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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "# Some nice default configuration for plots\n",
      "plt.rcParams['figure.figsize'] = 10, 7.5\n",
      "plt.rcParams['axes.grid'] = True\n",
      "plt.gray()\n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x10bce97d0>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "7. Nonlinear Regression Models"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The previous chapter discussed regression models that were intrinsically linear. Many of these models can be adapted to nonlinear trends in the data by manually adding model terms. However, to do this, one must know the specific nature of the nonlinearity in the data.\n",
      "\n",
      "There are numerous regression models that are inherently nonlinear in nature. When using these models, the exact form of the nonlinearity does not need to be known explicitly or specified prior to model training."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "7.1 Neural Networks"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Neural networks are powerful nonlinear regression techniques inspired by theories about how the brain works. Like partial least squares, the outcome is modeled by an intermediary set of unobserved variables (called *hidden variable* or *hidden units*). These hidden units are linear combinations of the original predictors, but, unlike PLS models, they are not estimated in a hierarchical fashion.\n",
      "\n",
      "As previously stated, each hidden unit is a linear combination of some or all of the predictor variables. However, this linear combinationis typically transformed by a nonlinear function $g(\\cdot)$, such as the logistic (i.e., sigmoidal) function: $$h_k(\\pmb{x}) = g \\left( \\beta_{0k} + \\sum_{j=1}^P x_j\\beta_{jk} \\right), \\text{where} \\\\ g(u) = {1\\over 1+e^{-u}}.$$ The $\\beta$ coefficients are similar to regression coefficients; coefficient $\\beta_{jk}$ is the effect of the $j$th predictor on the $k$th hidden unit. A neural network model usually involves multiple hidden units to model the outcome. Note that, unlike the linear combinations in PLS, there are no constraints that help define these linear combinations. Because of this, there is little likelihood that the coefficients in each unit represent some coherent piece of information.\n",
      "\n",
      "Once the number of hidden units is defined, each unit must be related to the outcome. Another linear combination connects the hidden units to the outcome: $$f(\\pmb{x}) = \\gamma_0 + \\sum_{k=1}^H \\gamma_kh_k.$$ For this type of network model and $P$ predictors, there are a total of $H(P+1)+H+1$ total parameters being estimated, which quickly becomes large as $P$ increases."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Treating this model as a nonlinear regression model, the parameters are usually optimized to minimize the sum of the squared residuals. The parameters are usually initialized to random values and then specialized algorithm for solving the equations are used. The back-propagation algorithm is a highly efficient methodology that works with derivatives to find the optimal parameters. However, it is common that a solution to this equation is not a *global* solution, meaning that we cannot guarantee that the resulting set of parameters are uniformly better than any other set.\n",
      "\n",
      "Also, neural networks have a tendency to over-fit the relationship between the predictors and the response due to the large number of regression coefficients. To combat this issue, several different approaches have been proposed. First, the iterative algorithms for solving for the regression equations can be prematurely halted. This approach is referred to as *early stopping* and would stop the optimization procedure when some estimate of the error rate starts to increase (instead of some numerical tolerance to indicate that the parameter estiamtes or error rate are stable). However, there are obvious issues with this procedure. First, how do we estimate the model error? The apparent error rate can be highly optimistic and further splitting of the training set can be problematic. Also, since the measured error rate has some amount of uncertainty associated with it, how can we tell if it is truely increasing?\n",
      "\n",
      "Another approach to moderating over-fitting is to use *weight decay*, a penalization method to *regularize* the model similar to ridge regression. Here, we add a penalty for large regression coefficients so that any large value must have a significant effect on the model errors to be tolerated. Formally, the optimization produced would try to minimize a alternative version of the sum of the squared errors: $$\\sum_{i=1}^n(y_i - f_i(x))^2 + \\lambda\\sum_{k=1}^H\\sum_{j=0}^P \\beta_{jk}^2 + \\lambda\\sum_{k=0}^H \\gamma_k^2$$ for a given value of $\\lambda$. As the regularization value increases, the fitted model becomes more smooth and less likely to over-fit the training set. The value of this parameter must be specified and, along with the number of hidden units, is a tuning parameter for the model. Reasonable values of $\\lambda$ range between $0$ and $0.1$. Also note that since the regression coefficents are being summed, they should be on the same scale; hence the predictors should be centered and scaled prior to modeling."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The structure of the model described here is the simplest neural network architecture: a single-layer feed-forward network. There are many other kinds, such as models where there are more than one layer of hidden units (i.e., there is a layer of hidden units that models the other hidden units). Also, other model architectures have loops going both directions between layers. There have also been several Bayesian approaches to neural networks. The Bayesian framework automatically incorporates regularization and automatic feature selection. This approach to neural networks is very powerful, but the computational aspects of the model become even more formidable. A model very similar to neural networks is self-organizing maps (SMO). This model can be used as an unsupervised, exploratory technique or in a supervised fashion for prediction."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given the challenge of estimating a large number of parameters, the fitted model finds parameter estimates that are locally optimal; that is, the algorithm converges, but the resulting parameter estimates are unlikely to be the globally optimal estimates. As an alternative, several models can be created using dfferent starting values and averaging the results of these model to produce a more stable prediction.\n",
      "\n",
      "These models are often adversely affected by high correlation maong the predictor variables (since they use gradients to optimize the model parameters). Two approach for mitigating this issue is to pre-filer the predictors to remove the predictors that are associated with high correlations. Alternatively a feature extraction technique, such as principal component analysis, can be used prior to modeling to eliminate correlations. One positive side effect of both these approaches is that fewer model terms need to be optimized, thus improving computation time."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# neural networks"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "7.2 Multivariate Adaptive Regression Splines"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Like neural networks and partial least squares, MARS uses surrogate features instead of the original predictors. However, whereas PLS and neural networks are based on linear combinations of the predictors, MARS creates two contrasted versions of a predictor to enter the model. Also, the surrogate features in MARS are usually a function of only one or two predictors at a time. The nature of the MARS features breaks the predictor into two groups and models linear relationships between the predictor and the outcome in each group. Specifically, given a cut point for a predictor, two new features are \"hinge\" or \"hockey stick\" functions of the original. The \"left-hand\" feature has values of zero greater than the cut point, while the second feature is zero less than the cut point. The new features are added to a basic linear regression model to estimate the slopes and intercepts. In effect, this scheme creates a *piecewise linear model* where each new feature models an isolated portion of the original data.\n",
      "\n",
      "How was the cut point determined? Each data point for each predictor is evaluated as a candidate cut point by creating a linear regression model with the candidate features, and the corresponding model error is calcuated. The predictor/cut point combination that achieves the smallest error is then used for the model. The nature of the predictor transformation makes such a large number of linear regression computationally feasible.\n",
      "\n",
      "After the initial model is created with the first two features, the model conducts another exhaustive search to find the next set of features that, given the inital set, yield the best model fit. This process continues until a stopping point is reached."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# training (transformed)\n",
      "trainX = pd.read_csv(\"../datasets/solubility/solTrainXtrans.csv\").drop(\"Unnamed: 0\", axis=1)\n",
      "trainY = pd.read_csv(\"../datasets/solubility/solTrainY.csv\").drop(\"Unnamed: 0\", axis=1)\n",
      "\n",
      "# test (transformed)\n",
      "testX = pd.read_csv(\"../datasets/solubility/solTestXtrans.csv\").drop(\"Unnamed: 0\", axis=1)\n",
      "testY = pd.read_csv(\"../datasets/solubility/solTestY.csv\").drop(\"Unnamed: 0\", axis=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pyearth import Earth\n",
      "\n",
      "mars = Earth()\n",
      "mars.fit(trainX.values, trainY.values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "Earth(penalty=None, min_search_points=None, endspan_alpha=None, check_every=None, max_terms=None, max_degree=None, minspan_alpha=None, thresh=None, minspan=None, endspan=None, allow_linear=None)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A few steps of the feature geneartion phase (prior to pruning)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print mars.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Earth Model\n",
        "--------------------------------------\n",
        "Basis Function   Pruned  Coefficient  \n",
        "--------------------------------------\n",
        "(Intercept)      No      -5.89861     \n",
        "h(x208-5.9269)   Yes     None         \n",
        "h(5.9269-x208)   Yes     None         \n",
        "h(x226-1.9554)   No      0.25068      \n",
        "h(1.9554-x226)   Yes     None         \n",
        "h(x210-3.04452)  Yes     None         \n",
        "h(3.04452-x210)  Yes     None         \n",
        "x136             No      0.691555     \n",
        "h(x220-1.38629)  No      2.48183      \n",
        "h(1.38629-x220)  No      -0.292833    \n",
        "h(x212-2.57858)  Yes     None         \n",
        "h(2.57858-x212)  No      -1.15829     \n",
        "x134             No      0.444174     \n",
        "x58              No      -0.55975     \n",
        "h(x208-5.7346)   No      -2.08834     \n",
        "h(5.7346-x208)   No      0.976211     \n",
        "h(x213-5.07858)  No      -1.22859     \n",
        "h(5.07858-x213)  No      0.140037     \n",
        "x171             No      -0.469389    \n",
        "x173             No      -0.303957    \n",
        "x98              No      0.376159     \n",
        "h(x227-4.66178)  No      -0.139951    \n",
        "h(4.66178-x227)  No      -0.204938    \n",
        "x175             No      0.548689     \n",
        "x203             No      -0.357652    \n",
        "x163             Yes     None         \n",
        "h(x217-5.62625)  Yes     None         \n",
        "h(5.62625-x217)  No      -1.3125      \n",
        "h(x209-3.93183)  Yes     None         \n",
        "h(3.93183-x209)  No      5.66787      \n",
        "h(x218-4.97559)  No      -1.85259     \n",
        "h(4.97559-x218)  Yes     None         \n",
        "h(x214-1.79176)  No      -1.17637     \n",
        "h(1.79176-x214)  Yes     None         \n",
        "x110             No      -0.440564    \n",
        "x74              No      0.450923     \n",
        "x153             No      -0.525719    \n",
        "x201             No      0.240704     \n",
        "x52              No      0.330042     \n",
        "x64              Yes     None         \n",
        "--------------------------------------\n",
        "MSE: 0.3539, GCV: 0.4514, RSQ: 0.9154, GRSQ: 0.8923\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first generated feature is Molecular Weight with a cut point of 5.9269."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "trainX.columns[208]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "'MolWeight'"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mars = Earth()\n",
      "mars.fit(trainX['MolWeight'].values, trainY.values)\n",
      "c_trainX = np.arange(np.min(trainX['MolWeight'].values), np.max(trainX['MolWeight'].values), 0.1)\n",
      "mars_predict = mars.predict(c_trainX)\n",
      "\n",
      "plt.scatter(trainX['MolWeight'].values, trainY.values, alpha=0.5)\n",
      "plt.plot(c_trainX, mars_predict, 'r', linewidth=2)\n",
      "plt.xlabel('Molecular Weight (transformed)')\n",
      "plt.ylabel('Log Solubility')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.text.Text at 0x10e23e590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mz4Z58zAOGdLkF+m+fUe5ejUJP79EAK5eLSUjY7lT7Q8P78/Zs1uoqkqkquo0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\nIpKGlKSJiIiIpCElaSIiIiJp6P8Hawne7UH6BWUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f3a5910>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are several advantages to using MARS. First, the model automatically conducts feature selection; the model equation is independent of predictor variables that are not involved with any of the final model features. The second advantage is interpretability. Each hinge feature is responsible for modeling a specific region in the predictor space using a piecewise linear model. When the MARS model is additive, the contribution of each predictor can be isolated without the need to consider the others. This can be used to provide clear interpretation of how each predictor relates to the outcome. Finally, the MARS model requires very little pre-processing of the data; data transformation and the filtering of predictors are not needed. Correlated predictors do not drastically affect model performance, but they can complicate model interpretation.\n",
      "\n",
      "Another method to help understand the nature of how the predictors affect the model is to quantify their importance to the model. For MARS, one technique for doing this is to track the reduction in the root mean squared error (as measured using the GCV statistic) that occurs when adding a particular feature to the model. This reduction is attributed to the original predictors associated with the feature. These improvements in the model can be aggregated for each predictor as a relative measure of the impact on the model."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "7.3 Support Vector Machines"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "SVMs are a class of powerful, highly flexible modeling techniques. The theory behind SVMs was originally developed in the context of classification models. For regression, it is motivated in the framework of *robust regression* where we seek to minimize the effect of outliers on the regression equations. Also, there are several flavors of support vector regression and we focus on one particular technique called $\\epsilon$-insentitive regression.\n",
      "\n",
      "Recall that linear regression seeks to find parameter estimates that minimize SSE. One drawback of minimizing SSE is that the parameter estimates can be influenced by just one observation that falls far from the overall trend in the data. When data may contain influential observations, an alternative minimization metric that is less sensitive, such as the Huber function, can be used to find the best parameter estimates. This function uses the squared residuals when they are \"small\" and uses the absolute residuals when the residuals are large.\n",
      "\n",
      "SVMs for regression use a function similar to the Huber function, with an important difference. Given a threshold set by the user (denoted as $\\epsilon$), data points with residuals within the threshold do not contribute to the regression fit while data points with an absolute difference greater than the threshold contribute a linear-scale amount. There are several consequences to this approach. First, since the squared residuals are not used, large outliers have a limited effect on the regression equation. Second, samples that the model fits well (i.e., the residuals are small) have no effect on the regression equation. In fact, if the threshold is set to a relatively large value, then the outliers are the only points that define the regression line. This is somewhat counterintuitive: the poorly predicted points define the line. However, this approach has been shown to be very effective in defining the mode."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The SVM regression coefficients minimize $$Cost \\times \\sum_{i=1}^n L_{\\epsilon} (y_i - \\hat{y}_i) + \\sum_{j=0}^P \\beta_j^2,$$ where $L_{\\epsilon} (\\cdot)$ is the $\\epsilon$-insensitive function. The $Cost$ parameter is the cost penalty that is set by the user, which penalizes large residuals. The penalty here is written as the reverse of ridge regression or weight decay in neural networks since it is attached to residuals and not the parameters."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall that the simple linear regression model predicted new samples using linear combinations of the data and parameters. For a new sample, $u$, the prediction equation is $$\\hat{y} = \\beta_0 + \\sum_{j=1}^P \\beta_j u_j$$ The linear support vector machine prediction function is very similar. The parameter estimates can be written as functions of a set of unknown parameters $(\\alpha_i)$ and the training set data points so that $$\\hat{y} = \\beta_0 \\sum_{j=1}^P \\beta_j u_j = \\beta_0 + \\sum_{j=1}^P \\sum_{i = 1}^n \\alpha_i x_{ij} u_j = \\beta_0 + \\sum_{i = 1}^n \\alpha_i (\\sum_{j=1}^P x_{ij} u_j).$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are several aspects of this equation worth pointing out. First, there are as many $\\alpha$ parameters as there are data points. From the standpoint of classical regression modeling, this model would be considered $over-parameterized$; typically, it is better to estimate fewer parameters than data points. However, the use of the cost value effectively regularizes the model to help alleviate this problem.\n",
      "\n",
      "Second, the individual training set data points (i.e., the $x_{ij}$) are required for new predictors. When the training set is large, this makes the prediction equation less compact than other techniques. However, for some percentage of the training set samples, the $\\alpha_i$ parameters will be exactly zero, indicating that they have no impact on the prediction equation. The data points associated with an $\\alpha_i$ parameter of zero are the training set samples that are within $\\pm \\epsilon$ of the regression line. As a consequence, only a subset of the training set data points, where $\\alpha \\neq 0$, are needed for prediction. Since the regression line is determined using these samples, they are called the support vectors as they support the regression line."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(3)\n",
      "\n",
      "# toy example\n",
      "x_sim = np.random.uniform(-2.5, 2.5, 100)\n",
      "y_sim = 1 + 4*x_sim + np.random.normal(0, 1, 100)\n",
      "\n",
      "# arbitrarily set outlier\n",
      "xmin_idx = np.argmin(x_sim)\n",
      "y_sim[xmin_idx] = 10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simple linear regression\n",
      "from sklearn.linear_model import LinearRegression\n",
      "\n",
      "ols = LinearRegression()\n",
      "ols.fit(x_sim[:, np.newaxis], y_sim)\n",
      "ols_pred = ols.predict(x_sim[:, np.newaxis])\n",
      "\n",
      "print \"y = {0} + {1} x\".format(ols.intercept_, ols.coef_[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "y = 1.11602295026 + 3.6516500913 x\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# support vectors machine regression\n",
      "from sklearn.svm import SVR\n",
      "\n",
      "eps = 0.1\n",
      "\n",
      "svr = SVR('linear', epsilon = eps)\n",
      "svr.fit(x_sim[:, np.newaxis], y_sim)\n",
      "svr_pred = svr.predict(x_sim[:, np.newaxis])\n",
      "\n",
      "print \"y = {0} + {1} x\".format(svr.intercept_[0], -svr.coef_[0][0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "y = 0.981450075744 + 3.87493669291 x\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(x_sim, y_sim, alpha=0.5, s=26)\n",
      "plt_ols, = plt.plot(x_sim, ols_pred, 'g')\n",
      "plt_svr, = plt.plot(x_sim, svr_pred, color='r')\n",
      "\n",
      "plt.xlabel(\"Predictor\")\n",
      "plt.ylabel(\"Outcome\")\n",
      "plt.ylim(-11, 11)\n",
      "plt.legend([plt_ols, plt_svr], ['Least Squares', 'SVM'], loc = 4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.legend.Legend at 0x112789e50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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88cWzsFqH4Zhj8jF+/HhDmxOSuUmAKJcwKSND+K8q+Rhz+dIV85QdxaQo+N5m\n3XUCKwx2ux2XX16Cs88+GS7XmRg//jjDS4+JJJh8n8vHmJsXkzIioiTpqfWDzFqqb/d9G17Q/9ln\nfWoIa7VaMXnyeGzc+FLYz1NUdFzc12TkWZ9EJsGkjAxhXxv5GHP5khHzvrR+SGYyZ61SUJA/LPSA\nEMBx8ZOo3uh/ns2b78bQof+Bx9OWtGVJvs/lY8zNi7sviYiSKNC9v6xsKgDjuw2N7MzslaIgbC4q\nCRui9D9PXd2/sHw5gpsYYp1IEEgw3W53xGYHubOFRJmIuy+JiEykLy0xtuzZgpFDRoU/mMbzKwNn\nfXo8yd9JSpSJ2KeMiCgDJTqbpMxXIObpHti9Gxg8OKljSlRfZwuJch1rysgQ1iDIx5jLl2kxP/iW\niIRMiJQlZH2pe4vV+iNSpsU8GzDm5sWZMiKiDPPl9i9x9IhjsE3/oISSjqTUvRFRXKwpIyKSIFnH\nJ0UtVwJSEjI9nl9JlBjWlBERmUAyj0+KSsh8vugDxiVgMkaUGqwpI0NYgyAfYy5fKmKejOOTPtj8\nAb5/fYz6sTQkZMnG97l8jLl5MSkjIkqRZHS3V+YrOGX0qXjvId2DLN8gykpMysgQnpUmH2MuX6yY\na5qWtuOBopYrJ0/OuoSM73P5GHPzYk0ZEVEMyagF62t3+9Z1rZj0+KTo5UoiymqcKSNDWIMgH2Mu\nnz7myagFAxI/C1OZr6DuxtxJyPg+l48xNy/OlBERRQjVgoWOFPLXgtWgrGxqQrsPE+lub4Z2F0SU\nPpwpI0NYgyAfYy5fKmPeU3f7Z9uejU7IFi3qNSFLZ71bsvB9Lh9jbl6cKSMiitDXWrC+UOb721ok\nslyZzN5nRGQenCkjQ1iDIB9jLp8+5onWgvWFMl/BsjrjCVlgZixZ9W5mwPe5fIy5eXGmjIgyjoxj\nfhKpBUvUff++D79p/o3h+jH9zJjP58Patetx2mn39rvejYjMhWdfElHGyIZlu5jLlcuXA+edF/c1\ntbWNaG72wel0wefT8OyzN6Gw8AZMnDgRAOD1dqKjowZLlsxiUkZkQjz7koiyTmDZzumsBAC43W4A\nTSgvL0nvwAzqS/2YfieoxWLH559/Ca/3cLS0PApA4Pjjj8GmTctTUu9GRHKxpowMYQ2CfIx5uGQc\nWdSbVMW88qXK4O7K/vQfW7nyS6xaJTBq1EwMG7YDbW1/wbvv/m9K6t1k4ftcPsbcvDhTRkTUi/7U\nsMWcHQPUfJsPAAAgAElEQVQMJ2SBnaAvvvgiVq8+EIMGnY7vvnsF3/teKY455kfo6LiXtWREWYI1\nZUSUMerqGuF2+yLaVFhStnzZ3xq2mAnZqlXA2LEJj+PZZ1/AHXfU4oADxmPs2JNxwglT4PNprCUj\nygCsKSOirONfomuCx1MDAHC5ClO6bNfXGrYZjTPw+EeP4wAv0Hmn7ok+/mPSbrfjiit+AkDA7fbh\niCMugM+npax3GhGlB2fKyJDW1lZ2gZaMMY8vVS0x9DHXNA0VFdVwOEJHLRnZ5djf5cqeqKqKhoYm\neDyZu/s0Et/n8jHm8nGmjIiylllnhlKZkAGp7Z1GROnHmTIiojiM1rCd9+R5eGXNKwAiErLOTuCA\nAySNlojMyuhMGZMyIqI4jCwXBmbHxm4HVt2vezF/RxFRNyZllFSsQZCPMZcvXszj1bClerkyF/B9\nLh9jLh9ryoiIkiQyGTv+L8fj868/B8CEjIiShzNlREQJCMyOAb1355dxcDoRmR9nyoiIkiyQkF3y\nGdD4D90TEQlZNhycTkTy8exLMoRnpcnHmMsXL+YD7xwYVj/WU0IGhJrOOhyVcDgq4Xb70NDQlPwB\nZwG+z+VjzM2LSRkRUQ+U+Qo6uzoBRCxXulxxlyxTfXA6EWUnLl+SIdypIx9jLl9kzBOpH6O+4ftc\nPsbcvDhTRkQUQZmvBBOyvz2fWEJmtVpRXFyI9nY3vN5OeL2daG93o7iYZ1QSUc+YlJEhrEGQjzH3\nLwXKXPJrbW2Nmh2r+I/uBoMzZKWlU+ByWdDRUYOOjhq4XJaUHpyeyfg+l48xNy8uXxKR6aRr9+Kk\nxyYBR/o/D5sdu/tu4OabDX8dnlFJRH3BPmVEZDq1tY1obu79zMneGO0Tpp8dA1g/RkTJxT5lRJSR\nQrsXK2Gz5QNA9+7FGpSVTTU065TITJs+Ieu4Gzh4r+5JJmREJFGvNWWKogxSFGWuoigPdV8frSjK\nxakfGpkJaxDkY8z7zmifsMj6sTYmZNLxfS4fY25eRgr9HwWgAjiz+3oTgDtTNiIiymn93b1opE+Y\nfnclELFc+dZbKUvIZG9cIKLMYmT5cqwQokxRlMsBQAjxnaL0uixKWYZ9beTL5Zj7dyo2weOpAQC4\nXIVJ272oT8YUH+BbEHquKEXJGI9dii+X3+fpwpibV6+F/oqivA1gMoC3hRATFUUZC6BOCHGajAHG\nGRML/YlyQF8P9K6ra4TbHb1RYPp/pwXvCZsdA1K6XJmsjQtElJmMFvobWb6cB6AZwGGKotQC8AC4\ntX/Do0zDGgT5GHN/MtaXdhKRfcKeHFtqKCFLRcx57FLP+D6XjzE3r16XL4UQyxVF+QDAGd0P/VoI\n8XVqh0VE1Hf6PmEDFob/mgtLyLZuBRwOqWMjIorHUJ8yRVFOBjAG/iROAIAQ4p8pHVnP4+HyJVGO\nM7K0qa8f892wDcrBB4eelPg7JN5yKpcviXKD0eVLIzVljwIYD6ANgC/wuBDimv4Osq+YlBHlLiNF\n8z02gwWkt7tQVRUNDU3weFjoT5SLkpmUrQRQaKYsiEmZfK2trdyxIxljHltvRfP9SchSHfO+blzI\nZnyfy8eYy5fMQv/3AJzQ/yEREfVPT0XzXV1d4b3HqkR4QtbVlfaGsH3duEBEucHITFkRgOcAbAGw\nv/thIYQ4KbVD63FMnCkjykGapqGiohoOR+gIJq+3E4vsA8PuExe9B3z/+7oH+PuCiNInmcuXqwH8\nL4BPEV5Ttq6fY+wzJmVEuSuyaD4qIZsX8QLd7wouHxJROiRz+bJDCPGcEGKNEGJd4KP/Q6RMwr42\n8jHmsQV6kG3p+ENYQha1XDl8eDAhU1UVtbWNqKioRkVFNerqGqGqatTXZszlY8zlY8zNy8gxSx92\nN419Hv4zMAH/8mXaWmIQUe6y2+3+RrCHhR4TVQLQH/8WMZMeOKDc6awEALjdbgBNbElBRKZiZPny\nse5Pw25kSwwiSofI3ZXasD/B8pvfhB6I+N2gaRquv34RHI7/RV7eYAD+OrSOjhosWTKLS5lElHJG\nly+NdPSfkZQRJUBRlAsB/BGAFcDDQoi7ZI+BiMyl09uJgYtCy5VPH70M06+YBiB+QqaqKp555gW8\n9dZHOOCAezB27Mk44YTkHGxORJRsvdaUKYriVBRlmaIo27o/GhRFOay31/WVoihWAH8GcCH8rTjK\nFUU5PlXfj4xhDYJ8jHmIMl+Jk5D5vT52Eupql0W9rr6+CcuXA8cdNwea9mP8978qPv54Gdrb3Sgu\nLoyaJWPM5WPM5WPMzctIof+j8LfEGN398Xz3Y6lyGoBV3RsKvACWArgkhd+PiEwscrmya05XWEI2\nr0rgpctejDrgW9/TbPz48TjmmHxYrcPwxRfP4oILBEpLOWNGROZiJCk7WAjxqBDC2/3xGIBUnuB7\nKIB23fWG7scojdj9Wb5cj/mOzh3RzWBbzoV1QKjqYl6VsdpSq9WK8eOPg8t1Js4++2RcfnlJzCOO\ncj3m6cCYy8eYm5eRpGy7oihXKYpiVRRlgKIoVwL4OoVjYgU/UY5T5is46O6DgtfB3ZWvvRZ87GdX\nNcDr7YTX2xlzOdJqtaK4uBDt7e7gfRs3voTJk8ezuJ+ITMlIS4xrAdwPoKb7+m0Aqdx5uRGAU3ft\nhH+2LMyMGTMwZswYAEBBQQEmTJgQzP4D6+W8Tt71ihUrcNNNN5lmPLlwHXjMLOORda3M6J4dO9L/\nPy3ntqBVUeB/Fmi95RZ4f/QjuL7+Dh5PDTZtWoNTTjkSpaW3RH290tIpWLnybnzwwYsYPfoouFyF\nGDFiEFp1Z//p74+MvRnike3Xf/zjH/n7W/I1f5/L+f3d2tqKdevWIRG9tsSQTVGUAQC+ADAZwCYA\n7wIoF0J8pruHLTEka9X9ESM5ci3mG3ZtgPPe0L/HRJWAqqqw5+UFH6urXYbS0inBpUejHfqN3pdr\nMTcDxlw+xly+ZB6z9ASAXwshvu2+HgbgHiHEtUkZaezv6UKoJcYjQojFEc8zKSPKIpHF/FHNYAHc\nPnsv2tvdcLksbPpKRBklmUnZCiHEhN4ek4lJGVH2MJKQBQr62fSViDJRMs++VBRFOUh3cRD8M1iU\nQ/Tr5CRHtsf8s22fRe+ujEjIFky7AbfP3ittTNkeczNizOVjzM3LSKH/PQDeURTlGQAKgEsB3JnS\nURFRVos5O7Z/P3DAAboHBY6ua4Tb7YbT6QKA7uXL6KavRETZwFChv6IohQCK4W9X4RFCrEz1wHoZ\nD5cviTKUkeXKwHFJqqqioaEJHk8bAKC4uDCs0J+IKBMks6bsSSHEVb09JhOTMiL5jO5gjOft9rdx\n1t/PCl6LQOPXOAlZMr83EVE6JbOm7MSILzwAwKl9HRhlJtYgyGeWmKuqitraRlRUVKOiohp1dY1Q\nVTWhr6HMV3pPyHbujJmQAf5kTEZCZpaY5xLGXD7G3LziJmWKosxWFGU3gPGKouwOfADogP8sTCLK\nAfX1TWhu9sHhqITDUQm324eGhibDr9cvVw6xD/EnZGvWhCdkQgBDh0a9VtO0sPMsiYiymZHly2oh\nxCxJ4zGEy5dEcmiahoqKajgclbDZ8gEYb0vx/BfP48dLfxy8TmS5UlVV1Nc3oaWFtWRElPmMLl8a\n2X3pVhTlh5EPCiFe79PIiCjrxSzmBwwlZEBods7prAQAuN1uAE1sGktEWc1ITdnNuo+5AJ4HMC+F\nYyITYg2CfGaIeaxDvWMd/q2nT8hOPuTk2AmZzxc3IdM0DS0tbXA6XbDZ8mGz5cPpdMHjaUv5UqYZ\nYp5rGHP5GHPz6nWmTAhxsf5aURQngD+lbERElBbxdjiWlk4B0ASPpwYA4HIVdj8W7u8f/h0/f+7n\nwetgMvaPfwCXXx66kaUHREQxJXwguaIoCoCVQojjUzMkQ2NgTRlRkhit3+qpLUV/lysj1dU1wu32\nRTSN5ZmXRJSZktmn7H7dpQXABABrhRBX9m+IfcekjCh5amsbu+u3+pYA6ROyS469BI2XN3Y/ofv9\nM2AA4PUaHhObxhJRNklmUvY/CC1zfgtgjRDirf4Pse+YlMnX2tqKoqKidA8jp8iIeazdlfv370FH\nx7148MHZPe6uXPTGItzuuT14HZwdA6LbXfRjfIC8prF8n8vHmMvHmMvX792XiqLY4D/j8loA67sf\nPhzAo4qivCuEMP7PXiIyPU1TsXJlE1av/gj79n2CpUv/hUsvvTjm7FTc5cprrgEee0z3RP/+8cQO\n/kSUS+LOlCmK8kcAgwH8rxBid/djQ+E/oHyvEOI30kYZPTbOlBElSaB+a+dOL9asUQAcjbFjFQwd\nuibmMqY+IbvxtBtxn+u+7if6Vj9GRJTtknHM0sUArg8kZAAghNgFoALARf0fIhGZQWnpFFxwgcAX\nXzwLq3UYjjkmH+PHj49qQzHzxZlhCZmoErETsl/8ggkZEVEf9JSU+YQQvsgHhRAagKjHKbuxr418\nsmJut9tx+eUlOPvsk+FynYnx44+LWjZU5iv42/t/C173WD/24IOpHnLK8H0uH2MuH2NuXj0lZZ8p\ninJ15IOKolwF4PPUDYmIZLNarZg8eTw2bnwpqknsgIWh0tPqydXh7S6SVNBPREQ915QdBuCfADoB\n/Kf74VMBDAQwTQixQcoIY4+NNWVESRbZhuLj417Eu3veCT4fd3YMMFVCJnvHJhFRb5LSEqO7UWwx\ngEIAAv6msa8mbZR9xKSMKHU0TQubHQOA6zYsDPUKy8sLPVFfD5SWSh5hbDzEnIjMKhmF/hB+rwoh\n7hNC3G+GhIzSgzUI8qUr5vqE7Kytv8ZsdS8cjkq4m7TwhEwI0yRkQOgQc4ej0j9etw8NDU0JfQ2+\nz+VjzOVjzM3LyIHkRJQDzn/y/LDdlddtWIhzh1XDZsvHnYsG4omnfhq62WQz1ek8xJyIKFmYlJEh\n7P4sn8yYK/MVvLzm5eB115yu4OfzIhrFal1dMErTtIxKivg+l48xl48xN6+4Hf2JKDfoZ8de/dmr\nKD6yGIC/Jqt8+sDgc5XT/obvXzoS5QYK6GXXd1mtVhQXF8Ltdkec4VnIgn8iyhicKSNDWIMgX6pj\nfuyfj41qBhtIyLBzJ8qnTws+94vrFuL7l45EaekUQ187GfVdiSotnQKXy4KOjhp0dNTA5bIYHm8A\n3+fyMebyMebmxZkyohwU9+xKIKrdhdbVhSWIbjERr/VEqL4rdMi5v76rBmVlU1M2c2W321FeXoKy\nsqkxx0VEZHZMysgQ1iDIl6qY6xOy/1z/H5wy6hTdk9H9xyJTG7O3nuhPMsb3uXyMuXyMuXkxKSPK\nEfY77PD6vMHrsNkxIDwh278fiJNkBZYmnc5KAIDb7QbQFDy4nPVdRER9w5oyMoQ1CPIlM+bKfCV+\nQvbxx9HHJcVJyIy2nkhGfVc68H0uH2MuH2NuXpwpI8py+uXKL2/8EuMOGqd7MjXHJcWr7+IRSERE\n8fV4zJJZ8Zglot71WMwP9Dkhq6trhNvti1iatASXL2Mxex0aEVEqJeXsS7NiUkYULnIGKqGELMH/\nliIPLjeSYNXWNnbXoRlP5IiIsgWTMkqq1tZW7tiRzEjMY81ATf9vqL/Ylt9uwSGDDwm94OGHgV/8\nInTdj/+OjC5FapqGiopqOByhFhlebyc6OmqwZMksUy1l8n0uH2MuH2Mun9GkjDVlRBlMvxNykX0g\nHv5v6LlkLVfGY6ZkiogoG3CmjMjkemrSGpiBWmQfGPZc15yu8Pv1Cdl55wHLl6dsvLH0pQ6NiChb\ncKaMKMMZLY7XJ2SV6mbs6ngk/Av1o34sWfztMJrg8dQAAFyuwoxokUFEJBNnysgQ1iDIN2fOQqxf\nf0Lc2aXIYv7Z6t7we666CnjqqdANJvhvxuwtMfg+l48xl48xl8/oTBmbxxKZkKZp+PDDtXGbtEYm\nZNdtWBjepFVRTJeQAf5kzKwJGRFRunGmjMiEetqx+PBhc4L3dd7eiQMGHBA+A6Vfrvzb34CKCsPf\nM/g1iIgoadgSgyjDRRbHRxbzR+2uBPpUP8bGrkREqcXlS0oqs5+Vpmla2NmL2WDEiEHB8yN7TciG\nDu1zQX+grYbDUQmHoxJutw8NDU39GXrGMvv7PBsx5vIx5ubF3ZeU0bJ5lsdms6G8vCSsGWzX3C5Y\nLRHLi/3oPxY6YDy0TOqvXatBWdlULmUSEUnEmTIyxKw7dbJ5lmfSa5PCCvpFleg5IfvgA9MU9Gcq\ns77PsxljLh9jbl5MyihjhWZ5Yu9QzGS9nl2padHLlRMnJvx9rFYriosL0d7uhtfbCa+3E+3tbhQX\nF3KWjIhIMiZlZAhrEOQQQoQSsrWA7/e+2MclDRigf1G/vmdp6ZRg7VpYW40cxPe5fIy5fIy5ebGm\njDJWYJbH7XZHNFjNzFmeyNmxlhktUCLrxZJ8fiUA2O12lJeXoKxsKgC2xCAiShe2xKCMpqoqGhqa\n4PFkdqF/r8uVQHhCtmMHUFCQ4lEREVEysE8Z5RSzND5NdBw+4YN1Qeje6zYsjE4sOzqAQw4JvSjB\n975ZYkNElKuYlFFS8ay0nvWlNUessyuB0BmXo0YVoGjSpPAXJfC+z+Z2IanC97l8jLl8jLl8bB5L\nJFGirTkiE7JZ+/bAas0L20GKfiRkfRkTERGlF2fKiPqpp3MqlyyZFbZs2OXrgu0OW/B67y17MWXK\nr7FjRxksljwceaQDRx99GKrvGhL6Bj5fdIF/EsdERESpZXSmjLsviSSJVcxfW9uIrq6DoWk7MHDg\nhchf8U9U//Ma3U38xwcRUa7g8iUZwr428RlpwBorIQs0vz3rrFtxzDF2vP3OgXhqTSgha21pSemY\nKBrf5/Ix5vIx5ubFmTKiJPA3W22Cx1MDAHC5/EX1+7r2If/O/OB9sVpdWK12NPwzdL7l1qHDMeKb\nrcAbb6RkTEREZE6sKSNKIn37CSO9x+rqGlE+PZSQ/eyqBrhcFpSXl6RkTEREJB93XxL1g6ZpfTo/\n02q1RiVkIwaOiN0M9v77wxKyX1y3MCVHHAXGRERE5saZMjIkV/ra9Le31/bd2zGiZkTw+qlxDfjJ\nT1zIz88PvzFiN6XW1QUgfDYrV2JuJoy5fIy5fIy5fJwpI+qD/vT2UuYrYQnZJR9+iKqqjzFlSgXq\n6hqhqmr3jaH/Lp+fWIS62mXQNI2zWUREOY4zZUTd+tPbS79ceZjvTJz26SNYtUpg0KBDsXfvvTjx\nxBNw0UW2sOXK22eHd/BPZh0ZERGZB2fKiCT4pvObsITsug0LcaW6HGvXdmDo0HGwWm2wWAbgVyuX\nRyVkNlt+WAf/vtSwERFR9mBSRobkQl+bRHt7KfMVDL97ePBaVIng632+/dC0Tuza5cYHH87BGR8+\nHLzv2GN+gra2L3pNwnIh5mbDmMvHmMvHmJsX+5QR6fTW2yuQSA1YGPpP5+qTr8ZjJY+FvX7TpmfQ\n3v4PfLnqkeB9Vxw2CW3Dz8W+HV/h7bf/Ap/veowff2L38iWbuhIR5TrWlBHFENnbK7Ar84XX3kHd\n6LuD98VsdQGgs7MT+QMHBq9POP58WCwzMGxYCXw+DV999SB8vn9hypQfYfLk8Qnt8CQioszCsy+J\n+iFy1qq+vglXfDkNGB16rPaYZbFffOaZyH/nneBl59698E28CgUFF8FqzYfVChx++HXYvv0t3H//\n76LbZRARUU5iTRkZkss1CJqm+ROybj8Qv8VsdW/s4nxFAXQJGYSA3W7H6NHDsHv3amiaF5rmxe7d\nq3HooQf1ODuWyzFPF8ZcPsZcPsbcvDhTRtSD1d+sxrj7xwWvq7qXzb3ojL5Z3xB282Zg5EgA/lm3\na645Hw8++Bp27/4aAFBQ0IZrrjmfdWRERBTEmjKiOCLPrrxqdQOcTheAiN5iqgrk5YVujPHeVFUV\nDQ1NePXVTwCAdWRERDnEaE0ZkzKiGPQJ2aLiRfjt6b9FQ0MTPJ6I45f0yRgQMyHT4+HgRES5h0kZ\nJVUmnpXWlwRo5baVKPxrYfA6cndl2NfUL1daLECSm79mYswzHWMuH2MuH2MuH3dfUs6Kdah4SckF\nsNvtho9KAmK3uwi+Xp+QqSpgsyU8Ts6aERGRHmfKKOvU1jaiudkHp9MFTdPw5psPw2b7EOPGHRNa\ndoyo5dInZD/85ieoOOOq2DVfW7cGC/gB9LpcGUuspJH1ZURE2YtnX1JO0jQNLS1tcDpdsNny8eWX\nG7Bz57nYseMojBjxG7jdPjQ0NAXv/2TrJ2EJ2Wx1L84e/FTUfQD8s2P9TMgAf8+z5mYfHI5KOByV\nsb8XERHlHCZlZEgm9rXx+XxYu7YDQ4aMhcUyIOrwb2W+gpOWnBS8f9a+PfEPCdcvV154YZ8Tssik\nsacDyTMx5pmOMZePMZePMTcvJmWUVSIPFff59mP37mYceWQhLJZQ7Zb+7MpbR/0ex9aVwu1+G598\n8nnshrABQgBud6p/DCIiykGsKaOsE+gJ5vG0YfXqdfB6D8ZZZ90Kq9WODzr+hObDbgve+/TRy9Dc\n7MPOnV6sWaMAOBpjxyoYOnQNrjh2DS6Yc3PoCyfpPVdX1wi32xe75xkREWUdtsSgnKZpWvCjsfEl\neDxtePiwOWH3dM3pQkVFNRyOSlgsVqxc2YTVqz/Cvn2f4PMvGsK/YBLfb/qkEWChPxFRtmNSRkmV\nKX1t4u1szFscavL69rVv4wfOH0DTtGBSZrP5DwXfv38PFlcPCX3BO+8EZs9OyVh7a4mRKTHPJoy5\nfIy5fIy5fOxTRjkpsLPR6awEAPy99S5M/2/oMHF977FA/Znb7Q4uJYYlZClO/NmfjIiI9DhTRlkj\ncuZrvtJ7M9jAUuL2R+vxq5ef1t3M9xcRESUHZ8oop+kTsmlbf4Vn7/9jzPvsdjvKp08Lf5AJGRER\npQFbYpAhmdDXxmq1YvD3d2GRfWDwsatWN+DScybHXyrUz6a9+aapErJMiHm2YczlY8zlY8zNizNl\nlDUiz668bsNCFLssKC2dEucFEf3HiIiI0og1ZZQV9AnZ5zd8jnHDxgGIU0x/771AZWXomu8lIiJK\nIdaUUU5Y+ulSlDeUB69jFfOHiSj+Z0JGRERmwZoyMsSMNQjKfKXvCdlXX5k+ITNjzLMdYy4fYy4f\nY25enCmjjKRfrtzwvxtw6NBD498sBGCxhF8TERGZDGvKKKM88P4DqHixInjd6+zY9OlAXV3omu8b\nIiKSLGNryhRFmQfgOgDbuh+6TQjRnL4RkVlE7q5k/RgREWUTM9aUCQA1QoiJ3R9MyEwg3TUI+oRs\n283bEkvIdu/OyIQs3THPRYy5fIy5fIy5eZkxKQOAXqf4KDfc9eZdYQmZqBIYMXBE/Bd0dkb3Hxs8\nOIUjJCIiSg7T1ZQpilIF4BoAOwG8D+C3QohvI+5hTVkOSHi50uEAtm0LXfM9QkREJmDqmjJFUV4G\nMDLGU7cD+BuABd3XdwC4B8DPI2+cMWMGxowZAwAoKCjAhAkTUFRUBCA0NcvrzL2e9Ngk4EgAAF74\nwQsYZB+EgJivnzQJRYHnTzsNuOuu0LUJfh5e85rXvOZ17lwHPl+3bh0SYbqZMj1FUcYAeF4IMT7i\ncc6USdba2hp806XS7FdnY/Gbi4PXvc6OAeHLlZoW3v4ig8mKOYUw5vIx5vIx5vKZeqasJ4qijBJC\nbO6+nAbgk3SOh+RJeLly82Zg9GjdC5ioExFR5jLdTJmiKE8AmAD/Lsy1AH4phNgacQ9nyrKMPiHb\nO3sv8m35vbyA7S6IiCgzGJ0pM906jxDiZ0KIk4QQJwshSiITMsout71yW9TuyoQSsrvuYkJGRERZ\nwXRJGZmTvngxWZT5Cqrfqg5eJ1w/JgRwyy29vkTTNGia1pchplUqYk49Y8zlY8zlY8zNy3Q1ZZQb\n9LNj6hwVNqut5xd88AFw6qmhawOzY6qqor6+CS0tbQCA4uJClJZOgd1u79OYiYiIUsl0NWVGsKYs\nc1W8UIEH/vNA8Drh2THA8HJlbW0jmpt9cDpdAID2djdcLgvKy0sMj5eIiKi/MramjLKXMl8JJmRD\n84YmnpA9/7zhhEzTNLS0tMHpdMFmy4fNlg+n0wWPpy0jlzKJiCj7MSkjQ/pbg6Bfruya24Wds3bG\nvC+s/iuyfuzii/s1hkzDug/5GHP5GHP5GHPzYlJGKXVZ/WVRuyutFmvUfaqqora2ERUV1Xjwgiuj\nE7IEWa1WFBcXor3dDa+3E15vJ9rb3SguLoTVGv39iYiI0o01ZZQy+mRs7LCxWPXrVXHvDdR/PfFk\nafgT/fj/WVVVNDQ0wePxF/oXFR2Pn/zEhfz8XlpuEBERJZHRmjImZZQS+oTM93sflMhifR1N01BR\nUY2HHp4TfOxP172HT/ESliyZ1e+Zrc7OTjQ0NOG11z4HwF2YREQkFwv9KamM1iBMb5getVzZU0IW\noE/I5lUJdDgKEx5jPMuWvYTlyxU4HJVwOCrhdvvQ0NCUtK+fKqz7kI8xl48xl48xNy8mZZQ0ynwF\ndZ/WAQCmHjPV2O7Ke++FdUCoXd7ts/cmtf6LuzCJiChTsHksGVJUVBT3OSEELAtC+X1vy5VBunvE\nQQdh6Z8fQYenBgDgcvmXGHNZTzGn1GDM5WPM5WPMzYs1ZdQvrqddaF7VHLw2NDsGhO+u3L4dOOgg\nAAjOXiVzh2RdXSPcbjaRJSKi9GBNGSVVrBoEZb4STMiuOukqYwmZpkW3u+hOyAB/MpbslhWlpVPg\nclnQ0VGDjo4auFyWjJiFY92HfIy5fIy5fIy5eXH5khIWuVxpeHbs6quBJ57Qf6Ekjyw2u92O8vIS\nlJVNBZDcWTgiIqJk4fIlJeT0h0/HuxvfDV73abnyoouAF15I8siIiIjMyejyJWfKyDB9q4sbT7sR\n97nuM/hC3ftQVQGbLckjIyIiynysKaNeaT4Nyozw3mOGErI9e6Lrx5iQGca6D/kYc/kYc/kYc/Ni\nUsdh8fsAABrYSURBVEY9OvexczHgjtCEquHlyhNOAIYMCV1zuZmIiKhHrCmjuPTLlfecfw8qf1Bp\n8IW62bG5c4EFC5I8MiIioszBmjLqsy5fF2x3hJYZDc+OAeEJmc8Xfk1ERERxcfmSwlxUe1HMhKzX\nGoSNG6Prx5iQ9QvrPuRjzOVjzOVjzM2LM2UUpF+uXFq6FJedeJmxF+bnA/v2ha65tExERJQw1pQR\nVE1F3sK84LWoEsaPO9LPhjU2ApdckoohEhERZSyjNWVMynLclf+8Ek9/8nTwev9t+1Ff34SWljYA\nQHGx/2Bwu90e/eLI5coIqTjHkoiIKNPw7EvqlTJfCSZknp95IKoE6uub0Nzsg8NRCYejEm63Dw0N\nTeE1CB980GNCpqoqamsbUVFRjYqKatTVNUJV1R7HomlaMIkjP9Z9yMeYy8eYy8eYmxdrynLQvq59\nyL8zP3gdKObXNA0tLW1wOiths/mfdzpd8HhqcPnlZ/hvjizejzFDFkjsnE5/Cw232w2gCeXlJVH3\nqqpqfGaOiIgoi3GmLMdcsvSSmAlZb4qKisITsg8+iLtk6U/sXLDZ8mGz5Xcndm0xZ8LizcxRd8xJ\nKsZcPsZcPsbcvJiUZTn9sqAyX8FzXzwHAHj72rejEjKr1Yri4kK0t7vh9XbC6+1Ee7sbxcWFsA7Q\nTaoKAUycmJSxJZLAERERZTMmZVlKX9d1XcUdYe0uRJXAD5w/iPm60tIpcLks6OioQUdHDX428gOU\nT5+G1u7n62qX9Vgf1mNix4L/hLDuQz7GXD7GXD7G3LxYU5alAsuCn4xZgxXWvwcf72250m63o7y8\nBGVlU8Nmx3YMdeL2X32B9h7qwwJKS6cAaILHUwMAcLkKux8LF0jg3G43nE4XAKC93Q2XiwkcERHl\nHrbEyEKapqGiohoPHzYn+Ngv1RXQOl7AkiWzjCU8uvqxRb9eC3XYGACA19uJjo4aQ1/HSEsMVVXR\n0NAEj4eF/kRElJ149mUO6/R2hiVkVULAi050GHmxEIAltKr9i+sWwjH4ENh6eEk8RpI//cyc0dcQ\nERFlI9aUZZmFry/EkLuGAAAO33M6Zqt7jdd1ud1hCRmECNaHrVr1Ukrrw6xWKxOyCKz7kI8xl48x\nl48xNy/OlGURfTH/2l+txTvLV/Ra1xV6sW5W9aabgHvvBRCqD3vqqWeQn/9+71+HiIiI+oQ1ZVkg\nXjNYwOBRR/qEbN8+IC8v6hYemURERNQ3PGYpR9R9UhdMyO678L6YvcfiJlKaFn1cUoyErNevQ0RE\nRP3GpCyDKfMVTP/ndADAt7d+ixtPv9H4ix96CIhsCNsD1iDIx5jLx5jLx5jLx5ibF2vKMtBe714M\nWjQoeG30qKQg/ezY008D06cnaWRERETUV6wpyzBPfPQErm68GgDwwMUP4PpTr0/sC+gTMk0L321J\nREREScc+ZVlIv7ty9227Mdg+2PiL9+4FBoVm13pbriQiIiK5OE2SAfaoe6LOrkwoIfvb3/qdkLEG\nQT7GXD7GXD7GXD7G3LyYlJncfzb9B0MW+5vBPnbJY32rH5s5s/uL/YczZERERCbFmjITu3n5zfh/\n7/w/AMD+OfthtyZ4HqSufkzr6gLgb23BnmNERETyGK0pY1JmUjXv1OC3y3+LuT+ciwWTFiT24l27\ngAMPDF7WPr0MLS1t0LQuDByoorMzDxaLNebh30zYiIiIkovNYzPcDd+/Ad/c8k3iCdmDD4YSsttv\nR+3Ty9Dc7IPDUYnt249DU9MIbN/+YzgclXC7fWhoaAIAqKqK2tpGVFRUo6KiGnV1jVBVNfhlWYMg\nH2MuH2MuH2MuH2NuXkzKTCpvQB6G5Q9L7EWKAvzyl/7PN22CNn8+Wlra4HS6YLXa0d6+CiNH/hzr\n1++C1ZoHp9MFj6cNmqahvr4pmLxFJmxERESUekzKskXkcUmjRhl+qaZpweTNZsuHzZYflrABQFFR\nUZIHTL1hzOVjzOVjzOVjzM2LSVmm27kzlJBNnhy2u9Jq9deNtbe7oWkqnM5x2LLlERx++FBo2n60\nt7tRXFzI+jEiIiITYFKWyerrgYIC/+fNzcArr0TdUlo6BS6XBR0dNRg+/HNMmfI1hg9/Dh0dNXC5\nLCgtnRKWvHm9nfB6O6MSNtYgyMeYy8eYy8eYy8eYmxc7+meqk08GPv7Y//l33wEDB8a8zW63o7y8\nBGVlUwHEb4lRWjoFQBM8nhoAgMtV2P0YERERycCWGJkosn4sidgSg4iIKLnYEiMbbdkSSsiuuCIl\n3fmtVisTMiIiojRgUpYpHnwwtKPy7beBp56S+u1ZgyAfYy4fYy4fYy4fY25erCnLBCecAHz2mf9z\nVQVstvSOh4iIiJKONWVmJgRw4onAypWhayIiIsoorCnLdN9+C1gs/oSsuZkJGRERUZZjUmZWtbX+\n/926FbjggvSOBaxBSAfGXD7GXD7GXD7G3LyYlJnVzJn+2TGHI90jISIiIglYU5ZF2GOMiIjIfIzW\nlHH3ZRZQVRX19U1oaWkDABQX+7vx2+32NI+MiIiIjOLyZRaor29Cc7MPDkclHI5KuN0+NDQ0JfV7\nsAZBPsZcPsZcPsZcPsbcvDhTluE0TUNLSxuczkrYbPkAAKfTBY+nBmVlU7mUSUQkmaL0ukpFWaw/\n5VVMysiQoqKidA8h5zDm8jHm8mVrzFn3nJv6m5Bz+TLDWa1WFBcXor3dDa+3E15vJ9rb3SguLuQs\nGRERUQZhUpYFSkunwOWyoKOjBh0dNXC5LCgtnZLU78EaBPkYc/kYc/kYc6IQLl9mAbvdjvLyEpSV\nTQXAlhhERESZiH3KiIiIkqi7J1W6h0FpEO//e559SURERJRBmJSRIaz7kI8xl48xl48xl2vMmDF4\n9dVXpXyv1tZWOJ3OHu/ZsGEDSktLcfDBB6OgoADjx4/H448/LmV8ZsSaMiIiohyhKIqp+qhdddVV\nmDhxItavX4+8vDx8/PHH2LJli/RxaJpminpszpSRIdnaS8jMGHP5GHP5GHNzEEKguroa48aNw4gR\nI3DZZZdhx44dwecvvfRSjBo1CgUFBTj33HOxcuXK4HNNTU0oLCzE0KFDcdhhh6GmpgZ79+6Fy+XC\npk2bMGTIEAwdOjRmsvX+++9jxowZyM/Ph8ViwYQJE3DhhRcGn3/yySdxxBFHYMSIEVi0aBHGjBkD\nj8cDAJgxYwbmzp0bvDdyZi7w8wwdOhSFhYVobGwMPvfYY4/hrLPOQmVlJUaMGIH58+dDVVX87ne/\nwxFHHIGRI0fif/7nf7Bv3z4AwNdff42LL74Yw4YNw/Dhw/HDH/4wJXWDTMqIiIhy3H333YfnnnsO\nr7/+OjZv3oxhw4bhhhtuCD5/0UUXYdWqVdi2bRtOOeUUXHHFFcHnfv7zn+PBBx/Erl270NbWhkmT\nJmHgwIFobm7G6NGjsXv3buzatQsjR46M+r5nnHEGZs6ciX/84x9Yv3592HMrV67EzJkz8fTTT2PT\npk3Yvn07Nm7cGHy+t1m/cePG4c0338SuXbtQVVWFK6+8Elu3bg0+/+6772Ls2LHo6OjA7Nmzceut\nt2LVqlX46KOPsGrVKmzcuBELFiwAANxzzz1wOp34+uuv0dHRgcWLF6dkxpFJGRnCug/5GHP5GHP5\ncjHmynwlKR/J9MADD2DhwoUYPXo0bDYbqqqqUF9fD5/PB8A/KzVo0KDgcx999BF2794NwN+Wqa2t\nDbt27cKBBx6IiRMnAjB2qsGzzz6Lc845B3fccQeOOuooTJw4Ee+//z4AoL6+HlOnTsXZZ58Nu92O\nO+64AxZLeNrS0/f46U9/GkwEy8rKcPTRR+Pf//538PnRo0fjhhtugMViQV5eHh566CHU1NSgoKAA\ngwcPxm233YalS5cGf8bNmzdj3bp1sFqtOOuss4yGNiGsKSMiIpJIVJmvXca6deswbdq0sKRnwIAB\n2Lp1KxwOB26//XbU19dj27ZtsFgsUBQFX3/9NYYMGYKGhgYsXLgQs2bNwkknnYTq6mqcccYZhr5v\nQUEBFi9ejMWLF2P79u343e9+h5KSEmzYsAGbNm3CYYcdFrx34MCBGD58uOGf6YknnsC9996LdevW\nAQD27NmD7du3B5/XL3Vu27YNe/fuxamnnhp8TAgRTEpvvvlmzJs3D+effz4A4Prrr8ett95qeCxG\ncaYsA2iaBk3T0jqGROo+zDDebMBaG/kYc/kYc3M4/PDD0dzcjB07dgQ/9u7di1GjRqG2thbPPfcc\nXn31/7d3/8FV1ekdx99PsqJoQiBQpIAjAVlYAQVqgVCobmpciFZBZiURSdARS3V3oVJHxRnq2OkU\nRqVOp/iLdbOCgLPFlaKAKwiMYruwXWRL+CHqEA0ggvJTwEkgT//IyTXBAAne3HPuvZ/XzJ05557v\nOXnykAlPvue55/sOR44cYdeuXbh7bJbquuuuY+nSpRw4cIAxY8Zwxx13AC1fB7Jjx45Mnz6dvXv3\ncvDgQbp27UpVVVXs+IkTJxoVVZdddhknTpyI7TfsWfv000+57777mDt3LgcPHuTQoUP079+/0cxa\nw/g6depE27Zt2bZtW+z7P3z4MEePHgUgKyuLp556ik8++YRly5YxZ86cWG9bPKkoi7Dq6moWLVrK\nlCmzmDJlFosXL6W6ujrssM4q2eIVEUlH1dXVfPPNN7HXqVOnmDJlCjNmzIj1dR04cIBly5YBdTNM\nF198Mbm5uRw/fpwZM2bErlVTU8PChQs5cuQImZmZZGdnxz7FePnll/PVV1/FCpumPPzww2zdupVT\np05x7NgxnnvuOXr37k1ubi7jxo3jzTff5P3336e6upqZM2fGZq4ABg4cyIoVKzh06BD79u3jmWee\niR07fvw4ZkanTp2ora2lvLycioqKs8aRkZHB5MmTmTZtGgcOHABgz549vP322wAsX76cjz/+GHen\nXbt2ZGZmtsqnNVWURdiSJSt4661aOnd+kM6dH2Tlylpee21FKLE0p+8jSvGmgnTstQmbcp54ynni\nFRUVcemll8ZeTzzxBFOnTuXWW2/lpptuol27duTn57Nx40YASktLufLKK+nWrRv9+/cnPz+/0SzT\nK6+8Ql5eHjk5Obz44ossXLgQgL59+1JSUkLPnj3Jzc1t8tOXJ0+eZOzYsXTo0IFevXpRVVUVKwb7\n9evH3LlzufPOO+natSu5ubmNbmdOnDiRa6+9lh49ejBq1CiKi4tjcV199dVMnz6d/Px8unTpQkVF\nBSNGjIid29SHBGbPns1VV13FsGHDyMnJobCwkJ07dwLw0UcfUVhYSHZ2NsOHD+eBBx7g+uuvj8c/\nRyNaZimiTp8+zZQps+jc+UEuuqgtADU1J9m/fw7PP/9Iwp+nsm7dunPeZohavKngfDmX+FPOEy8V\nc65lllpPXl4eL730EgUFBWGH0iQtsyQJkWq/NJOBcp54ynniKeci31JRFlGZmZkUFPSjqmolNTUn\nqak5SVXVSgoK+kVy1inZ4hUREYkaFWURNm5cEaNHZ7B//xz275/D6NEZjBtXFEoszen7iFK8qUC9\nNomnnCeeci4tsWvXrsjeuowHPacswtq0aUNJyRjuuONvASI/45Rs8YqIiESJGv1FRETiSI3+6UuN\n/iIiIiIpQEWZNIv6PhJPOU885TzxlHORb6koExEREYmAUHrKzOynwONAX+Av3X1Tg2OPAvcAp4Ff\nuPvbTZyvnjIREYkk9ZSlr2TtKdsCjAXebfimmV0NjAeuBkYBz5qZZvNERETiYP369QwfPpz27dvT\nsWNHRowYwfr168nKyuL48ePfGT9o0CCeffZZKisrycjIYPDgwY2Of/nll7Rp04a8vLxEfQspLZSC\nx913uPvOJg7dBix29xp3rwQ+BoYkNDhpkvo+Ek85TzzlPPGU88Q5evQot9xyC1OnTuXQoUPs2bOH\nxx9/nJycHLp3786SJUsaja+oqGD79u2UlJTE3jt58iRbt26N7S9atIiePXt+Zx1JuTBRm4XqCuxu\nsL8b6BZSLCIiIilj586dmBnjx4/HzLjkkku48cYbGTBgAGVlZcyfP7/R+Pnz53PzzTfToUOH2HsT\nJ07k5Zdfju0vWLCA0tJS3a6Nk1Z7eKyZrQK6NHFohru/0YJLNfkvPWnSJHr06AFA+/btGThwYGwN\ntfq/vLQf3/16UYlH+9qP9/4NN9wQqXjSYb/+vajEE6/9KOrTpw+ZmZlMmjSJ4uJihg4dGiu47rrr\nLmbOnMnu3bvp3r07tbW1LF68mLlz5za6xoQJExg5ciSzZ89m+/btfP311wwdOpR58+aF8S1FUv3P\nwLp166isrGzRuaE+PNbM1gLT6xv9zewRAHefFey/BfyTu2844zw1+ouISCSdt9E/Xrf6LuD/wR07\ndjB79mxWr17Nvn37KCoqYt68eXTu3JnCwkIKCgp49NFHWbVqFRMmTODzzz8nMzOTyspKevbsSU1N\nDaNGjeKhhx5izZo15OTkMGTIEO6991527doVn+8riSVro39DDYNcBhSbWRszywN6AxvDCUsaivJf\nf6lKOU885Tzx0jLn7vF5XYC+fftSXl5OVVUVFRUV7N27l2nTpgFQVlbGggULgLrbkiUlJd9ZLs/M\nKC0tpby8nFdffZWJEyfq1mUchVKUmdlYM6sChgHLzWwlgLtvA34DbANWAvdrSkxERCT++vTpQ1lZ\nGRUVFQCMHTuW3bt3s3btWl5//XXKysqaPO/2229nxYoV9OrVi+7duycy5JSntS9FRETiKKrPKfvw\nww9Zvnw548ePp1u3blRVVVFcXEz//v154YUXALjnnntYs2YN2dnZbNmyJXZu/e3LU6dOkZGRwaZN\nm+jQoQN5eXmsXr2ayZMn6/YlqXH7UkRERFpZdnY2GzZsYOjQoWRlZZGfn88111zD008/HRtTVlbG\nZ599Rmlp6XfOb/jYi8GDBzd6NpkeiREfmimTZmn46ShJDOU88ZTzxEvFnEd1pkxan2bKRERERFKA\nZspERETiSDNl6UszZSIiIiIpQEWZNEtaPksoZMp54inniaeci3xLRZmIiIhIBKinTEREJI7UU5a+\nvm9PWastSC4iIpKu9NwuuRC6fSnNor6PxFPOE085T7xUzLm7R/q1du3a0GNI5df3oaJMmmXz5s1h\nh5B2lPPEU84TTzlPPOU8ulSUSbMcPnw47BDSjnKeeMp54inniaecR5eKMhEREZEIUFEmzVJZWRl2\nCGlHOU885TzxlPPEU86jK2kfiRF2DCIiIiLN5c14JEZSFmUiIiIiqUa3L0VEREQiQEWZiIiISASo\nKBMRERGJgKQtyszsn83sT2a22czeMbMrwo4p1ZnZk2a2Pcj7b80sJ+yYUp2Z/dTMtprZaTMbHHY8\nqczMRpnZDjP7yMweDjueVGdmvzKzL8xsS9ixpAszu8LM1ga/UyrM7Bdhx5TqzOwSM9sQ1CrbzOxf\nzzk+WRv9zSzb3Y8F2z8HrnX3e0MOK6WZWSHwjrvXmtksAHd/JOSwUpqZ9QVqgReA6e6+KeSQUpKZ\nZQIfAjcCe4A/ACXuvj3UwFKYmY0Evgbmu/uAsONJB2bWBeji7pvNLAv4IzBGP+ety8wudfcTZvYD\nYD3wj+6+vqmxSTtTVl+QBbKAL8OKJV24+yp3rw12NwDdw4wnHbj7DnffGXYcaWAI8LG7V7p7DfAq\ncFvIMaU0d38POBR2HOnE3fe5++Zg+2tgO9A13KhSn7ufCDbbAJnAwbONTdqiDMDM/sXMPgPKgFlh\nx5Nm7gFWhB2ESJx0A6oa7O8O3hNJSWbWAxhE3R/Y0orMLMPMNgNfAGvdfdvZxv4gcWG1nJmtAro0\ncWiGu7/h7o8Bj5nZI8C/AXcnNMAUdL6cB2MeA6rdfVFCg0tRzcm5tLrk7OMQuQDBrcslwNRgxkxa\nUXCHaWDQh/07M7vB3dc1NTbSRZm7FzZz6CI0axMX58u5mU0CioC/SUhAaaAFP+fSevYADT8sdAV1\ns2UiKcXMLgJeA15x96Vhx5NO3P2ImS0HrgPWNTUmaW9fmlnvBru3AR+EFUu6MLNRwEPAbe7+Tdjx\npKHzLtEhF+x/gd5m1sPM2gDjgWUhxyQSV2ZmwEvANnd/Jux40oGZdTKz9sF2W6CQc9QryfzpyyVA\nH+A08Anw9+6+P9yoUpuZfURdo2J9k+L/uPv9IYaU8sxsLPDvQCfgCPCBu48ON6rUZGajgWeoa8R9\nyd3P+dF1+X7MbDFwPdAR2A/MdPfycKNKbWY2AngX+D++vWX/qLu/FV5Uqc3MBgAvUzcJlgEscPcn\nzzo+WYsyERERkVSStLcvRURERFKJijIRERGRCFBRJiIiIhIBKspEREREIkBFmYiIiEgEqCgTERER\niQAVZSKSlMzstJl9YGZbzOw3wYMZL/RavzazccH2PDP70TnGXm9m+Rf6tUREzkZFmYgkqxPuPsjd\nBwDVwJSGB82sJcvIefDC3Se7+/ZzjP0xMLwlgZpZZkvGi0h6UlEmIqngPeCqYBbrPTP7L6DCzDLM\n7Ekz22hmfzKz+6BuuRkz+w8z2xEsCN+5/kJmts7M/iLYHmVmfzSzzWa2ysyuBP4O+Idglu6vgqWZ\n1gTXX21mVwTn/trMnjez3wOzE50QEUk+kV6QXETkfIIZsSJgRfDWIKCfu38aFGGH3X2ImV0MrDez\nt4HBwA+BHwFdgG3UrQkIwayZmf0Z8CIwMrhWe3c/bGbPA8fcfU7w9d8Ayt19gZndTd2yWGODa3UF\n8l1Lp4hIM2imTESSVVsz+wD4A1AJ/Iq6Rds3uvunwZibgNJg3O+BXKA3MBJY5HU+B9accW0DhgHv\n1l/L3Q+fcbzeMGBRsP0KMCLYduA/VZCJSHNppkxEktVJdx/U8A0zAzh+xrifufuqM8YV0biwakpL\niqmzXetEC64hImlOM2Uiksp+B9xf3/RvZj80s0uBd4HxQc/Zn1PXvN+QUzez9tdm1iM4Nzc4dgzI\nbjD2v4HiYHtCcG0RkRbTTJmIJKumZrL8jPd/CfQANlndNNp+YIy7v25mBdT1kn1GXWHV+ELuXwY9\nab81swzgC+AnwBvAEjO7DfgZ8HOg3MweCq5/93liFBFpkqndQURERCR8un0pIiIiEgEqykREREQi\nQEWZiIiISASoKBMRERGJABVlIiIiIhGgokxEREQkAlSUiYiIiETA/wM6cD5xCNWkdQAAAABJRU5E\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11275d490>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "svr_residuals = np.delete(svr_pred - y_sim, xmin_idx, 0)\n",
      "\n",
      "plt.scatter(np.delete(x_sim, xmin_idx, 0), svr_residuals, alpha=0.5, s=26)\n",
      "plt.xlim(-3, 3)\n",
      "plt.plot(plt.xlim(), (eps, eps), 'g--', linewidth=2)\n",
      "plt.plot(plt.xlim(), (-eps, -eps), 'g--', linewidth=2)\n",
      "plt.xlabel('Predicted Value')\n",
      "plt.ylabel('Residual')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<matplotlib.text.Text at 0x112791bd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pccVybqb1Oxpa8+aaSqWypujxt3j02RtpzhZT9atuYzp4cH/LOGIYb95xxQu5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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x112797110>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Out of 100 data points, {0} of these were support vectors.\".format(np.sum(np.abs(svr_residuals) >= eps))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Out of 100 data points, 94 of these were support vectors.\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that in the previous equation, the new samples enter into the prediction function as sum of cross products with the new sample values. In matrix algebra terms, this corresponds to a *dot product* (i.e., $\\pmb{x}^T \\pmb{u}$). The regression equation can be rewritten more generally as $$f(\\pmb{u}) = \\beta_0 + \\sum_{i=1}^n \\alpha_i K(\\pmb{x}_i, \\pmb{u}),$$ where $K (\\cdot)$ is called the kernel function. When predictors enter the model linearly, the kernel function reduces to a simple sum of cross products shown above: $$K(\\pmb{x}_i, \\pmb{u}) = \\sum_{j=1}^P x_{ij}u_j = \\pmb{x}_i^T \\pmb{u}$$. However, there are other types of kernel functions that can be used to generalize the regression model and encompass nonlinear functions of the predictors: \n",
      "$$\\text{polynomial} = (\\phi(\\pmb{x}^T \\pmb{u}) + 1)^{degree}$$\n",
      "$$\\text{radial basis function} = \\exp(- \\sigma\\| \\pmb{x}^T - \\pmb{u} \\|^2)$$\n",
      "$$\\text{hyperbolic tangent} = \\tanh(\\phi(\\pmb{x}^T \\pmb{u}) + 1),$$\n",
      "where $\\phi$ and $\\sigma$ are scaling parameters. Since these functions of the predictors lead to nonlinear models, this generalization is often called the \"kernel trick\"."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(3)\n",
      "\n",
      "# sin wave\n",
      "x_sim = np.random.uniform(2, 10, 145)\n",
      "y_sim = np.sin(x_sim) + np.random.normal(0, 0.4, 145)\n",
      "\n",
      "# arbitrarily set outlier\n",
      "x_outliers = np.arange(2.5, 5, 0.5)\n",
      "y_outliers = -5*np.ones(5)\n",
      "\n",
      "x_sim_idx = np.argsort(np.concatenate([x_sim, x_outliers]))\n",
      "x_sim = np.concatenate([x_sim, x_outliers])[x_sim_idx]\n",
      "y_sim = np.concatenate([y_sim, y_outliers])[x_sim_idx]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simple linear regression\n",
      "from sklearn.linear_model import LinearRegression\n",
      "\n",
      "ols = LinearRegression()\n",
      "ols.fit(np.sin(x_sim[:, np.newaxis]), y_sim)\n",
      "ols_pred = ols.predict(np.sin(x_sim[:, np.newaxis]))\n",
      "\n",
      "print \"y = {0} + {1} sin(x)\".format(ols.intercept_, ols.coef_[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "y = -0.145817806709 + 1.10984549112 sin(x)\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# support vectors machine regression\n",
      "from sklearn.svm import SVR\n",
      "\n",
      "eps = 0.1\n",
      "\n",
      "svr = SVR('rbf', epsilon = eps)\n",
      "svr.fit(x_sim[:, np.newaxis], y_sim)\n",
      "svr_pred = svr.predict(x_sim[:, np.newaxis])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(x_sim, y_sim, alpha=0.5, s=26)\n",
      "plt_ols, = plt.plot(x_sim, ols_pred, 'g')\n",
      "plt_svr, = plt.plot(x_sim, svr_pred, color='r')\n",
      "\n",
      "plt.xlabel(\"Predictor\")\n",
      "plt.ylabel(\"Outcome\")\n",
      "plt.ylim(-5.2, 2.2)\n",
      "plt.legend([plt_ols, plt_svr], ['Least Squares', 'SVM'], loc = 4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "<matplotlib.legend.Legend at 0x112a2cdd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aBYMGwdGjlm2kMAvJ4bIiS81l57bRbJkbO2k4/ktuz5rBXldvu8vnAOskdTp6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\nte0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x112797390>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A linear regression model with a term for $sin(x)$ was fit to the data and the regression line is pulled towards the outlying points. An SVM model with a radial basis kernel function is represented by the red line and it better describes the overall structure of the data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The kernel function should be used depending on the problem. The radial basis function has been shown to be very effective. However, when the regression line is truly linear, the linear kernel function will be a better choice.\n",
      "\n",
      "Note that some of the kernel functions have extra parameters. These parameters, along with the cost value, constitute the tuning parameters for the model. In case of the radial basis function, it is suggested to estimate the distribution of $\\| x - x^, \\|$ from the training set points and use the midpoint of the 10th and 90th percentiles for $\\sigma$, instead of searching over a grid of candidate values.\n",
      "\n",
      "The cost function is the main tool for adjusting the complexity of the model. When the cost is large, the model becomes very flexible since the effect of error is amplified. When the cost is small, the model will \"stiffen\" and become less likely to over-fit (but more likely to under-fit) because the contribution of the squared parameters is proportionally large in the modified error function. One could also tune the model over the size of the funnel (e.g., $\\epsilon$). However, there is a relationship between $\\epsilon$ and the cost parameter. Since the cost provides more flexibility for tuning the model, we suggest fixing a value for $\\epsilon$ and tuning over the other kernel parameters."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since the predictors enter into the model as the sum of cross products, differences in the predictor scales can affect the model. Therefore, we recommend centering and scaling the predictors prior to building an SVM model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "SVMs were applied to the solubility data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pprint import pprint\n",
      "\n",
      "# radial basis kernel\n",
      "opt_sigma = 0.0039\n",
      "\n",
      "svr = SVR(kernel='rbf', gamma=opt_sigma, epsilon=0.1)\n",
      "svr_params = {\n",
      "    'C': np.logspace(-2, 11, num=14, base=2),\n",
      "}\n",
      "pprint(svr_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{'C': array([  2.50000000e-01,   5.00000000e-01,   1.00000000e+00,\n",
        "         2.00000000e+00,   4.00000000e+00,   8.00000000e+00,\n",
        "         1.60000000e+01,   3.20000000e+01,   6.40000000e+01,\n",
        "         1.28000000e+02,   2.56000000e+02,   5.12000000e+02,\n",
        "         1.02400000e+03,   2.04800000e+03])}\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.grid_search import GridSearchCV\n",
      "from sklearn.cross_validation import ShuffleSplit\n",
      "\n",
      "cv = ShuffleSplit(trainX.shape[0], n_iter=10, random_state=3)\n",
      "\n",
      "gs_svr = GridSearchCV(svr, svr_params, cv=cv, scoring=\"mean_squared_error\", n_jobs=-1)\n",
      "gs_svr.fit(trainX.values, trainY.values[:,0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "GridSearchCV(cv=ShuffleSplit(951, n_iter=10, test_size=0.1, random_state=3),\n",
        "       estimator=SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma=0.0039,\n",
        "  kernel='rbf', max_iter=-1, probability=False, random_state=None,\n",
        "  shrinking=True, tol=0.001, verbose=False),\n",
        "       fit_params={}, iid=True, loss_func=None, n_jobs=-1,\n",
        "       param_grid={'C': array([  2.50000e-01,   5.00000e-01,   1.00000e+00,   2.00000e+00,\n",
        "         4.00000e+00,   8.00000e+00,   1.60000e+01,   3.20000e+01,\n",
        "         6.40000e+01,   1.28000e+02,   2.56000e+02,   5.12000e+02,\n",
        "         1.02400e+03,   2.04800e+03])},\n",
        "       pre_dispatch='2*n_jobs', refit=True, score_func=None,\n",
        "       scoring='mean_squared_error', verbose=0)"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gs_grid_rmse = [np.sqrt(-d[1]) for d in gs_svr.grid_scores_]\n",
      "\n",
      "plt.plot(np.logspace(-2, 11, num=14, base=2), gs_grid_rmse, '-x')\n",
      "plt.xscale('log', basex=2)\n",
      "plt.xlim(2**-2.5, 2**11.5)\n",
      "plt.xlabel('Cost')\n",
      "plt.ylabel('RMSE (Cross-Validation)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<matplotlib.text.Text at 0x112a55090>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZZ9ddIklSZ5rnwisi/gJ8DrgrpbQe8FBEnNzyshZyr3nuJk6E734XZsyY+3NK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\nevRr7+cYasbLhZe62quvwr7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       "text": [
        "<matplotlib.figure.Figure at 0x112a38e50>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Best cost value associated with the smallest RMSE was {0}\".format(gs_svr.best_params_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Best cost value associated with the smallest RMSE was {'C': 16.0}\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "SVMs with polynomial kernel was also evaluated. We tuned over the cost, the polynomial degree, and a scale factor."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# polynomial kernel\n",
      "svr_poly = SVR(kernel='poly', epsilon=0.1)\n",
      "\n",
      "svr_poly_params = {\n",
      "    'C': np.logspace(-2, 5, num=8, base=2),\n",
      "    'gamma': [0.001, 0.005, 0.01],\n",
      "    'degree': [1, 2]\n",
      "}\n",
      "pprint(svr_poly_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{'C': array([  0.25,   0.5 ,   1.  ,   2.  ,   4.  ,   8.  ,  16.  ,  32.  ]),\n",
        " 'degree': [1, 2],\n",
        " 'gamma': [0.001, 0.005, 0.01]}\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cv = ShuffleSplit(trainX.shape[0], n_iter=10, random_state=3)\n",
      "\n",
      "gs_svr_poly = GridSearchCV(svr_poly, svr_poly_params, cv=cv, scoring=\"mean_squared_error\", n_jobs=-1)\n",
      "gs_svr_poly.fit(trainX.values, trainY.values[:,0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "GridSearchCV(cv=ShuffleSplit(951, n_iter=10, test_size=0.1, random_state=3),\n",
        "       estimator=SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma=0.0,\n",
        "  kernel='poly', max_iter=-1, probability=False, random_state=None,\n",
        "  shrinking=True, tol=0.001, verbose=False),\n",
        "       fit_params={}, iid=True, loss_func=None, n_jobs=-1,\n",
        "       param_grid={'C': array([  0.25,   0.5 ,   1.  ,   2.  ,   4.  ,   8.  ,  16.  ,  32.  ]), 'degree': [1, 2], 'gamma': [0.001, 0.005, 0.01]},\n",
        "       pre_dispatch='2*n_jobs', refit=True, score_func=None,\n",
        "       scoring='mean_squared_error', verbose=0)"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def split_rmse_scores(grid_scores, scale, degree):\n",
      "    '''get the grid scores for each combination of scale and degree'''\n",
      "    rmse_scores = [np.sqrt(-d[1]) for d in grid_scores if (d[0]['degree'] == degree and d[0]['gamma'] == scale)]\n",
      "    return rmse_scores"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True)\n",
      "\n",
      "line1, = ax1.plot(np.logspace(-2, 5, num=8, base=2), split_rmse_scores(gs_svr_poly.grid_scores_, 0.001, 1), '-x')\n",
      "line2, = ax1.plot(np.logspace(-2, 5, num=8, base=2), split_rmse_scores(gs_svr_poly.grid_scores_, 0.001, 2), '-o')\n",
      "ax1.set_xscale('log', basex=2)\n",
      "ax1.set_xlim(2**-2.5, 2**5.5)\n",
      "ax1.set_title('scale: 0.001')\n",
      "\n",
      "ax2.plot(np.logspace(-2, 5, num=8, base=2), split_rmse_scores(gs_svr_poly.grid_scores_, 0.005, 1), '-x')\n",
      "ax2.plot(np.logspace(-2, 5, num=8, base=2), split_rmse_scores(gs_svr_poly.grid_scores_, 0.005, 2), '-o')\n",
      "ax2.set_xscale('log', basex=2)\n",
      "ax2.set_xlim(2**-2.5, 2**5.5)\n",
      "ax2.set_title('scale: 0.005')\n",
      "\n",
      "ax3.plot(np.logspace(-2, 5, num=8, base=2), split_rmse_scores(gs_svr_poly.grid_scores_, 0.01, 1), '-x')\n",
      "ax3.plot(np.logspace(-2, 5, num=8, base=2), split_rmse_scores(gs_svr_poly.grid_scores_, 0.01, 2), '-o')\n",
      "ax3.set_xscale('log', basex=2)\n",
      "ax3.set_xlim(2**-2.5, 2**5.5)\n",
      "ax3.set_title('scale: 0.01')\n",
      "\n",
      "fig.legend([line1, line2], ('Degree 1', 'Degree 2'), loc='upper center', ncol=2, frameon=False)\n",
      "fig.text(0.08, 0.5, 'RMSE (Cross-Validation)', ha='center', va='center', rotation=90)\n",
      "fig.text(0.5, 0.07, 'Cost', ha='center', va='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.text.Text at 0x112f92110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IUS/CQtz/TbumMoZZLxRZOE7KGGZN9YSfemnUVMZw6hXlImzWfbMYcuwQTv/j6Qw5dgiz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x112f5ead0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In general, quadratic models have smaller error rates than the linear models. Also, models associated with large-scale factors have better performance. It is important to point out that tuning the radial basis function kernel parameters was easier than tuning the polynomial model (which has more parameters)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "7.4 K-Nearest Neighbors"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The KNN approach simply predicts a new sample using the K-cloest samples from the training set. It cannot be clearly summarized by a model. Instead, its construction is solely based on the individual samples from the training data. To predict a new sample for regression, KNN identifies that sample's KNNs in the predictor space. The predicted response for the new sample is then the mean of the K neighbors' responses. Other summary statistics, such as the median, can also be used in place of the mean to predict the new sample.\n",
      "\n",
      "The basic KNN method depends on how the user defines distance between samples. Euclidean distance is the most commonly used metric and is defined as follows: $$(\\sum_{j=1}^P (x_{aj} - x_{bj})^2)^{1/2},$$ where $\\pmb{x}_a$ and $\\pmb{x}_b$ are two individual samples. Minkowski distance is a generalization of Euclidean distance and is defined as $$(\\sum_{j=1}^P |x_{aj} - x_{bj}|^q)^{1/q},$$ where $q > 0$. It is easy to see that when $q = 2$, then Minkowski distance is the same as Euclidean distance. When $q = 1$, then Minkowski distance is equivalent to Manhattan distance, which is a common metric used for samples with binary predictors. \n",
      "\n",
      "Because the KNN method fundamentally depends on distance between samples, the scale of the predictors can have a dramatic influence on the distances among samples. That is, predictors with the largest scales will contribute most to the distance between samples. To avoid the potential bias and to enable each predictor to contribute equally to the distance calculation, we recommend that all predictors be centered and scaled prior to performing KNN.\n",
      "\n",
      "In addition to the issue of scaling, using distances between samples can be problematic if one or more of the predictor values for a sample is missing, since it is then not possible to compute the distance between samples. If this is the case, then the analyst has a couple of options. First, either the samples or the predictors can be excluded from the analysis. If a predictor contains a sufficient amount of information across the samples, then an alternative approach is to impute the missing data using a naive estimator such as the mean of the predictor, or a nearest neighbor approach that uses only the predictors with complete information."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Upon pre-processing the data and selecting the distance metric, the next step is to find the optimal number of neighbors. Like tuning parameters from other models, K can be determined by resampling. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.neighbors import KNeighborsRegressor\n",
      "\n",
      "knnreg = KNeighborsRegressor()\n",
      "\n",
      "knn_params = {\n",
      "    'n_neighbors': np.arange(1, 21, 1)\n",
      "}\n",
      "pprint(knn_params)\n",
      "\n",
      "cv = ShuffleSplit(trainX.shape[0], n_iter=10, random_state=3)\n",
      "\n",
      "gs_knnreg = GridSearchCV(knnreg, knn_params, cv=cv, scoring='mean_squared_error', n_jobs=-1)\n",
      "gs_knnreg.fit(trainX.values, trainY.values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{'n_neighbors': array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
        "       18, 19, 20])}\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "GridSearchCV(cv=ShuffleSplit(951, n_iter=10, test_size=0.1, random_state=3),\n",
        "       estimator=KNeighborsRegressor(algorithm='auto', leaf_size=30, metric='minkowski',\n",
        "          metric_params=None, n_neighbors=5, p=2, weights='uniform'),\n",
        "       fit_params={}, iid=True, loss_func=None, n_jobs=-1,\n",
        "       param_grid={'n_neighbors': array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
        "       18, 19, 20])},\n",
        "       pre_dispatch='2*n_jobs', refit=True, score_func=None,\n",
        "       scoring='mean_squared_error', verbose=0)"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gs_knnreg_rmse = [np.sqrt(-d[1]) for d in gs_knnreg.grid_scores_]\n",
      "\n",
      "plt.plot(np.arange(1, 21, 1), gs_knnreg_rmse, '-x')\n",
      "plt.xlim(None, 21)\n",
      "plt.xlabel('#Neighbors')\n",
      "plt.ylabel('RMSE (Cross-Validation)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "<matplotlib.text.Text at 0x112fc6d90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rry+6Ekmd7Ysv4He/g4cfTrmx3r2LrkhSpWkrQ9bW4eK3NXsYmb4xbASIMf64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\nJ/HQQ2kwmzgxDWZ77NH+weybb2CzzWC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       "text": [
        "<matplotlib.figure.Figure at 0x10374a650>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Typically, small values of K usually over-fit and large values of K ususally underfit the data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The elementray version of KNN is intuitive and straightforward and can produce decent predictions, especially when the response is dependent on the local predictor structure. However, this version does have some notable problems, of which researchers have sought solutions. Two commonly noted problems are computational time and the disconnect between local structure and the predictive ability of KNN.\n",
      "\n",
      "First, to predict a sample, distances between the sample and all other samples must be computed. Computational time therefore increases with n because the training data must be loaded into memory and because distances between the new sample and all of the training samples must be computed. To mitigate this problem, one can replace the original data with a less memory-intensive representation of the data that describes the locations of the original data. One specific example of this representation is a k-dimensional tree. A k-d tree orthogonally partitions the predictor space using a tree approach but with different rules. After the tree has been grown, a new sample is placed through the structure. Distances are only computed for those training observations in the tree that are close to the new sample. This approach provides significant computational improvements, especially when the number of training samples is much larger than the number of predictors.\n",
      "\n",
      "The KNN method can have poor predictive performance when local predictor structure is not relevent to the response. Irrelevant or noisy predictors are one culprit, since these can cause similar samples to be driven away from each other in the predictor space. Hence, removing irrelevant, noise-laden predictors is a key pre-processing step for KNN. Another approach to enhancing KNN predictivity is to weight the neighbors' contribution to the prediction of a new sample based on their distances to the new sample. In this variation, training samples that are closer to the new sample contribute more to the predicted response, while those that are farther away contribute less to the predicted response."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}