -0.123308   \n",
       "\n",
       "           991_g_at    992_at    993_at    994_at  995_g_at    996_at  \\\n",
       "1000_at    0.045566  0.015008  0.041214 -0.015864  0.045199  0.021438   \n",
       "1001_at    0.226201 -0.044464 -0.207977  0.247879  0.274741 -0.144453   \n",
       "1002_f_at  0.108818 -0.038409  0.108815  0.101355  0.007600  0.050601   \n",
       "1003_s_at -0.242421 -0.095101 -0.211643 -0.051440 -0.140417  0.049930   \n",
       "1004_at    0.240481  0.064276  0.098117  0.158331  0.128278 -0.145383   \n",
       "...             ...       ...       ...       ...       ...       ...   \n",
       "994_at     0.043115 -0.000925 -0.012285  1.000000  0.768621 -0.042210   \n",
       "995_g_at  -0.018871  0.034726  0.082119  0.768621  1.000000 -0.142548   \n",
       "996_at    -0.053980  0.022772 -0.008240 -0.042210 -0.142548  1.000000   \n",
       "998_s_at   0.112331  0.158404  0.206916  0.080972  0.071190  0.067519   \n",
       "999_at    -0.140219  0.224675  0.189403 -0.088436  0.077247 -0.114431   \n",
       "\n",
       "           998_s_at    999_at  \n",
       "1000_at    0.038466 -0.094613  \n",
       "1001_at   -0.186025 -0.105916  \n",
       "1002_f_at  0.097334 -0.069340  \n",
       "1003_s_at -0.506415 -0.098000  \n",
       "1004_at    0.246493 -0.010224  \n",
       "...             ...       ...  \n",
       "994_at     0.080972 -0.088436  \n",
       "995_g_at   0.071190  0.077247  \n",
       "996_at     0.067519 -0.114431  \n",
       "998_s_at   1.000000  0.213583  \n",
       "999_at     0.213583  1.000000  \n",
       "\n",
       "[12533 rows x 12533 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Fill diagonal with np.nan because we don't care about self correlation\n",
    "np.fill_diagonal(correlations.values, np.nan)\n",
    "ranked_correlations = correlations.unstack().abs().sort_values(kind=\"quicksort\", ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top 25 correlated features:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "769_s_at    31444_s_at    0.996305\n",
       "31444_s_at  769_s_at      0.996305\n",
       "33273_f_at  33274_f_at    0.996099\n",
       "33274_f_at  33273_f_at    0.996099\n",
       "38406_f_at  216_at        0.991874\n",
       "216_at      38406_f_at    0.991874\n",
       "41839_at    661_at        0.991816\n",
       "661_at      41839_at      0.991816\n",
       "1430_at     37782_at      0.991006\n",
       "37782_at    1430_at       0.991006\n",
       "41827_f_at  33274_f_at    0.990270\n",
       "33274_f_at  41827_f_at    0.990270\n",
       "33671_f_at  31960_f_at    0.989805\n",
       "31960_f_at  33671_f_at    0.989805\n",
       "38784_g_at  700_s_at      0.987599\n",
       "700_s_at    38784_g_at    0.987599\n",
       "39209_r_at  39208_i_at    0.987142\n",
       "39208_i_at  39209_r_at    0.987142\n",
       "31477_at    37897_s_at    0.986867\n",
       "37897_s_at  31477_at      0.986867\n",
       "35726_at    2027_at       0.985865\n",
       "2027_at     35726_at      0.985865\n",
       "36300_at    36299_at      0.985747\n",
       "36299_at    36300_at      0.985747\n",
       "37065_f_at  33671_f_at    0.985108\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Top 25 correlated features:\")\n",
    "ranked_correlations[0:25]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full rank!\n"
     ]
    }
   ],
   "source": [
    "# Feature matrix is rank deficient if it is not full rank\n",
    "# Full rank means its rank = min(# of rows, # of columns)\n",
    "\n",
    "rank = np.linalg.matrix_rank(X)\n",
    "if (rank == min(X.shape[0], X.shape[1])):\n",
    "    print('Full rank!')\n",
    "else:\n",
    "    print('Rank deficient!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Using assumptions about the observations (namely independence and constant variance), we can form hypothesis tests and confidence intervals on the parameters $\\hat{\\beta}_j$. Constant variances means \"different response variables have the same variance in their errors, regardless of the values of the predictor variables.\"  These tests are used to determine the importance of keeping certain variables in the model and how confident we are that our $\\hat{\\beta}_j$ is close to the real value. It is important to note that $\\beta$ represents the population parameter while $\\hat{\\beta}$ represents a point estimate based on our *sample*. In general, you usually do not have complete info on the entire population. To have this info,  you would have to have an observation for every possible point in the feature space. This is why we perform these tests, \"The least squares estimators are point estimates of the linear regression model parameters $\\beta_j$. However, generally we also want to know how close those estimates might be to the true values of parameters.\"\n",
    "\n",
    "If you want to test whether groups of variables (e.g. a one hot encoded variable) should be included in the model, you can use an F statistic. We can also use the same method to obtain a confidence estimate for the entire parameter vector. The F statistic measures the change in residual sum-of-squares per additional parameter in the bigger model.\n",
    "\n",
    "**Example 3.2.1** \n",
    "When determining whether to drop the features \"age, lcp, gleason, and pgg45\" they calculate an F statistic. The null hypothesis is that the more complicated model is not significantly better than the less complicated one.  The F statistic corresponds to a p value of 0.17, and hence is not significant.  Thus, we do not reject the null hypothesis and we can use the simpler model.\n",
    "\n",
    "**Section 3.2.2**\n",
    "The Gauss-Markov theorem asserts that \"Least squares estimates for $\\beta$ have the smallest variance among all linear unbiased estimates\". However, restricting to unbiased estimates is not necessarily wise. This will come into play with shrinkage/regularization methods, which trade some bias for large reduction in variance.\n",
    "\n",
    "**Section 3.2.3**\n",
    "With > 1 feature, this is called *multiple linear regression*.  When feature vectors are orthogonal, they have no effect on each other, but this almost never occurs with observation data.  However, we can use this in order to create an efficient algorithm for multiple linear regression. For orthogonal inputs, $\\beta_j = \\frac{<x_j, y>}{x_j, x_j}$ making the coefficients easy to compute. To orthogonalize the input space we can use the Gram-Schmidt process, which gives us a QR decomposition where Q and R represent the orthogonal and upper triangular matrices.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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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",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "\n",
    "non_orthogonal = np.array([\n",
    "    [1, 2, 5],\n",
    "    [3, 7, 6],\n",
    "    [5, 2, 4]\n",
    "])\n",
    "\n",
    "x,y,z = ((0,0,0), (0,0,0), (0,0,0))\n",
    "u,v,w = zip(*non_orthogonal)\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.clf()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.quiver(x,y,z,u,v,w)\n",
    "ax.set_xlim([0, 8])\n",
    "ax.set_ylim([0, 8])\n",
    "ax.set_zlim([0, 8])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33\n",
      "43\n",
      "60\n"
     ]
    }
   ],
   "source": [
    "# Our vectors are not orthogonal because their dot products != 0\n",
    "print(np.dot(u, v))\n",
    "print(np.dot(u, w))\n",
    "print(np.dot(v, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Q,R = np.linalg.qr(non_orthogonal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.16903085, -0.20777993, -0.96346047],\n",
       "       [-0.50709255, -0.81988839,  0.2657822 ],\n",
       "       [-0.84515425,  0.53348902,  0.03322277]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q is orthogonal (we will verify later)\n",
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.91607978, -5.57801808, -7.26832659],\n",
       "       [ 0.        , -5.08780054, -3.82427391],\n",
       "       [ 0.        ,  0.        , -3.08971805]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R is upper triangular\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.1102230246251565e-16\n",
      "-5.898059818321144e-17\n",
      "-3.469446951953614e-17\n"
     ]
    }
   ],
   "source": [
    "# We have nearly 0 dot product between all vectors => orthogonal\n",
    "u,v,w = zip(*Q)\n",
    "print(np.dot(u, v))\n",
    "print(np.dot(u, w))\n",
    "print(np.dot(v, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, you can see our vectors are orthogonal\n",
    "fig.clf()\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.quiver(x,y,z,u,v,w)\n",
    "ax.set_xlim([-1, 1])\n",
    "ax.set_ylim([-1, 1])\n",
    "ax.set_zlim([-1, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Section 3.2.4**\n",
    "Multiple outputs does not change the problem much. Our RSS is just the sum of the RSS of the individual output regressions. However, if the errors between the outputs are correlated, it might be worthwile to modify the error function in favor of the multivariate version, which takes into account the co-variance matrix of the errors. However, it will have the same solution until we make the assumption that the covariance matrix varies between observation (i.e. not constant covariance)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Section 3.3\n",
    "\n",
    "Improvements to least-squares:\n",
    "* Prediction accuracy - predictions often have low bias but large variance. Accuracy can be improved by shrinking some coefficients.\n",
    "\n",
    "* Interpretation - large amount of predictors often hard to interpret. It is often worthwile to determine the smaller subset of predictors that exhibit the strongest effects.\n",
    "\n",
    "**Section 3.3.1**\n",
    "Best-subset selection finds the subset of size k that gives the smallest RSS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Load toy dataset from sklearn\n",
    "from sklearn.datasets import load_diabetes\n",
    "X,y = load_diabetes(return_X_y=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Feature indices\n",
    "feature_indices = range(X.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Generate possible subsets of size k=5\n",
    "import itertools\n",
    "subsets = list(itertools.combinations(feature_indices, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "252\n"
     ]
    }
   ],
   "source": [
    "# Have to check 252 subsets\n",
    "print(len(subsets))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Create a 67/33 split\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "subset_rss = []\n",
    "\n",
    "for subset in subsets:\n",
    "    # Filter to subset of features\n",
    "    X_train_subset = X_train[:, subset]\n",
    "    X_test_subset = X_test[:, subset]\n",
    "\n",
    "    # Create linear regression object\n",
    "    lr = LinearRegression()\n",
    "\n",
    "    # Train the model using the training sets\n",
    "    lr.fit(X_train_subset, y_train)\n",
    "\n",
    "    # Predict and compute RSS on test set\n",
    "    predictions_test = lr.predict(X_test_subset)\n",
    "    rss = np.mean((predictions_test - y_test) ** 2)\n",
    "    \n",
    "    subset_rss.append([rss, subset])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[3089.077254505267, (1, 2, 3, 6, 8)],\n",
       " [3179.440717843419, (2, 3, 6, 7, 8)],\n",
       " [3201.012237371069, (1, 2, 3, 7, 8)],\n",
       " [3202.0885123941525, (1, 2, 3, 8, 9)],\n",
       " [3208.136508836399, (2, 3, 6, 8, 9)],\n",
       " [3212.9625445111797, (0, 2, 3, 6, 8)],\n",
       " [3220.31693490342, (0, 1, 2, 3, 8)],\n",
       " [3227.4693460433427, (1, 2, 3, 5, 8)],\n",
       " [3237.8204652439217, (1, 2, 3, 4, 8)],\n",
       " [3259.5219188395827, (0, 2, 3, 8, 9)],\n",
       " [3259.992269910702, (2, 3, 4, 5, 8)],\n",
       " [3268.374565877309, (2, 3, 7, 8, 9)],\n",
       " [3270.7775628189534, (0, 2, 3, 7, 8)],\n",
       " [3282.6162533372135, (2, 3, 4, 6, 8)],\n",
       " [3288.5818014105303, (2, 3, 5, 6, 8)],\n",
       " [3292.6428272387834, (1, 2, 6, 8, 9)],\n",
       " [3299.8522835523113, (1, 2, 6, 7, 8)],\n",
       " [3306.81707060353, (2, 3, 5, 8, 9)],\n",
       " [3309.5231768447507, (0, 2, 3, 5, 8)],\n",
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       " [3720.429334513805, (1, 3, 4, 7, 8)],\n",
       " [3722.9714518296996, (0, 3, 5, 8, 9)],\n",
       " [3742.201771340592, (3, 4, 5, 6, 8)],\n",
       " [3744.010756869122, (3, 4, 5, 8, 9)],\n",
       " [3750.5105494920367, (3, 5, 6, 8, 9)],\n",
       " [3752.701535417999, (1, 3, 5, 7, 8)],\n",
       " [3754.5739714178403, (2, 3, 4, 5, 7)],\n",
       " [3759.524210377542, (0, 3, 4, 5, 8)]]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# RSS and subset indices ranked ascending\n",
    "sorted_rss = sorted(subset_rss)\n",
    "sorted_rss[0:100]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Section 3.3.2**\n",
    "\n",
    "Rather than search through all possible subsets (which becomes computationally infeasible), we can seek an appropriate path through them.\n",
    "\n",
    "*Forward-stepwise selection* starts with the intercept, then sequentially adds into the model the predictor that most improves the fit.  This can be efficient if we have done the Gram-Schmidt orthogonalization process to exploit the QR decomposition.  This is a greedy algorithm (meaning it uses local optimum in hopes of finding global). Compared to best-subset, this is a more constrained search so it will have lower variance and perhaps more bias."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "\n",
    "*Backward-stepwise selection* starts with the full model and sequentially deletes the predictor that has the least impact on the fit. i.e. the one with the smallest Z-score.  Can only be used for N > p (number of samples > number of features).\n",
    "\n",
    "Some software packages use a hybrid approach between the two, considering the best forward and backward moves at each step and select the \"best\" of the two.\n",
    "\n",
    "For one-hot encoded variables, smart stepwise packages will add or drop whole groups at a time, taking proper account of their degrees-of-freedom."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "*Forward-stagewise regression* - even more constrained than forward-stepwise. Start with only an intercept and all $\\hat{\\beta}$ initialized to 0. Then, identify the variable most correlated with the current residual.  Compute the univariate coefficient of the residual and the chocsen variable, then add it to the coefficient of the variable.  Repeat until no variables have any correlation with the residuals.  Inefficient algorithm that can pay dividends in high dimensional cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**sklearn and statsmodels packages do not have stepwise/stagewise algorithms out of the box**\n",
    "\n",
    "For future: write these algorithms manually here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "\n",
    "**Section 3.3.4**\n",
    "\n",
    "Cross-validation works by dividing the training data randomly into K equal parts (this can vary). The learning method is fit on (K-1)/K of the data and the prediction error is computed on the remaining 1/K.  This is then repeated for each \"fold\" of the data.  Afterwards, the K prediction error estimates are averaged."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Section 3.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Ridge/Lasso regression minimizes a penalized RSS.  The penalty is a function of the parameters $\\beta$, and generally \"shrinks\" them so that no particular parameter is too large.  This controls the effect that any particular dimension can have on the final prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Ridge = penalize the loss function by $\\lambda\\sum_{i=1}^{p}\\beta_{i}^2$.\n",
    "\n",
    "* $\\lambda$ is known as the complexity parameter and can be tuned to control the amount of desired penalization.\n",
    "\n",
    "\n",
    "* In standard least squares regression, correlated variables can each get a large coeficient with opposing signs (one large positive one large negative). Regularization methods help alleviate this problem.\n",
    "\n",
    "\n",
    "* We normally standardize (i.e. scale and center) the input variables so variables are on even footing for contributing to the loss penalty.\n",
    "\n",
    "\n",
    "* We leave the intercept out of the penalty term, so that the procedure does not depend on the origin chosen for Y.\n",
    "\n",
    "\n",
    "* The intercept is estimated as the average of $Y$.  We then run the ridge regression on centered/normalized inputs.\n",
    "\n",
    "\n",
    "* Original motivation behind Ridge - it adds a positive constant to the diagonal of $X^TX$ before inversion, making it non-singular even if it was not previously of full rank.\n",
    "\n",
    "\n",
    "* With orthonormal inputs, the Ridge estimates are just scaled down values of the least squares estimates.\n",
    "\n",
    "\n",
    "* Ridge regression can also be derived from a Bayesian framework.\n",
    "\n",
    "\n",
    "* SVD - singular value decomposition. Very useful factorization of a matrix into $X = UDV^T$, where $U$ and $V$ are $N x p$ and $p$ x $p$ orthogonal matrices with the columns of $U$ spanning the column space of $X$, and the columns of $V$ spanning the row space. $D$ is a $p$ x $p$ diagonal matrix, with positive and decreasing values values on the diagonal $d_j$ (from upper left to lower right).  If one or more values of $D$ is 0, then $X$ is singular, meaning it cannot be inverted.\n",
    "\n",
    "\n",
    "* With an SVD decomposition, Ridge solutions are $\\sum_{j=1}^p u_j \\frac{d_{j}^2}{d_{j}^2 + \\lambda}u_{j}^Ty$.  Thus, it computes the coordinates of $y$ with respect to the orthonormal basis $U$, then shrinks them. Note that greater amount of shrinkage happens with smaller $d_{j}^2$. These have a correlation with the principal components of $X$. $z_1$ = $u_1d_1$ is the first principal component of $X$.  So Ridge regression shrinks the directions with least variance the most, and maintains the coefficients of those with variance (the top principal components).\n",
    "\n",
    "\n",
    "* Assumption is that the response will tend to vary most in the directions of high variance of the inputs.\n",
    "\n",
    "\n",
    "* The sum of the shrinkage factor $\\sum_{j=1}^p \\frac{d_{j}^2}{d_{j}^2 + \\lambda}$, is called the **effective degrees of freedom** of the ridge regression.\n",
    "\n",
    "\n",
    "* Penalty is often referred to as the L2 penalty in reflection of the L2 vector norm of the coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import pandas\n",
    "\n",
    "# Load data, this set uses ? for nulls but we can pass that as an option to pandas\n",
    "data = pandas.read_csv('./data/Chapter3/crime_data.csv', na_values='?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Define target and what features should be treated as categorical\n",
    "target_column = 'ViolentCrimesPerPop'\n",
    "categorical_features = ['state', 'county', 'community', 'communityname']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Dummy encode categoricals\n",
    "encoded_data = pandas.get_dummies(data, prefix=categorical_features, columns=categorical_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Get feature columns from encoded data\n",
    "feature_columns = [col for col in encoded_data if col not in ['fold', target_column]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Let's tune the hyper-parameter alpha, which corresponds to the aggressiveness of regularization\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.impute import SimpleImputer\n",
    "import numpy as np\n",
    "\n",
    "# We will compute test error for each alpha and each of the 10 folds and 100 alphas\n",
    "alphas = np.linspace(0.01, 1, 100)\n",
    "test_errors = np.zeros((10, 100))\n",
    "test_variances = np.zeros((10, 100))\n",
    "    \n",
    "for i in range(1,11):\n",
    "    # train = all but fold i. test = fold i\n",
    "    X_train = encoded_data.loc[encoded_data.fold != i, feature_columns].values\n",
    "    y_train = encoded_data.loc[encoded_data.fold != i, target_column].values\n",
    "    X_test = encoded_data.loc[encoded_data.fold == i, feature_columns].values\n",
    "    y_test = encoded_data.loc[encoded_data.fold == i, target_column].values\n",
    "\n",
    "    # Impute on train and transform on train/test\n",
    "    imp = SimpleImputer(strategy='mean')\n",
    "    X_train_imputed = imp.fit_transform(X_train)\n",
    "    X_test_imputed = imp.transform(X_test)\n",
    "\n",
    "    # For each alpha, fit the model and compute the error and prediction variance\n",
    "    for j in range(len(alphas)):\n",
    "        ridge = Ridge(alpha=alphas[j], fit_intercept=True, normalize=False, copy_X=True, max_iter=None, \n",
    "                      tol=0.001, solver='auto', random_state=10)\n",
    "\n",
    "        ridge.fit(X_train_imputed, y_train)\n",
    "        predictions = ridge.predict(X_test_imputed)\n",
    "        test_errors[i-1, j] = mean_squared_error(y_test, predictions)\n",
    "        test_variances[i-1, j] = predictions.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Take the mean error and variance along the folds\n",
    "alpha_errors = test_errors.mean(axis=0)\n",
    "alpha_variances = test_variances.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe7c74c76d8>"
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     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
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    {
     "data": {
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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",
    "%matplotlib inline\n",
    "plt.clf()\n",
    "plt.plot(np.linspace(0,1,100), alpha_errors)\n",
    "plt.plot(np.linspace(0,1,100), alpha_variances)\n",
    "plt.title('Ridge Error')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('SSE')\n",
    "plt.legend(['errors', 'variance'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Show effect of Ridge coefficient on one fold by comparing to Least Squares\n",
    "X_train = encoded_data.loc[encoded_data.fold != 10, feature_columns].values\n",
    "y_train = encoded_data.loc[encoded_data.fold != 10, target_column].values\n",
    "X_test = encoded_data.loc[encoded_data.fold == 10, feature_columns].values\n",
    "y_test = encoded_data.loc[encoded_data.fold == 10, target_column].values\n",
    "\n",
    "imp = SimpleImputer(strategy='mean')\n",
    "X_train_imputed = imp.fit_transform(X_train)\n",
    "X_test_imputed = imp.transform(X_test)\n",
    "\n",
    "# Compute full ridge with alpha = 1\n",
    "ridge = Ridge(alpha=1, fit_intercept=True, normalize=False, copy_X=True, max_iter=None, \n",
    "              tol=0.001, solver='auto', random_state=10)\n",
    "ridge.fit(X_train_imputed, y_train)\n",
    "ridge_predictions = ridge.predict(X_test_imputed)\n",
    "alpha1_coeff=ridge.coef_\n",
    "\n",
    "# Compute least squares (equivalent to Ridge with alpha = 0)\n",
    "ridge0 = LinearRegression(fit_intercept=True, normalize=False, copy_X=True)\n",
    "ridge0.fit(X_train_imputed, y_train)\n",
    "ls_coeff = ridge0.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ridge</th>\n",
       "      <th>Least Squares</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.043645</td>\n",
       "      <td>-1.054303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.070931</td>\n",
       "      <td>-0.494987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.007213</td>\n",
       "      <td>0.230165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.082213</td>\n",
       "      <td>0.052361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.029705</td>\n",
       "      <td>-0.306334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2858</th>\n",
       "      <td>0.102409</td>\n",
       "      <td>0.078977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2859</th>\n",
       "      <td>-0.065052</td>\n",
       "      <td>-0.109405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2860</th>\n",
       "      <td>-0.028612</td>\n",
       "      <td>-0.136661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2861</th>\n",
       "      <td>-0.011659</td>\n",
       "      <td>0.170971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2862</th>\n",
       "      <td>-0.006246</td>\n",
       "      <td>0.066087</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2863 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         Ridge  Least Squares\n",
       "0    -0.043645      -1.054303\n",
       "1     0.070931      -0.494987\n",
       "2     0.007213       0.230165\n",
       "3    -0.082213       0.052361\n",
       "4    -0.029705      -0.306334\n",
       "...        ...            ...\n",
       "2858  0.102409       0.078977\n",
       "2859 -0.065052      -0.109405\n",
       "2860 -0.028612      -0.136661\n",
       "2861 -0.011659       0.170971\n",
       "2862 -0.006246       0.066087\n",
       "\n",
       "[2863 rows x 2 columns]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pandas.DataFrame(list(zip(alpha1_coeff, ls_coeff)), columns = ['Ridge', 'Least Squares'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Regularization improves the conditioning of the problem and reduces the variance of the estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Lasso = penalize the loss function by $\\lambda\\sum_{i=1}^{p}|\\beta_{i}|$.\n",
    "\n",
    "* No closed form solution for Lasso. Computing the solution is a quadratic programming problem. \n",
    "\n",
    "\n",
    "* Some of the coefficients will be exactly 0, unlike Ridge.  This can make it be used as a continuous subset selection problem, and also for *feature reduction*.\n",
    "\n",
    "\n",
    "* Penalty is often referred to as the L1 penalty in reflection of the L1 vector norm of the coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Let's tune the hyper-parameter alpha, which corresponds to the aggressiveness of regularization\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.impute import SimpleImputer\n",
    "import numpy as np\n",
    "\n",
    "# We will compute test error for each alpha and each of the 10 folds and 100 alphas\n",
    "alphas = np.linspace(0.01, 1, 100)\n",
    "test_errors = np.zeros((10, 100))\n",
    "test_variances = np.zeros((10, 100))\n",
    "    \n",
    "for i in range(1,11):\n",
    "    # train = all but fold i. test = fold i\n",
    "    X_train = encoded_data.loc[encoded_data.fold != i, feature_columns].values\n",
    "    y_train = encoded_data.loc[encoded_data.fold != i, target_column].values\n",
    "    X_test = encoded_data.loc[encoded_data.fold == i, feature_columns].values\n",
    "    y_test = encoded_data.loc[encoded_data.fold == i, target_column].values\n",
    "\n",
    "    # Impute on train and transform on train/test\n",
    "    imp = SimpleImputer(strategy='mean')\n",
    "    X_train_imputed = imp.fit_transform(X_train)\n",
    "    X_test_imputed = imp.transform(X_test)\n",
    "\n",
    "    # For each alpha, fit the model and compute the error and predictino variance\n",
    "    for j in range(len(alphas)):\n",
    "        \n",
    "        lasso = Lasso(alpha=alphas[j], fit_intercept=True, normalize=False, precompute=False, copy_X=True, max_iter=1000, \n",
    "                      tol=0.0001, warm_start=False, \n",
    "                      positive=False, random_state=10, selection='cyclic')\n",
    "\n",
    "        lasso.fit(X_train_imputed, y_train)\n",
    "        predictions = lasso.predict(X_test_imputed)\n",
    "        test_errors[i-1, j] = mean_squared_error(y_test, predictions)\n",
    "        test_variances[i-1, j] = predictions.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Take the mean error and variance along the folds\n",
    "alpha_errors = test_errors.mean(axis=0)\n",
    "alpha_variances = test_variances.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe7c9b92860>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "plt.plot(np.linspace(0,1,100), alpha_errors)\n",
    "plt.plot(np.linspace(0,1,100), alpha_variances)\n",
    "plt.title('Lasso Error')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('SSE')\n",
    "plt.legend(['errors', 'variance'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "l = Lasso(alpha=0.001, fit_intercept=True, normalize=False, precompute=False, copy_X=True, max_iter=1000, tol=0.0001, \n",
    "          warm_start=False, positive=False, random_state=None, selection='cyclic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0., -0., ..., -0., -0., -0.])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l.fit(X_train_imputed, y_train)\n",
    "l.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "lasso_predictions = l.predict(X_test_imputed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of non-zero coefficients: 27\n",
      "Total number of features: 2863\n"
     ]
    }
   ],
   "source": [
    "# Number of non-zero coefficents\n",
    "print('Number of non-zero coefficients: {0}'.format(len(l.coef_[l.coef_ != 0])))\n",
    "print('Total number of features: {0}'.format(len(l.coef_)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>feature</th>\n",
       "      <th>coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>agePct16t24</td>\n",
       "      <td>-0.035346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>pctUrban</td>\n",
       "      <td>0.033075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>pctWRetire</td>\n",
       "      <td>-0.060745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>PersPerFam</td>\n",
       "      <td>0.074503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>PctKids2Par</td>\n",
       "      <td>-0.667551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>PctYoungKids2Par</td>\n",
       "      <td>-0.010601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>PctPersDenseHous</td>\n",
       "      <td>0.075529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>MedNumBR</td>\n",
       "      <td>0.006253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>HousVacant</td>\n",
       "      <td>0.133451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PctHousOccup</td>\n",
       "      <td>-0.004092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PctVacantBoarded</td>\n",
       "      <td>0.105395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>MedYrHousBuilt</td>\n",
       "      <td>0.000986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>PctHousNoPhone</td>\n",
       "      <td>0.004673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>MedRent</td>\n",
       "      <td>0.006583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>NumStreet</td>\n",
       "      <td>0.052022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>PctUsePubTrans</td>\n",
       "      <td>0.031758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>LemasGangUnitDeploy</td>\n",
       "      <td>0.020641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>LemasPctOfficDrugUn</td>\n",
       "      <td>0.017540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>state_1</td>\n",
       "      <td>0.071467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>state_6</td>\n",
       "      <td>0.068869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>state_12</td>\n",
       "      <td>0.123940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>state_25</td>\n",
       "      <td>0.045465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>state_36</td>\n",
       "      <td>-0.006650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>state_37</td>\n",
       "      <td>0.017034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>state_45</td>\n",
       "      <td>0.103404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>state_47</td>\n",
       "      <td>0.017094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>state_51</td>\n",
       "      <td>-0.012138</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                feature  coefficient\n",
       "0           agePct16t24    -0.035346\n",
       "1              pctUrban     0.033075\n",
       "2            pctWRetire    -0.060745\n",
       "3            PersPerFam     0.074503\n",
       "4           PctKids2Par    -0.667551\n",
       "5      PctYoungKids2Par    -0.010601\n",
       "6      PctPersDenseHous     0.075529\n",
       "7              MedNumBR     0.006253\n",
       "8            HousVacant     0.133451\n",
       "9          PctHousOccup    -0.004092\n",
       "10     PctVacantBoarded     0.105395\n",
       "11       MedYrHousBuilt     0.000986\n",
       "12       PctHousNoPhone     0.004673\n",
       "13              MedRent     0.006583\n",
       "14            NumStreet     0.052022\n",
       "15       PctUsePubTrans     0.031758\n",
       "16  LemasGangUnitDeploy     0.020641\n",
       "17  LemasPctOfficDrugUn     0.017540\n",
       "18              state_1     0.071467\n",
       "19              state_6     0.068869\n",
       "20             state_12     0.123940\n",
       "21             state_25     0.045465\n",
       "22             state_36    -0.006650\n",
       "23             state_37     0.017034\n",
       "24             state_45     0.103404\n",
       "25             state_47     0.017094\n",
       "26             state_51    -0.012138"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pandas.DataFrame(list(zip(np.array(feature_columns)[np.array(l.coef_ != 0)], l.coef_[l.coef_ != 0])), \n",
    "                 columns = ['feature', 'coefficient'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Least Angle Regression (LAR)\n",
    "1. Standardize the predictors to have mean zero and unit norm. Start with the residual $r=y-\\bar{y}, \\beta_j = 0$.\n",
    "2. Find the predictor $x_j$ most correlated with $r$.\n",
    "3. Move $\\beta_j$ from 0 towards its least square coefficient until some other competitor $x_k$ has as much correlation with the current residual as does $x_j$.\n",
    "4. Move $\\beta_j$ and $\\beta_k$ in the direction defined by their join least squares coefficient of the current residual until some other competitor has as much correlation with the current residual.\n",
    "5. Continue until all $p$ predictors have been entered. After $min(N-1, p)$ steps, we arrive at the full least squares solution.\n",
    "\n",
    "\n",
    "* The name \"least angle\" arises from the geometrical interpretation of the process. The new fit direction makes the smallest (and equal) angle with each of the predictors in the active set.\n",
    "\n",
    "\n",
    "* LAR can be modified to include a lasso element -- if a non-zero coefficient hits zero, drop its variable from the active set of variables and recompute the current joint least squares direction.\n",
    "\n",
    "\n",
    "* Effective degrees of freedom for traditional linear model = # of linearly independent feature vectors.  For adaptively fitted models (and can be applied to any general prediction), the definition is:\n",
    "$df(\\hat{y}) \\frac{1}{\\sigma^2}\\sum_{i=1}^{N} Cov(\\hat{y_i}, y_i)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "lars = Lars(fit_intercept=True, verbose=False, normalize=True, precompute='auto', n_nonzero_coefs=30, \n",
    "            eps=0.01, copy_X=True, fit_path=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., ..., 0., 0., 0.])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lars.fit(X_train_imputed, y_train)\n",
    "lars.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "lars_predictions = lars.predict(X_test_imputed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of non-zero coefficients: 29\n",
      "Total number of features: 2863\n"
     ]
    }
   ],
   "source": [
    "# Number of non-zero coefficents\n",
    "print('Number of non-zero coefficients: {0}'.format(len(lars.coef_[lars.coef_ != 0])))\n",
    "print('Total number of features: {0}'.format(len(lars.coef_)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>feature</th>\n",
       "      <th>coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>pctUrban</td>\n",
       "      <td>2.020467e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>PersPerFam</td>\n",
       "      <td>1.689546e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>PctKids2Par</td>\n",
       "      <td>-7.821069e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>PctLargHouseFam</td>\n",
       "      <td>-1.408916e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>PctLargHouseOccup</td>\n",
       "      <td>1.173122e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>PctPersDenseHous</td>\n",
       "      <td>2.419105e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>HousVacant</td>\n",
       "      <td>1.595435e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>PctVacantBoarded</td>\n",
       "      <td>7.542666e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NumInShelters</td>\n",
       "      <td>1.472550e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NumStreet</td>\n",
       "      <td>1.444477e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PctUsePubTrans</td>\n",
       "      <td>5.607289e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>LemasPctOfficDrugUn</td>\n",
       "      <td>6.809759e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>state_1</td>\n",
       "      <td>1.983401e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>state_6</td>\n",
       "      <td>2.834283e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>state_12</td>\n",
       "      <td>7.290371e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>state_23</td>\n",
       "      <td>-6.517418e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>state_25</td>\n",
       "      <td>8.610580e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>state_45</td>\n",
       "      <td>6.186020e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>state_51</td>\n",
       "      <td>-7.528042e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>community_29333.0</td>\n",
       "      <td>8.411968e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>community_43554.0</td>\n",
       "      <td>7.708802e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>community_47138.0</td>\n",
       "      <td>1.465341e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>communityname_GlensFallscity</td>\n",
       "      <td>1.465081e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>communityname_Hawthornecity</td>\n",
       "      <td>3.086627e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>communityname_LaCanadaFlintridgecity</td>\n",
       "      <td>3.087937e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>communityname_Opelikacity</td>\n",
       "      <td>1.643791e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>communityname_PlantCitycity</td>\n",
       "      <td>4.617263e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>communityname_Vernoncity</td>\n",
       "      <td>2.869026e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>communityname_WestHollywoodcity</td>\n",
       "      <td>2.029893e-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 feature   coefficient\n",
       "0                               pctUrban  2.020467e-02\n",
       "1                             PersPerFam  1.689546e-01\n",
       "2                            PctKids2Par -7.821069e-01\n",
       "3                        PctLargHouseFam -1.408916e+00\n",
       "4                      PctLargHouseOccup  1.173122e+00\n",
       "5                       PctPersDenseHous  2.419105e-01\n",
       "6                             HousVacant  1.595435e-01\n",
       "7                       PctVacantBoarded  7.542666e-02\n",
       "8                          NumInShelters  1.472550e-02\n",
       "9                              NumStreet  1.444477e-01\n",
       "10                        PctUsePubTrans  5.607289e-02\n",
       "11                   LemasPctOfficDrugUn  6.809759e-03\n",
       "12                               state_1  1.983401e-02\n",
       "13                               state_6  2.834283e-02\n",
       "14                              state_12  7.290371e-02\n",
       "15                              state_23 -6.517418e-03\n",
       "16                              state_25  8.610580e-03\n",
       "17                              state_45  6.186020e-02\n",
       "18                              state_51 -7.528042e-04\n",
       "19                     community_29333.0  8.411968e-02\n",
       "20                     community_43554.0  7.708802e-03\n",
       "21                     community_47138.0  1.465341e-01\n",
       "22          communityname_GlensFallscity  1.465081e-13\n",
       "23           communityname_Hawthornecity  3.086627e-02\n",
       "24  communityname_LaCanadaFlintridgecity  3.087937e-01\n",
       "25             communityname_Opelikacity  1.643791e-02\n",
       "26           communityname_PlantCitycity  4.617263e-02\n",
       "27              communityname_Vernoncity  2.869026e-01\n",
       "28       communityname_WestHollywoodcity  2.029893e-01"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pandas.DataFrame(list(zip(np.array(feature_columns)[np.array(lars.coef_ != 0)], lars.coef_[lars.coef_ != 0])), \n",
    "                 columns = ['feature', 'coefficient'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ridge MSE: 0.016334366171554954\n",
      "Lasso MSE: 0.015712497273211105\n",
      "LARS MSE: 0.01603354580343012\n"
     ]
    }
   ],
   "source": [
    "# Error comparison on test for fold = 1\n",
    "print('Ridge MSE: {0}'.format(mean_squared_error(ridge_predictions, y_test)))\n",
    "print('Lasso MSE: {0}'.format(mean_squared_error(lasso_predictions, y_test)))\n",
    "print('LARS MSE: {0}'.format(mean_squared_error(lars_predictions, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Section 3.5 - Derived Input Directions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Principal Components**\n",
    "\n",
    "* Using SVD, orthogonalize the input vectors and choose the top M with the most variance. What this amounts to is determining a basis for the input space (the eigenvectors) and using the associated singular values (which rank the corresponding directional variance in the basis) to select the derived input columns that best explain the variance.\n",
    "\n",
    "* Then, we regress on the principal component vectors. Since these are orthogonal its just a sum of the univariate regressions.\n",
    "\n",
    "* Principal components depend on the scaling of the inputs, so we standardize them first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '2-D Projection')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate a 3D figure\n",
    "from mpl_toolkits.mplot3d import axes3d\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.clear()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# Grab some test data.\n",
    "X, Y, Z = axes3d.get_test_data(0.05)\n",
    "\n",
    "# Plot a basic wireframe.\n",
    "ax.plot_wireframe(X, Y, Z, rstride=10, cstride=10)\n",
    "plt.title(\"3D Feature Surface\")\n",
    "plt.show()\n",
    "\n",
    "# convert the sample points in the surface to a typical design matrix\n",
    "zipped = np.dstack((X,Y,Z))\n",
    "design_matrix = zipped.reshape(-1,3)\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2, copy=True, whiten=False, svd_solver='auto', tol=0.0, iterated_power='auto', \n",
    "          random_state=10)\n",
    "\n",
    "components = pca.fit_transform(design_matrix)\n",
    "plt.scatter(components[:, 0], components[:, 1], color='green')\n",
    "plt.title(\"2-D Projection\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Partial Least Squares**\n",
    "\n",
    "* Also not scale-invariant.\n",
    "* Uses both Y and X in its construction.\n",
    "\n",
    "*Note for understanding algorithm:*\n",
    "* When two vectors are unit length, their dot product represents \"...what amount of one vector goes in the direction of another.\" For example, if you move a box at an angle to a horizontal vector, what amount if displaced in the horizontal direction for movement on the angled vector?  This is why orthogonal vectors have a dot product of 0.\n",
    "\n",
    "* Since the $x_j$ are standardized, the first directions $\\hat{\\phi_{1j}}$ are the univariate regression coefficients. This is not the case for subsequent directions.\n",
    "\n",
    "*Algorithm*\n",
    "1. Standardized each $x_j$ to have mean zero and variance one.\n",
    "\n",
    "2. For m = $1, 2, \\dots, M$ where $M < p$:\n",
    "\n",
    "    a) $z_m = \\sum_{j=1}^{p} \\hat{\\phi_{mj}}x_{j}^{(m-1)}$, where $\\hat{\\phi_{mj}} = <x_{j}^{(m-1)}, y>$. This is the PLS input direction.\n",
    "    \n",
    "    b) $\\hat{\\theta_{(m)}} = <z_m, y>/<z_m, z_m>$.  This is the univariate regression coefficient of y with $z_m$.\n",
    "    \n",
    "    c) $\\hat{y^{(m)}} = \\hat{y^{(m-1)}} + \\hat{\\theta_{(m)}}z_m$.  Add to previous approximation this univarate directional improvement.\n",
    "    \n",
    "    d) Orthogonalize $x_{j}^{(m-1)}$ with respect to $z_m$: $x_{j}^{(m)} = x_{j}^{(m-1)} - [<z_m, x_{j}^{(m-1)}>/<z_m, z_m>] z_m, \\ j = 1, 2, \\dots p$.\n",
    "       \n",
    "3. Output the set of fitted values $\\hat{y}^{(m)}$. $m = 1, \\dots, M$\n",
    "\n",
    "\n",
    "* PLS seeks directions that have high variance and high correlation with the response.\n",
    "\n",
    "\n",
    "* If input matrix is orthogonal, PLS finds the least squares estimates after m=1 steps. Subsequent steps have no effect.\n",
    "\n",
    "\n",
    "* Sequence of PLS coefficients represent the conjugate gradient sequence for computing the least squares solution. \"In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PLS MSE: 0.01930939036807998\n"
     ]
    }
   ],
   "source": [
    "# Use the same data prepared above. Fold = 1 of the crime data\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "pls = PLSRegression(n_components=2, scale=True, max_iter=500, tol=1e-06, copy=True)\n",
    "\n",
    "pls.fit(X_train_imputed, y_train)\n",
    "pls_predictions = pls.predict(X_test_imputed)\n",
    "print('PLS MSE: {0}'.format(mean_squared_error(pls_predictions, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
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   "source": [
    "**Comparison of methods**\n",
    "* Ridge regression shrinks all directions, but shrinks low-variance directions more.\n",
    "* Principal components regression leaves M high-variance directions alone and discards the rest.\n",
    "* PLS tends to shrink low-variance directions but actually inflate some of the higher variances directions, making it a little unstable.\n",
    "* For minimizing prediction error, Ridge regression is generally preferable to variable subset selection, PCR, and PLS. \n",
    "* Ridge shrinks smoothly, rather than in discrete steps like PLS and PCR. Lasso falls somewhere in between the two."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Multiple Outcome Shrinkage**\n",
    "\n",
    "* Techniques can be applied to each of the outcomes individually or all at the same time.\n",
    "\n",
    "* Canonical correlation analysis (CCA) is the multiple output analog to PCA.  Finds uncorrelated input vectors and a corresponding sequence of uncorrelated linear combinations of the responses in order to maximize the squared correlation of the responses and inputs. This approach is formalized in *reduced ranked regression*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Incremental Forward Stagewise Regression**\n",
    "\n",
    "*  Works just like LAR but updates to the $\\beta_j$ are done by adding $\\epsilon*sign[<x_k, r>]$ for a small step size $\\epsilon$ at each iteration.\n",
    "\n",
    "\n",
    "1. Start with the residual $r$ equal to to $y$ and $\\beta_j = 0$.  Standardized inputs to be mean 0 and unit norm.\n",
    "\n",
    "2. Find the predictor $x_j$ most correlated with $r$.\n",
    "\n",
    "3. Update $\\beta_j \\leftarrow \\beta_j + \\delta_j$, where $\\delta_j = \\epsilon*sign[<x_k, r>]$ and $\\epsilon > 0$ is a small step size, and set $r \\leftarrow r - \\delta_jx_j$.\n",
    "\n",
    "4. Repeat steps 2 and 3 many times, until the residuals are uncorrelated with all the predictors.\n",
    "\n",
    "\n",
    "* If we let $\\epsilon$ approach 0, we call the limiting procedure *infintesimal forward stagewise regression*.  This is also sometimes referred to as L2boost because of its connections to boosting.\n",
    "\n",
    "**Other algorithms**\n",
    "\n",
    "* Piecewise-Linear Path Algorithms\n",
    "    * Generalization of Lasso like algorithms but with different loss and and penalization functions.\n",
    "\n",
    "\n",
    "* The Dantzig Selector\n",
    "    * Resembles the Lasso but replaces the squared error loss with the maximum absolute value of its gradient.\n",
    "\n",
    "\n",
    "* The Grouped Lasso\n",
    "    * Allows you to regularize variables in groups. E.g. a group of one-hot encoded categoricals.\n",
    "\n",
    "**Misc. Lasso Notes**\n",
    "*  Estimates for $\\beta$ are not consistent, meaning as sample size grows they do not necesarilly converge to the true values.\n",
    "\n",
    "* One approach to reducing bias - run the Lasso to identify non-zero coefficients and then fit an non-regularized linear model to the non-zero predictors.\n",
    "\n",
    "* If instead, we apply Lasso a second time this is known as the *relaxed Lasso*.\n",
    "\n",
    "* *Smoothly clipped absolute deviation penalty* - replace the penalty function in Lasso so that large coefficients are shrunken less severely.\n",
    "\n",
    "* *Adaptive lasso* - Uses a weight penalty function where the weight for each coefficient is proportional to the least squares estimate.\n",
    "\n",
    "**Pathwise Coordinate Optimization**\n",
    "* Alternative algorithm to the LARS algorithm for computing Lasso solution is to use simple coordinate descent. This can be faster for a large set of data.  It also returns the soultion of a grid of the hyper-parameter $\\lambda$. Can also be used for elastic, grouped lasso, and other models for which the penalty is a sum of the individual $\\beta_j$.\n",
    "\n",
    "\n",
    "**Computation Considerations**\n",
    "* Whether to use a Cholesky or QR decomposition for computing the least squares estimates depends on the relationship of N and p.  Depending on their releative side, there are tradeoffs of speed/stability/etc."
   ]
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