choct155/SKLtutorial.ipynb

## SKLtutorial.ipynb
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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "[scikit-learn](http://scikit-learn.org/stable/) Tutorial"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "While I am familiar with [machine learning](http://en.wikipedia.org/wiki/Machine_learning) (ML) in the abstract, I have never sat down to actually utilize ML techniques.  The good folks developing the scikit-learn (SKL) module have created a [tutorial](http://scikit-learn.org/stable/tutorial/) to help folks like me gain familiarity with the operational requirements of such analyses.  This Notebook is intended to serve as a walk-through of basic of the SKL functionality contained within said tutorial."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import *\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "from pandas import Series, DataFrame"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/choct155/analysis/Anaconda/lib/python2.7/site-packages/sklearn/pls.py:7: DeprecationWarning: This module has been moved to cross_decomposition and will be removed in 0.16\n",
        "  \"removed in 0.16\", DeprecationWarning)\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Data Input"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "SKL requires input sets to be formed as 2d arrays."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iris=datasets.load_iris()\n",
      "print type(iris)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'sklearn.datasets.base.Bunch'>\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "SKL provides a number of datasets that can be accessed from within the package.  The **load_iris()** method generates an instance of a dataset **Bunch**.  This appears to be a JSON or dictionary-type structure.  The object contains meta-data, labeling, etc. in addition to the base data.  The base data may be accessed by keyword."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iris_data=iris['data']\n",
      "print type(iris_data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<type 'numpy.ndarray'>\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As can be seen above, the data component is simply a ndarray.  It appears that this common format will provide the bridge to [pandas](http://pandas.pydata.org/) functionality.  \n",
      "\n",
      "These data are already in the appropriate format."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iris_data.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(150, 4)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Some data, however, must be pre-processed.  In particular, higher dimensional data must be reshaped to stack the extra dimensions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "digits=datasets.load_digits()\n",
      "digits.images.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "(1797, 8, 8)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The third dimension in the image data means that there are 8 cross-sections that must be stacked instead of extended into a third dimension.  We can achieve this with the **numpy.reshape** method.  It takes a tuple argument describing the new shape.  In this instance, we want a 2-D shape.  The first dimension will be unchanged from the original ndarray.  The second can be specified directly with a positive integer, but we are going to use -1.  \n",
      "\n",
      "In this context, -1 is a signal to the **reshape** method indicating that the analyst wants **numpy** to infer the proper length of the dimension based upon the shape of the data.  In this case, we know that we have 1797 2-D ndarrays of dimension 8 $\\times$ 8.  **numpy** will flatten these ndarrays into a 1-D vector of length 64."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data=digits.images.reshape((digits.images.shape[0],-1))\n",
      "data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([[  0.,   0.,   5., ...,   0.,   0.,   0.],\n",
        "       [  0.,   0.,   0., ...,  10.,   0.,   0.],\n",
        "       [  0.,   0.,   0., ...,  16.,   9.,   0.],\n",
        "       ..., \n",
        "       [  0.,   0.,   1., ...,   6.,   0.,   0.],\n",
        "       [  0.,   0.,   2., ...,  12.,   0.,   0.],\n",
        "       [  0.,   0.,  10., ...,  12.,   1.,   0.]])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Estimator Objects"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An estimator is any SKL object that learns from data.  This covers operations like classification, regression, clustering, and transformation.  An example of an estimator would be **sklearn.cluster.KMeans**.  All of these objects have a **fit** method that serves as a the primary data input vehicle.\n",
      "\n",
      "The general form would be:\n",
      "\n",
      "    estimator.fit(data)\n",
      "    \n",
      "Estimator parameters can be set when the estimator is instantiated or after the fact as a modeification of an estimator attribute.\n",
      "\n",
      "    estimator=Estimator(param1=1,param2=2)\n",
      "    \n",
      "In addition to input parameters, estimators also generate estimated parameters.  These are identified by the parameters that end in an underscore.\n",
      "\n",
      "    estimator.estimated_param_"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Supervised Learning"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In a nutshell, supervised learning seeks to identify a link between two datasets.  There are two main strategies here:\n",
      "\n",
      "1. Regression seeks to predict a continuous variable.\n",
      "2. Classification seeks to split observations into a finite set of groups.\n",
      "\n",
      "All supervised estimators carry a **fit(X,y)** method to fit the data and a **predict(X)** methods returns the predicted labels *y*.  The classification approach can be exemplified with the iris dataset.  In particular, we need to identify three types of irises from petal and sepal length and width.  In the iris **Bunch** object, the characteristics are captured in **data**, while the group membership information is captured in **target**."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iris_X=iris.data\n",
      "iris_y=iris.target"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can verify that there are only three groups to choose from."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set(iris_y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "{0, 1, 2}"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we opted to explore the data visually, we can generate a plot based upon sepal length and width."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Take only the first two features\n",
      "iris_X_sub=iris_X[:,:2]\n",
      "\n",
      "#Generate plot figure\n",
      "plt.figure(figsize=(12,8))\n",
      "\n",
      "#Plot the training points\n",
      "plt.scatter(iris_X_sub[:,0],iris_X_sub[:,1],c=iris_y,cmap=plt.cm.Paired)\n",
      "plt.xlabel('Sepal Length')\n",
      "plt.ylabel('Sepal Width')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.text.Text at 0x4f2d1d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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aok7Fz21qaip6W+vAQKfxqX+QkxEyrlyTNC8R0YPirqU6KCgIy5cvR1xcHJYt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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4f24f90>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To capture the interaction between all four dimensions a bit better, we can look at the first three Principal Component Analysis (PCA) dimensions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate plot figure\n",
      "fig=plt.figure(figsize=(12,8))\n",
      "\n",
      "#Generate 3D axes\n",
      "ax=Axes3D(fig,elev=-150,azim=110)\n",
      "\n",
      "#Perform PCA and retain 3 dimensions\n",
      "X_reduced=decomposition.PCA(n_components=3).fit_transform(iris_X)\n",
      "\n",
      "#Plot scatter\n",
      "ax.scatter(X_reduced[:,0],X_reduced[:,1],X_reduced[:,2],c=iris_y,cmap=plt.cm.Paired)\n",
      "\n",
      "#Set title and labels\n",
      "ax.set_title('First Three PCA Dimensions')\n",
      "ax.set_xlabel('1st Eigenvector')\n",
      "ax.set_ylabel('2nd Eigenvector')\n",
      "ax.set_zlabel('3rd Eigenvector')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.text.Text at 0x4f1b050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Sju3ar9EiH8o/A0A+n7e9/WZxc3GSWq2GQqGAWCzW66Z0zM19Ty6XQyQSaTq6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CKVSlsJhUgkEm5ZcBO33HY7S//1FIUDBzP8lHH8/MNqBl9wbtjtpaenY7OYOFJSRLfu+dRWVXKs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\ntmzZgvr6eowaNQq/+c1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y5cuxcuVKbNq0SfGLzH79+rV7zMGDB1FeXo7i4mIAwNSpU7F7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\n/wG9QmTlDyaLFgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4f24a10>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "k-Nearest Neighbor Classification (kNN)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is perhaps the simplest classification method.  The tutorial defines the method as follows:\n",
      "\n",
      ">[G]iven a new observation `X_test`, find in the training set (i.e. the data used to train the estimator) the observation with the closest feature vector.\n",
      "\n",
      "Coming from a bit more of a spatial bent, this seems to me an awkward way of stating the process.  It seems clearer to me to say that new observations should belong to the dominant class in their local training neighborhood.  Then again, maybe that's a confusing explanation for other folks.\n",
      "\n",
      "To implement kNN, or any other learning algorithm, the data must first be split into two groups: train and test.  With the **iris** data, we can split the data in half to serve these purposes.  One might ask, what if the order of the rows in the data is meaningful?  This issue can be mitigated by running the data through a random permutation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Set seed \n",
      "np.random.seed(0)\n",
      "\n",
      "#Permute the data index\n",
      "indices=np.random.permutation(len(iris_X))\n",
      "\n",
      "#Capture training set\n",
      "iris_X_train=iris_X[indices[:-10]]\n",
      "iris_y_train=iris_y[indices[:-10]]\n",
      "\n",
      "#Capture test set\n",
      "iris_X_test=iris_X[indices[-10:]]\n",
      "iris_y_test=iris_y[indices[-10:]]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "kNN is implemented here with the **KNeighborsClassifier** object."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "knn=neighbors.KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\\\n",
      "                                   n_neighbors=5, p=2, weights='uniform')\n",
      "type(knn)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "sklearn.neighbors.classification.KNeighborsClassifier"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is our first opportunity to see a particular implementation of the general **estimator** structure from above.  In the previous cell we set the classifier parameters, and now we will fit the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Fit the data\n",
      "knn.fit(iris_X_train,iris_y_train)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
        "           n_neighbors=5, p=2, weights='uniform')"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can compare the values predicted by the classifer with the values of the actual data from the test set."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Print actual data\n",
      "print iris_y_test\n",
      "\n",
      "#Print predicted values\n",
      "print knn.predict(iris_X_test)\n",
      "\n",
      "#Print difference\n",
      "print iris_y_test - knn.predict(iris_X_test)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1 1 1 0 0 0 2 1 2 0]\n",
        "[1 2 1 0 0 0 2 1 2 0]\n",
        "[ 0 -1  0  0  0  0  0  0  0  0]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Only one miss seems like a pretty good hit rate given the small size of the training set.  Still, it's a bit abstract.  We can go a step further to visualize the pattern we are attempting to capture.  It's actually possible to plot classification regions with the data overlaid with the aid of **np.meshgrid**.  This method basically increases the resolution of $n$ vectors (by setting the step size) in pursuit of building an $n$-dimensional coordinate array.  The initial output is comprised of $n$ ndarrays that each capture one position in individual coordinates.  These ndarrays can be flattened (with **np.ravel**) and zipped to capture the full list of coordinates as tuples in a 1-D vector.  An example of this operation can be seen below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Establish step size\n",
      "step=.5\n",
      "\n",
      "#Create coordinate matrices\n",
      "new_a,new_b=np.meshgrid(np.arange(0,2,step),\\\n",
      "                        np.arange(0,1,step))\n",
      "print '**First Dimension**'\n",
      "print new_a\n",
      "print '\\n**Second Dimension**'\n",
      "print new_b\n",
      "print '\\n**List of Coordinates**'\n",
      "print zip(new_a.ravel(), new_b.ravel())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "**First Dimension**\n",
        "[[ 0.   0.5  1.   1.5]\n",
        " [ 0.   0.5  1.   1.5]]\n",
        "\n",
        "**Second Dimension**\n",
        "[[ 0.   0.   0.   0. ]\n",
        " [ 0.5  0.5  0.5  0.5]]\n",
        "\n",
        "**List of Coordinates**\n",
        "[(0.0, 0.0), (0.5, 0.0), (1.0, 0.0), (1.5, 0.0), (0.0, 0.5), (0.5, 0.5), (1.0, 0.5), (1.5, 0.5)]\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The coordinate array from our new vectors allows for finer control over any boundaries we might want, so let's get back to the task at hand.\n",
      "\n",
      "Note that we will be plotting in 2-D space, so we will again use only sepal length and width to define our axes.  This means that while in the context of our data *y* indicates the target values (flower classes), in the context of the region, *y_min* and *y_max* refer to the dimensions of the second data dimension (sepal width)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Create color maps\n",
      "cmap_light=matplotlib.colors.ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])\n",
      "cmap_bold = matplotlib.colors.ListedColormap(['#FF0000', '#00FF00', '#0000FF'])\n",
      "\n",
      "#Define the region to be colored\n",
      "x_min, x_max = iris_X_sub[:, 0].min() - 1, iris_X_sub[:, 0].max() + 1\n",
      "y_min, y_max = iris_X_sub[:, 1].min() - 1, iris_X_sub[:, 1].max() + 1\n",
      "\n",
      "#Set step size in mesh\n",
      "h=.02\n",
      "\n",
      "#Create coordinate matrices\n",
      "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\\\n",
      "                     np.arange(y_min, y_max, h))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have fine resolution of individual positions in the sample space, we will fit the subset of data (again, sepal length and width), and use this data as a training set to predict the class of each of the individual sample space positions we have just defined.  We are defining the local neighborhood as having a size of 15 neighbors."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Instantiate kNN object with parameters\n",
      "knn_sub=neighbors.KNeighborsClassifier(15,weights='uniform')\n",
      "\n",
      "#Fit the data\n",
      "knn_sub.fit(iris_X_sub,iris_y)\n",
      "\n",
      "#Predict coordinate position classes\n",
      "Z=knn_sub.predict(np.c_[xx.ravel(),yy.ravel()])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To plot this business, we want to use the shape of the coordinate system, which we could capture from either *xx* or *yy*. Each coordinate will be colored using the **plt.pcolormesh** method, which appears to be analogue to the psuedocolor function **plt.pcolor**.  The difference is the former takes dimension-specific ndarrays and a value overlay, whereas the latter just uses the values in a single ndarray."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Reshape the predicted position classes\n",
      "Z=Z.reshape(xx.shape)\n",
      "\n",
      "#Generate figure object\n",
      "plt.figure(figsize=(12,8))\n",
      "\n",
      "#Map colors to positions\n",
      "plt.pcolormesh(xx,yy,Z,cmap=cmap_light)\n",
      "\n",
      "#Plot training points\n",
      "plt.scatter(iris_X_sub[:,0],iris_X_sub[:,1],c=iris_y,cmap=cmap_bold)\n",
      "\n",
      "#Set limits\n",
      "plt.xlim(xx.min(), xx.max())\n",
      "plt.ylim(yy.min(), yy.max())\n",
      "\n",
      "#Set title\n",
      "plt.title('3-Class classification (k = 15, weights = Uniform')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<matplotlib.text.Text at 0x56a1d90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iYyWTq5Fx5zYiIiIiUgQWvkRERESkCBbN8SUiKs/+M2cw54cfIIRAXN++aNuk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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4f0a210>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As can be seen above, this is a very effective way of displaying class scope in 2-D space."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "[The Curse of Dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I don't think the explanation offered in the tutorial is particularly clear, so we will deviate rely a bit more heavily on the general information provided by [Wikipedia](http://en.wikipedia.org/wiki/Main_Page).  Basically, the curse of dimensionality occurs when an increase in the number of dimensions causes an increase in the parameter space at such a rapid rate that the available data becomes sparse.  This sparsity can be thought of as decreasing the frequency with which observations vary.  Variation in this sense is not referring to the magnitude of the variation, but rather whether or not variation occurs at all.\n",
      "\n",
      "To use a very simple (and unrealistic) example, suppose one wanted to test whether flipping a light switch would cause a light to turn on.  We already know that the switch is not a sure thing, and merely increases the probability of the light illuminating.  The greater the number of tests that result in non-events (the light not turning on or off), the more data is required to establish that the switch has a non-zero probability of turning on the light (if that is indeed the case in the underlying data generating process).  In a nutshell, we need variation in the data and the target to identify the relationship between them.  The more variation we have, the greater the precision with which we can identify the relationship.  The sparsity driven by high dimensionality discussed above is an enemy of this identification.\n",
      "\n",
      "Within the context of machine learning, the implication of high-dimensionality is an increase in the amount of training samples that are fit to the target.  If the training set is fixed, predictive power reduces with each additional dimension.  This is, apparently, known as the Hughes Effect."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Regression"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To examine regression, we will be using the diabetes dataset which ties disease progression to a vector of 10 physiological variables.  We can set up our train and test sets at the outside."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate Bunch object\n",
      "diabetes=datasets.load_diabetes()\n",
      "\n",
      "#Capture train set\n",
      "diabetes_X_train=diabetes.data[:-20]\n",
      "diabetes_y_train=diabetes.target[:-20]\n",
      "\n",
      "#Capture test set\n",
      "diabetes_X_test=diabetes.data[-20:]\n",
      "diabetes_y_test=diabetes.target[-20:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can roll through a basic regression analysis and extract the coefficients.  Measures of predictive fit like mean squared error (MSE) can be built, and measures of regression-type fit like explained variance (analagous to $R^2$ but restricted to the test set) can be extracted directly."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate regression object\n",
      "reg=linear_model.LinearRegression(copy_X=True,fit_intercept=True,normalize=False)\n",
      "\n",
      "#Fit the data\n",
      "reg.fit(diabetes_X_train,diabetes_y_train)\n",
      "\n",
      "#Examine coefficient estimates\n",
      "print '**Coefficients**\\n',reg.coef_\n",
      "\n",
      "#Calculate MSE\n",
      "mse=np.mean((reg.predict(diabetes_X_test) - diabetes_y_test)**2)\n",
      "print '\\n**Mean Squared Error**\\n',mse\n",
      "\n",
      "#Extract explained variance\n",
      "exp_var=reg.score(diabetes_X_test,diabetes_y_test)\n",
      "print '\\n**Explained Variance**\\n',exp_var"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "**Coefficients**\n",
        "[  3.03499549e-01  -2.37639315e+02   5.10530605e+02   3.27736980e+02\n",
        "  -8.14131709e+02   4.92814588e+02   1.02848452e+02   1.84606489e+02\n",
        "   7.43519617e+02   7.60951722e+01]\n",
        "\n",
        "**Mean Squared Error**\n",
        "2004.56760269\n",
        "\n",
        "**Explained Variance**\n",
        "0.585075302269\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "[Ridge Regression](http://en.wikipedia.org/wiki/Tikhonov_regularization)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Least squares is a very widely used estimator because it is the Best Linear Unbiased Estimator even when the errors are not Gaussian (by virtue of the Gauss-Markov Theorem).  However, by virtue of specifying it as the best among unbiased estimators, one is lead to question whether the variance around estimates can be reduced if the unbiased property can be relaxed.  This would be useful when one does not have enough data in each dimension to drive down the standard error around an estimate.  In fact, there are techniques that are able to capture more precise estimates, one of which is ridge regression.  (An excellent, brief discussion of the similarity between ridge regression, principal components analysis, and bayesian estimation can be found on [Open Mind](http://tamino.wordpress.com/2011/02/12/ridge-regression/).)  \n",
      "\n",
      "In a nutshell, ridge regression is more sensitive to drivers of target variation.  It achieves this, however, at the expense of being able to provide an effect estimate that reflects the true impact of whatever is being estimated.  Said differently, it increases [precision at the expense of accuracy](http://en.wikipedia.org/wiki/Accuracy_and_precision).\n",
      "\n",
      "The following example can shed some light on what this means.  First we define a train target set that maps 1-to-1 to the train data, and a test data set that extends beyond the boundaries of the train set."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Define train set\n",
      "ridge_X=np.c_[.5,1].T\n",
      "ridge_y=[.5,1]\n",
      "\n",
      "#Define test set\n",
      "test=np.c_[0,2].T\n",
      "\n",
      "print 'Train Data\\n',ridge_X\n",
      "print '\\nTrain Target\\n',ridge_y\n",
      "print '\\nTest Data\\n',test"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Train Data\n",
        "[[ 0.5]\n",
        " [ 1. ]]\n",
        "\n",
        "Train Target\n",
        "[0.5, 1]\n",
        "\n",
        "Test Data\n",
        "[[0]\n",
        " [2]]\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we will generate six variations on `ridge_X`, fit regression objects with the variations and `ridge_y`, and plot `test` against the predictions yielded by the same regression objects."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate plot object\n",
      "plt.figure(figsize=(12,8))\n",
      "\n",
      "#Set random seed\n",
      "np.random.seed(0)\n",
      "\n",
      "#Instantiate regression object\n",
      "regr=linear_model.LinearRegression()\n",
      "\n",
      "#Create container for coefficients\n",
      "reg_coef_list=[]\n",
      "\n",
      "#For six iterations...\n",
      "for _ in range(6):\n",
      "    #...generate a variant of ridge_X...\n",
      "    this_X=.1*np.random.normal(size=(2,1)) + ridge_X\n",
      "    #...fit the variant and ridge_y...\n",
      "    regr.fit(this_X,ridge_y)\n",
      "    #...plot test against the regression objects predictions...\n",
      "    plt.plot(test,regr.predict(test))\n",
      "    #...overlay scatters of ridge_y vs the variant of ridge_X...\n",
      "    plt.scatter(this_X,ridge_y,s=3)\n",
      "    #...and capture the coefficient\n",
      "    reg_coef_list.append(regr.coef_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XrzZvfncs5Iu9XzAmb4wVfoflDCM6qht9A6VFCsMiItI+PvoIrr7avPK8887u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\nZxGGAQAA4LMIwwAAAPBZhGEAAAD4rP8PMvxdJ2n51+YAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b65610>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's unpack this a bit.  Basically, we have explored the following regression model.\n",
      "\n",
      "$$y = \\beta X + \\epsilon$$  \n",
      "\n",
      "realized as \n",
      "\n",
      "`ridge_y = reg.coef_ * this_X` plus assumed $iid$ errors.\n",
      "\n",
      "The slope of each of the lines in the plot above is the coefficient of X.  Note the wide variation in coefficients from (and this is key) small random normal deviations on the train data.  These are peturbations in the train data that would be legitimately captured by the error term.\n",
      "\n",
      "If we were to perform the analagous procedure using ridge regression..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate plot object\n",
      "plt.figure(figsize=(12,8))\n",
      "\n",
      "#Set random seed\n",
      "np.random.seed(0)\n",
      "\n",
      "#Instantiate regression object\n",
      "ridge_reg=linear_model.Ridge(alpha=.1)\n",
      "\n",
      "#Create container for coefficients\n",
      "ridge_coef_list=[]\n",
      "\n",
      "#For six iterations...\n",
      "for _ in range(6):\n",
      "    #...generate a variant of ridge_X...\n",
      "    this_X=.1*np.random.normal(size=(2,1)) + ridge_X\n",
      "    #...fit the variant and ridge_y...\n",
      "    ridge_reg.fit(this_X,ridge_y)\n",
      "    #...plot test against the regression objects predictions...\n",
      "    plt.plot(test,ridge_reg.predict(test))\n",
      "    #...overlay scatters of ridge_y vs the variant of ridge_X...\n",
      "    plt.scatter(this_X,ridge_y,s=3)\n",
      "    #...and capture the coefficient\n",
      "    ridge_coef_list.append(ridge_reg.coef_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0yQTz5y+lVavn8fJ6m9tuG25XX3nFeYxbP47D5w+zc/hOfOpeZQ/yb4N0Z87A\n6tXwX/cYiJQHWikWERG5AQyLQersVBJGJuC/0p8Tw6vRKTKSB2vX5vu2be0KxGfO5DN//kiaNn2T\nkJBtdgfio+lH6bi4I5WdKrNv1L6/DsT/PUh3990QEaFALOWSVopFRET+ZqYsE3GD4yjJLiF4fzBL\nyOTVmFQ+9/HhwTp17Kq5a1c8KSmhNG7cjkceOYCzs7tddb449AVTN09l7n1zGdZ+2F+/efdu6yCd\nlxccOADNm9v1TJGbgUKxiIjI3yjvcB5Hex+lzsN1aDSnGWNTk4jKy2NPcDAt3NxsrmcY8NVX31Cz\n5rPUr/8m998/Egc79vDmm/KZsGEC4afD2TZ0G23rt/3zN2dlwfTpsH69BunklqHtEyIiIn+Tc1+d\n4/C9h2k+uznOczzpHnMYk2Gw185AnJtbwMKFY3B1nUmrVlt44IFRdgXi+Ix4bvv0NkxmEwdGH/jz\nQGwYsHy5dZCuUiUN0sktRSvFIiIi15ml2ELS5CSyNmXRbms7whsXMygykmlNmjDJ09OuIBsbe4zI\nyH64uPjyj39EUM3OW+6+if6GZzc+yxt3v8Go4L8I1cnJ1kG6c+dgzRro3Nmu54ncrBSKRURErqPC\n04XEhsbi7OFM8IFg5uWcZV78ab7186NHrVp21dyw4TtKSp7GyWk2w4aNxdHR9lBdWFLIsz8/y9bU\nrWwevJn2Ddpf+Y3FxfDuu9b/TZsGkyaBs7NdfYvczBSKRURErpOsbVnEPRlH42caU+v5Rgw8lsDJ\noiL2Bwfj5XqVCzCuwGQq5Ntvn6Ny5U14eW3ikUeC7Oor6WISoStDaV2nNRFjIqjuUv3Kb/xtkK5J\nEzh4EJo1s+t5IuWBQrGIiEgZMwyDU++c4tS7p/D9ypeMrq50ORTF7TVqsMzXF1cnJ5trpqUls3Nn\nKLm5LXj88QgaNqxhV28rY1by1IanmNVjFuM7jL/ydomsLOuq8E8/wfvvQ9++2jcstzyFYhERkTJU\nkltC/PB4ik4UEbI/hE1V8hgVFcVrzZszplEju2qGh68mPX08mZkzGDNmAs7OtgfUopIipmyawoak\nDWx8ciMhjUL++KbfbqR77jno3RtiY6GGfeFbpLxRKBYRESkjl+MuE9M7hhp31MDnK19ePXeSzxPP\nsa5tWzrbES4tliLWrZtKUdF6XFw2MGFCB7v6SslKod+qfnhV9yJiTAQ1XWv+8U3/PUi3di3cdptd\nzxIpr3SIWc6hAAAgAElEQVQkm4iISBlIX5nOoTsO4TXVi/oLvHk0MYbt2dkcDAmxKxBnZ6fw/ffd\nSE09TUBAJI89Zl8gXhu/lts+vY0nA55kdb/VfwzExcXwxhvWEHzffda9wwrEUgFppVhEROQaWEos\nHJ9+nIzVGQT+EkhKawd6R0TQq25d3vb2xtnR9vWn2NjvOX58LHFxLzFx4kSqV7d9u0SxuZjpW6az\nOm416wauo7PnFY5Q27XLOkjXrJkG6aTCUygWERGxU9G5ImIHxOLo6kjIwRBWl1zkmcNJvN+yJU96\neNhcz2IpZtu2aWRmruXixfW89FInu+bbTl46Sb+V/ahXtR5RY6Oo7Vb792+4eNF6I91PP8EHH0Cf\nPhqkkwpP2ydERETscGnPJSI6RFDzzpr4/diW6VkneDElhc2BgXYF4vz8E/z00x0cOpRM/foRjBtn\nXyD+6dhPdFzckd6+vflhwA+/D8SGAd98Y72RrnJl6yCdTpYQAbRSLCIiYhPDMEj7KI0Tr56gzWdt\nsNxfnftjonFxcOBgSAi17bjY4sSJHzl6dBQ7d/6TiROfw9PT9pBaYinhX1v/xdfRX7O632q6Nen2\n+zckJ8P48XD+vAbpRK5AoVhERKSUzJfNJIxN4PLRywTvDSa6nom+EREM8fBgVvPmONm44mqxmNi/\n/0XS0lZw5MhaXnutC5Ur295XWk4aA1YPoKpzVSLHRFKvar3//2JxMbzzDrz3nnXLxLPP6kY6kSvQ\n9gkREZFSyE/KJ7JLJA6ODgTvCeabKtk8HB3NBy1b8pq3t82BuLDwFJs338mePbEUFUUya5Z9gXhT\n8iY6LO5AzxY92fDkht8H4l27ICgI9uyBiAiYMkWBWORPaKVYRETkKjLWZZAwKoFmM5tRZ2wDJiQl\nsf3SJXa0b49P1ao21zt/fgNRUSNYv/45Ro+eQrt2tq9RmS1mZobN5LNDn7G8z3J6NOvx/1+8eNF6\nI93PP1sH6Xr31r5hkatQKBYREfkThtkg5ZUUzn95nrbr2pLb3oUehw7RyMWFfcHBVK9k2x+jFksJ\n0dH/IiXlazZuXMWcOd2oeYV7NK7mXN45nlj9BA4ODkSOicTD/f8G+34bpJsyxTpAFxOjG+lESkmh\nWERE5AqKM4qJeyIOw2QQEhFCeOV8BkRG8kzjxkxv0gQHG1dei4rS2Lt3AIcPV6WwMJKPP66HHUcY\nszVlK4PWDGJMyBhevuNlnBydrC8kJVkH6S5cgB9+gE6dbC8uUoFpT7GIiMj/yDmYQ0SHCNzbuxO4\nKZCFxemExsTwhY8PLzRtanMgzsz8hR07OvDtt//Ax2cD06bZHojNFjOzt8/myTVP8uVjXzKzx0xr\nIC4uhtdeg86doWdP6yUcCsQiNtNKsYiIyH858+kZUl5IofXC1lR9rDZDEuKJyc8nPDiY5m5uNtWy\nWEpITJxJYuIXLF36LW+/faddl8alX05n0JpBFJYUEjEmgkbVGllf2LnTeiOdt7d1kK5pU9uLiwig\nUCwiIgKAudBM4tOJ5OzJof3O9pxv6sh9kZEEuLuzOyiIKk5ONtUrKjrLwYMDOXLEmaNHI1i61ANX\nV9v72nFiB0+sfoIh7Ybw6l2vUsmxkgbpRK4DbZ8QEZEKryC1gKhuUZhzzATvC2ZnvUK6REYysmFD\nlvr42ByIL17cwu7dISxbdjfOzhv56CPbA7HFsDBn1xz6rezHv3v9mzfueYNKDk6wbJn1Rjo3N+uN\ndLqiWaRMaKVYREQqtIu/XCRuSBxNpjWh8aTGzDl1igVpaaz09+cOG4+GMAwzx4/PJjFxMe+/v4zZ\ns++mY0fbe8rMz2TI2iFkFWRxYPQBvGp4QWKidZAuM1ODdCLXgUKxiIhUSIbF4MQbJzjz8Rn8V/jj\n2NWdvrGxnC0u5kBICI1dXGyqV1R0jsOHnyQmxmDdugiWLWtA3bq297X31F4GrB5AqF8ob97zJs4l\nFusg3fvvw4svwsSJYONRcCJydfpdJSIiFY4p20T84HhMF02EHAghpWYJj0dG0qNmTZb7+eFi49EQ\nWVnbOHx4EN9/Pwp39xmsWuWEjTsuMAyDeeHzeGv3WyzutZhH2jwCO3bAuHHQooUG6USuM4ViERGp\nUPKO5HG091HqPFgH/9X+/HApkzGHjvGWtzcjGja0qZZhmDlx4g2Skj7mzTeXMnHifTz6qO09ZRVk\nMfyH4ZzJPcO+UftoZqkOo0bBxo3w4Yfw+OPaNyxynSkUi4hIhXFu2TmSJyfT8v2W1H2iPi+npLDs\n/Hk2BATQsXp1m2oVF6dz9Oggjh0rYv78CL74ohGtWtne04G0A/Rf1Z9erXuxou93VP52pfVGun79\nrIN0NvYlIvZRKBYRkVuepdhC8vPJXNx4kXa/tqPY14WHjhyhyDA4EBJC/cqVbaqXnb2D6Ogn+Pnn\noZw8OYtNmypRtaptPRmGwYL9C5i9YzafPPQJfZwDoedD1uPWfvwRuyb0RMRuOpJNRERuaUVpRRzq\ncYjCE4UEHwgmqblBh4gI2latyubAQJsCsWFYOHHiTaKi+jF79qc0bPg6X31leyC+VHiJfqv68fmh\nz9k7KIw+q2OhSxd46CHYv1+BWOQG0EqxiIjcsrLCsoh7Io7GTzemyfQmfHMhnUlJScxv2ZIBHh42\n1SouziAubjCpqbm8/PJBPvnEk65dbe8p6mwUoStDuc/7Ppa1HovL3X2gVSuIjIQmTWwvKCJlQqFY\nRERuOYZhcPq905ycexLfpb5Uu7cmk5OTWJ+ZydZ27Qhwd7ep3qVLuzl6dCA7dz7Bxo2z2bTJmQYN\nbO9pUcQiXt72Mgs7v06fL/bBpuHWQbrHHtMgncgNplAsIiK3lJLcEhJGJFCYWkjIvhAuNXTk3sOH\ncXdy4kBICLWcnUtdyzAsnDr1Dikp7zFv3hK8vR9i82awoQQAuUW5jF0/lqPnozlSdSoNQ2dA//4Q\nE6NBOpGbhPYUi4jILeNy3GUiO0VSqVYl2u9sz6GaRXSIiKBHzZr8GBBgUyA2mTKJjn6E2Ni1jBu3\nn4EDH+K992wPxNHno+mwuAPN001ErapDw0+/tQ7SffCBArHITUQrxSIicktIX5VO4vhEvOd402BE\nA/599iwvp6SwpE0betl4tdylS+HExPTnyJFQPvjgTVatcsbf3/aePo/6nH9tnMr603cS9N02eOkl\neOYZ3UgnchPS70oRESnXLCUWUl5I4cKqCwRuDMS5fRVGJySwNyeHXUFBtK5SpdS1DMPg9Ol5pKa+\nxZIli8nJeYR9+2xf0L1cfJkJGyZgCdvG8Z+q4+JXokE6kZucQrGIiJRbxeeLiR0Qi0NlB0IOhnCu\nqpk+hw7R1NWVfcHBuNuwImsyZREfP5yMjLNMnLiPQYOa8c9/2j7/FnchjpGfP8acX8x0O2bGcf4H\n1kE6EbmpaU+xiIiUS5f2XiKiQwQ1utUgcEMgux3z6BQZSWi9eqzw87MpEOfk7CciIpijR5sxePBO\n3n+/GdOm2R6Ilx3+igXPdGLL2+fo3vYhHGPjFIhFygmtFIuISLliGAZnPj5D6qxU2ixpQ52H6zDv\n9GnePnmSZb6+3Fu7tk210tI+JDX1ddauXcTOnY+zdy94ednWU4GpgNc/HcrD89bT260ZVTYuhQ4d\nbPxmInIjKRSLiEi5Yc43c2zsMfKO5BG0JwijuQtPxMVxLD+f8OBgmrm5lbqWyZRNQsJIsrNPMG1a\nOIGB3uzYAS4utvWUeOYom8fey7TtWTjPmIXrpCkapBMph7R9QkREyoX8pHwiu0QCELw3mLONHegS\nGYmLgwO7goJsCsS5uRFERIRw8mQjQkN3M3q0N598Ynsg3vr5K9C+Pf/I8cD9aCKuU6YrEIuUU/qd\nKyIiN72MHzNIGJlAs1ea0eipRvx88SLD4+N5pVkzxjdqhEMpN/8ahsGZMx+TmjqLPXs+4pNPQtmw\nAYKCbOun8Nxpogbfi8/BJArefYvmI56341uJyM1EoVhERG5ahtkgdWYq5744R9u1banWpTqvnTjB\nwjNnWNO2LV1r1Ch1rZKSSyQkjCYnJ5G5c/dQXNySgwfBhi3IYBikf/wOTi+8SGa3pvgdS6VRPU/b\nv5iI3HQUikVE5KZkyjQR+0QsliILIQdDKKjjyONHj5JhMnEwJISGNux1yM09RGxsKEVF9zF06FKG\nDnVlxgxwtGUTYUICF4b04WxaAnEfPkv/oXNLvUItIjc/7SkWEZGbTm5ELgdDDuIe6E67Le1IcjfR\nKSICLxcXtrVvX+pAbN0usYgjR+4jPn42fft+zIIFrsycaUMgLiqi5JUZ5HVqz8eNz1K0ezsDhr2j\nQCxyi9FKsYiI3FTOLjnL8enHafVJK+r3rc+q9HTGJybyTosWDG3QoNR1SkpyOXZsLLm5MXz99S72\n7GlDeDh4e9vQTFgYptEj2e2exdLXu/HOyO+o7WbLfgsRKS8UikVE5KZgLjSTNDGJSzsv0X5He1za\nuDEtOZnv0tPZGBhISLVqpa6Vl3eEmJhQHBzuZPz4cAIC3NizB0p943NGBkydSsEv6xl/v4mAMS+z\npMtzWh0WuYVp+4SIiNxwhScKieoWRUlWCcH7gylo4cw/oqOJyM3lYEhIqQOxdbvEpxw+fA+ZmTN4\n+OF/M3q0G198UcpAbBjw5ZcYbduy81I0wc+4MGb2Bp6//XkFYpFbnFaKRUTkhrq4+SJxg+NoMrUJ\nns95EpWXR5/IGPrVq8frzZtTqZSbf0tK8khMHE9ubhRhYTtZuNCHdeugc+dSNpKQAOPGUZyVybgx\nHpxrU5+dj2+kbpW69n85ESk3FIpFROSGMCwGJ+ecJG1BGn7f+lGrRy2WnjvH88nJfNyqFaH165e6\nVl7eUWJjQ6lcuQszZ+6nsLAKERFQqhKFhTBnDixYQNy4vtxb7Xuevn0Sn3abhqOD/kJVpKJwMAzD\n+Fse5ODA3/QoERG5yZmyTcQPiceUYcJ/pT8ODZ15LimJTVlZfN+2Lf5Vq5a61tmzX3D8+FQcHd9h\n4MCh9O8Pr79eyovltm2DceOw+Pkxt78n8898z9e9v+bOZnfa/+VE5IazJ3dqpVhERP5WedF5xPSO\noXbP2viv8ue8YSL00CFqOzuzPziYms7OpapjNueTmDiBnJx9JCeH8fzz/ixcCH36lOLDGRkwZQps\n3crFt2fRu/BLnE15RIyJwMPd49q+oIiUS1f9e6ERI0bg4eFBQEDAn75n4sSJtGrVinbt2hEVFVWm\nDYqIyK3j/NfnOXz3YZq+0pRW81sRXpBLx4gI7q9dm7Vt25Y6EF++HEdERCdKSswsWXKAOXP82bmz\nFIHYMOCLL8DfH2rXJmz9R7RNe4m7mt3Fxic3KhCLVGBXXSkePnw4zzzzDEOGDLni6xs2bCApKYnE\nxET27dvH+PHjCQ8PL/NGRUSk/LIUW0iekkzmhkza/dqOqgFV+TgtjZmpqXzu48NDdeqUuta5c1+R\nnPwc1avPYdiwEXh7O7BvH1z1gIr4eBg3DvLyMP+0ntfyNrBo81i+evwr7vG+59q+oIiUe1ddKe7e\nvTu1atX609fXrVvH0KFDAbjtttvIzs7m/PnzZdehiMhNrKCggIkTpzJjxmwsFss11Vq37kcGDBhB\nXFxcqd5/9OhRWrduT2joE9f87Cv5+ONFDB8+nvT0dLtrnDt3jnGhk/jF7xcKUwoJORiCk78bIxIS\n+OTMGfYEBZU6EJvNBcTHj+LEide5fHkr9947kieecOC7764SiAsL4ZVXoHt36NOH87+uo2fci2xL\n3UbEmAgFYhEByuCc4rS0NLy8vP7z/z09PTl9+vS1lhURKReWL1/O4sU7eeedL9i+ffs11erX7wm+\n+87E009PL9X7Bw8eSWKiC6tW/cqOHTuu6dn/6/Tp00yaNJWvvkpj7tx5dtdZ9NRn3LvqXr5NWUm9\nf9fjjKuZ7lFRFJjNhAcH07KUt2nk5ycQGXkbZnMBW7ceYNiwAFasgOeeg788PnjrVggMhOhoiIpi\ne69AQpZ04rbGt7FlyBYaVmto93cTkVtLmQza/e90358dcD5z5sz//LpHjx706NGjLB4vInLDdOjQ\nAUfH53F1rYKPj8811brjjnvZsmU5//jHu6V6/0MP9eTQoTlUquSCr6/vNT37f9WtW5cmTZpx4sRm\n7rprnM2fNwyD0/NO031bZ15yfJmsVgUcruTE0IgI/tmkCZM9PUt9Gcb588tJSpqIh8frPPfcaDIy\nHDhwABo3/osPXbhgHaQLC4P587H0epg5u+bw4b4P+eKxL+jZsqfN30lEbl5hYWGEhYVdU41SHcmW\nmppKr169iI6O/sNr48aNo0ePHgwYMAAAHx8ftm/fjofH74cVdCSbiNyqCgsLcXJywrmUQ2J/xjAM\nLl++jLu7e6k/k5GRQbVq1XBxcbmmZ1+J2WymqKiIKqW+G9mqJLeEhJEJFBwvwH+VP+a6Zj7KzOT9\ntDS+8fXlrr/Ykvf75xeSlDSJ7OxfcXZeSb9+7XnwQXjnHahc+U8+9Nsg3fTpMGgQzJpFhmMhg78f\nTG5RLt/2/RbP6p42fR8RKX/syZ3XvH3ikUceYenSpQCEh4dTs2bNPwRiEZFbmaur6zUHYrD+S9yW\nQAzWFd3rEYgBnJycbA7El+MvE3lbJE7VnQjaFYTZ05kRJ06wKiODfcHBpQ7E+fmJREZ2pqQki6Sk\nCB54oD0zZ8KHH/5FII6Ph7vugo8/hp9/hnffZffFwwQvCiawfiDbhm5TIBaRP3XV7RMDBw5k+/bt\nZGRk4OXlxaxZszCZTACMHTuWBx98kA0bNtCyZUuqVq3K559/ft2bFhGRm8+F1Rc4Nu4Yzd9sTqNR\njUjMz+exyKN0rl6dne3b4+rkVKo66ekrSEx8Gi+vWcydO46ff3bg11+tW4OvqLAQ3nwTPvrIOlD3\n1FMYjo68u+cd5u6Zy5JHlvBw64fL7ouKyC1JN9qJiMg1sZRYSHkxhfQV6fiv8qd6h+r8mJHByIQE\nZjdvzpiGDUu1f9hiKSIp6XkuXtxI/forGDw4mDp1YOlSqFnzTz60dav1mLWAAPjgA/D05GLBRYat\nHcb5y+dZ0XcFTWs2LdsvLCI3Pd1oJyIif6vi9GJi+8fi4OxAyMEQKtVx5pWUFD47d451bdvSuUaN\nUtUpKEgmJqYfrq7NKSyMoFu3GkyYAC+8AI5X2uh34QI8/zxs3w4LFkCvXgDsO72P/qv687jP46zq\nt4rKTn+210JE5PeueU+xiIhUTJfCLxEREkH1rtUJ/DmQ/BoOPBIdzbbsbA4EB5c6EF+4sJrIyC40\naDCMTZtWMmBADb74Al566QqB2DDgs8+gbVuoVw9iYqBXLwzD4IPwD+i1vBfvPfAe83rOUyAWEZto\npVhERGxiGAZnPjlD6sxU2nzahrqP1OVoXh6Px8TwYO3avNOiBc5XXN79PYulmOTkqWRm/kiLFj8x\ncWJHjh+H8HBo1uwKH4iLs26VKCiAjRshKAiAS4WXGLFuBKnZqYSPCse7lnfZfmERqRC0UiwiIqVm\nzjcTPzSeMwvPELQ7iLqP1OW79HTuOnyYV5o25YNWrUoViAsKUomK6kZh4QmqV4/g7rs7Ur067Np1\nhUBcWAgzZlhvpAsNhb17/xOII89GEvzvYBpUbcDuEbsViEXEbgrFIiJSKgXJBUR2icQwGwTvDaZy\nC1emJCXxwvHjbA4MZFCDBqWqk5HxA5GRt1G//kCOHfueO++sxXPPwaefgqvr/7z5t2MnYmPh8GF4\n+mlwcsIwDD458AkPLHuAN+5+g48e+gjXSv/7YRGR0tP2CRERuaqM9RkkjEig6YymNJ7QmAyTif5H\nYnF2cOBASAh1SnFOs8VSzPHj07lwYQ2+vj8wZ05nVqyADRugY8f/efOfDNIB5BblMvrH0cRlxLF7\nxG5a12ldxt9WRCoirRSLiMifMswGKa+kcGzcMdqubYvn055E5ObSISKCztWrsyEwsFSBuLDwJFFR\nd1BQkESzZpH07duZQ4fg4MH/CcQWCyxZYh2kq1//P4N0vzly/ggdFnegukt1wkeGKxCLSJnRSrGI\niFyRKdNE7JOxWAoshBwMwaWBC5+dPcu048dZ1Lo1vevVK1WdjIz1JCSMxMtrKmlpz/PQQw4MGQKz\nZsHv7vOIjbUO0hUW/m6QDqzDfUuilvDCry8w74F5DAocVMbfVkQqOoViERH5g9zIXGL6xFC3T128\n3/SmxAnGHzvGtqwsdrRvj2/VqletYbGYSEl5ifT0b/H3/57ly2/nlVese4cfeeS/3lhQAG+8AQsX\nWm+kGz/+d2n5cvFlxv80nsizkewYtgPfer7X4RuLSEWnUCwiIr9z9vOzHP/ncVp93Ir6ofVJKyqi\nb3QMHs7O7A8JoXqlq//RUVh4itjYAVSqVAM/v0gmTqxLZCTs3g2tWv3XG7dssYbg9u3h0CFo3Ph3\ndWLSYwhdGUqnxp3YN2ofVStfPYyLiNhDoVhERACwFFlInJhI9vZs2m9vT1W/quzMzmZAbCwTGjdm\nepMmOJbiuubMzJ+Jjx+Op+ckSkr+yZ13OuLvbz1/+D8LzOnp1kG6nTutg3QPP/yHOl8e+pLnNz3P\n3PvmMjxoeBl/WxGR31MoFhERCk8WEtM3BpcmLoTsD8GpmhPzT5/mtRMn+NLHh5516ly1hsVSQmrq\nDM6f/wp//5Xs2dOd4cPhX/+ynqTm4IB1kO7zz633Nw8dah2k+5+tGPmmfJ7Z8Ay7T+1m29BtBHgE\nXKdvLSLy/ykUi4hUcBe3XCRuUBxeU7zwet6LAouFcfHxHMnLY29wMN5ubletUVSURmzsQBwd3QgK\nimDOnPp8+imsWQNdu/7fm34bpCsqgk2brFsm/kdCRgKhK0MJ8AjgwOgDVHOpVsbfVkTkynQkm4hI\nBWVYDE68eYL4wfH4LfejyZQmpBYW0jUqCrNhsKeUgfjixU1ERHSgdu0H8PT8md6967N1q/W4ta5d\nsQ7S/etfcOed0L8/7NlzxUC8PHo53T7vxoSOE1j2+DIFYhH5W2mlWESkAiq5VELc0DhM500EHwjG\n1dOVTRcvMjgujhebNmVi48Y4XGX/sGGYSU2dydmzn+Hru5zU1B7cdRc89hi89RY4OwObN1sH6YKC\nrDfSNWr0hzqFJYVM3jiZLSlb2DRoE0ENg/74MBGR60yhWESkgsmLziOmTwy17quF/3f+OFR2YM6J\nE3yYlsYKf3/urFnzqjWKis4SF/cE4ESHDpF8840HU6daZ+b698c6SPfcc7BrF3z0ETz00BXrJF1M\not/KfrSo3YKDow9Sw7VG2X5ZEZFS0vYJEZEK5Pzy8xy++zBNX25K649ac9nJQt+YGNZmZLA/OLhU\ngTgr61ciIkKoWbMHPj6/MHGiB2++CWFh0D/UYj2IuG1b66pwTMyfBuLVsau5fcntjAgawYq+KxSI\nReSG0kqxiEgFYCm2kDw1mcz1mbTb0g73du4k5Ofz2NGj3FGjBt/4+eHi+NfrJIZh5sSJ1zhzZhG+\nvl+Rl3cPd95pPVr4wAGofjoW7hwLJpN120S7dlesU1RSxNTNU1l/bD0bntxAh0YdrsdXFhGxiVaK\nRURucUVnijh09yEKkgsIORiCezt31l64QPeoKJ739GRRmzZXDcTFxec5fPgBsrPDCAmJIDLyHjp1\ngj59YPWyAqq//X+DdAMHWm/o+JNAnJKVQvfPu3Py0kkixkQoEIvITUOhWETkFpa9I5uIjhHU7lmb\ngHUBONasxL+OH2diUhLrAwIYdYXBt/+VlRXGwYMh1KhxO4GBW3j//YYMGgRffw3/DNqMQ2AAHDtm\nHaR76qnfXdH8336I/4HbPr2NAW0H8H3/76nlVqusv66IiN20fUJE5BZkGAan3z/NyTkn8fnShzo9\n63DRZOLJuDgKzGYOhoRQv3Llq9SwcOLEG5w58xE+Pl9SqdL99O0LaWlw8KfzNH73Oeuq8F8M0gGY\nzCamb5nOqrhV/DDgB7p4dSnrrysics0UikVEbjEleSUkjEygIKmA4PBg3Jq7cTgvj95Hj/Jo3bq8\n7e1Npatul7hAXNwgLJYCQkIOkpTUmN694Z67LHx37xKce74Ew4Zd8Ua6/3bq0in6r+pPLbdaRI6J\npE6Vq9+MJyJyI2j7hIjILSQ/IZ/I2yJxqupE0K4g3Jq78c3589x7+DCvNW/Oey1bXjUQZ2fvJCIi\nmGrVQmj3/9i777Aq6/+P4082CKIiLgQEFZkyzkGz5c/2/FYO3OVKbViZja9WljYsbVvp15VppjnT\ntNTU1JzIUIvDlCEIgrI3nHH//rgLJYYjMMf7cV1dV5773Pf9+XRd4cuP78/nHfQrGzd2pl8/mP2E\njnkxfbFavkTdSDdnTqOB+OeknwldFMqj3o+yedhmCcRCiKuarBQLIcR14uyGsyROTMRzliednuyE\nQVF4+cQJfszNZVdQEIEODo3erygm0tPncOrUZ/j4LMXR8QFefhm2bqjgj0fepeNnC+Htt2HChAbr\nhgEMJgPTf53Oij9WsC5sHbd3ub2ppyqEEE1OQrEQQlzjTAYTqW+kcmbVGXr+3BPHXo7kVFczRKej\nhYUFkVotbaysGn1GdXUu8fGjMBgK0WojKCx046674PaKX4gxfwaLUi38/jt06tToc7JKshi2fhi2\nlrZETYiivX37ppyqEEI0GymfEEKIa1j1mWp+v/d3SqNK0UZpcezlSHhxMb2iori9dWs29+x5wUBc\nVHSAqCgN9vb+BAfvISrKjftDcviycATv5k7E4su5sHr1BQPxjuQdaBdquafrPWwdsVUCsRDimiIr\nxUIIcY0qDi9GF6ajw+Md8HzbEzMLMxZlZfF6aiqLvL151Nm50fsVRSEj42MyMj7E23sJbds+zBef\nmzg5fSHhFm9g88AYeDOm0bphAKPJyNt732bx0cWsHLCSOzzvaMppCiHEFSGhWAghrjGKopC1IIu0\nN3TUgY4AACAASURBVNPwXuSN86POVJlMPJeQyP6iIvaFhODdokWjz9Dr84mPH41efxatNgKj0Z2p\nD8cwbM9EfHoYsVm2EwIDLziW7NJsRmwYgaIoRE2IoqNDx6aaphBCXFFSPiGEENcQY7mR+NHxZH2V\nRciBEJwfdeZUZSV9jx4lX68nXKO5YCAuKjpMZKQGOzsvgoP3ciqpHSs9XuP1XXfg9/7j2EYdvKhA\nvDt1N9qFWm51u5Udj++QQCyEuKbJSrEQQlwjKlIqiBkQg72/PZrDGizsLdhbWMiw2FhecHXlVTc3\nzMzMGrxfURROnfqM9PQP8PZeiLPzoxycsR2Xd57hjpBetPzxd8xcGq8bBjApJmbtm8VXEV+x7LFl\n3Nvt3qacphBC/CskFAshxDUg7+c84sfE0+WNLnSe1BmAzzIy+CA9nW99fbnHyanR+/X6AhISxlJV\nlYlGcxjrfDuO+w/HNeEw5R99hc+LD1zUOM6WnWXkDyMp15cTOT6Szo6d//HchBDiaiDlE0IIcRVT\nTAqpM1JJmJBAwIYAXJ9zpcJkYmRcHMtzcjis0VwwEBcXRxAVpcXGxp2QoN8wzN9BiWcgsaXu2J6I\nuehAvD99P5qFGkI6hrB71G4JxEKI64qsFAshxFVKn68nbmQcxjIj2kgtNh1tSKmooH9MDEEODhwI\nCcGukSYaiqKQmfklJ0++Q48e82mX402J9i6S4k3sHbGT5xYFYnkRvwuYFBMfHfyIjw99zNePfM1D\nPR5qwlkKIcTVQUKxEEJchUqOlqAbqMO5vzNdP+iKuZU5W/PyGB0fz/QuXXi2c+dG64cNhiLi48dR\nWZmKxvdX7D78joovn2Km8g43r5jAi2EX9xeFeeV5jNo4iryKPCLGR+Deyr2ppiiEEFcVCcVCCHGV\nOf3NaVJeScHrKy/aD26PSVF4Ny2N+VlZrPf357bWrRu9v6QkGp1uME5O9+OXOQrCHuGIWW9e7vg7\nCzd3wsfn4sZx+NRhhq4bykDfgbx/9/tYW1g3weyEEOLqJKFYCCGuEqYqE0kvJFG4u5DgvcHY+9lT\nZDAwKi6OM3o9EVotLjY2Dd6vKApZWfNJS5uBV7t3af/WbvQHXmCKzTxyQu7n56/BweHC41AUhc8O\nf8b7+99n4X8W8pjPY004SyGEuDpJKBZCiKtAZUYluoE6bFxt0EZosXS0JK6sjMdiYrirTRvW+Ptj\nbd5wyYPBUExCwgQqyhMISZhEi/5vkHLHOO6sXMLzk1sw90VopNqiRmFlIWM3jSWjOIPwJ8PxbOPZ\nhLMUQoirl5w+IYQQ/7KCXQVE946mXVg7/Nf7Y+loyYazZ+l77BhT3d2Z16NHo4G4pOQYUVGhWBab\nCHnJBrvF21gweBe37XufZWtbMGXKxQXiyKxINAs0uDq6sn/MfgnEQogbiqwUCyHEv0RRFNJnp5P5\neSa+3/nS5s42GBWFN1JSWJmTw9aePQl1dGz0/tOnF5Ga8jrdo26hw7u7KX/tXYbuGk/eUXMiIqDz\nRZyapigK8yLmMWPvDOY9OI8w/7AmnKUQQlwbJBQLIcS/wFBkIH50PFWnq9Ac0WDrZkueXs+w2FiM\nikKkVks764Y3thkMpSQmTqQs+yAhb9jQoksLYlf/wSMTOvLgg7DuI2jk9hrFVcU8+eOTJOUncXDs\nQbzaejXhLIUQ4toh5RNCCHGFlcaUEtUrCutO1oTsDcHWzZajJSWERkUR5ODA9sDARgNxaekfRB0J\nxnzvITTPKLR4czErHlrF/w3pyMyZMHfuxQXiY9nH0C7U4mTnxKFxhyQQCyFuaLJSLIQQV1DOqhxO\nPH+Cbh91o+OojgB8m53NlORkvvLyYnD79g3eqygK2VmLSYmbQrf5ZnT0nkT14TeYPL0F27bBrl0Q\nGHjhMSiKwqLoRbz+6+t8fv/nDO85vKmmJ4QQ1ywJxUIIcQWY9CaSX0kmb3MegTsCaRncEr3JxEvJ\nyWzNz2d3UBABjZyXZjSWkRg+lJKMXQSv8sb+3W/JbBNA2IPg7AwREXCB44sBKK0u5aktT3E85zj7\nxuzDx/kiDy0WQojrnJRPCCFEM6s6XcXxO49TkVSBNlJLy+CWZFdVcefx46RWVhKh0TQaiMtyI4na\n2gWz7TvQFs/GfkMUe/MC6NULHnoINm68uEAccyaGXot6YW1hTfiT4RKIhRDiPLJSLIQQzahwXyGx\nQ2NxmehClze6YGZuxqGiIgbHxvJkp05M79IF80bOS8v+5SWSqz6ja1QvOj29EaVDRz7+BD78EJYv\nh3vvvbhxfHPsG17Z8Qof3fMRo4JHNdHshBDi+iGhWAghmoGiKGTOzeTkrJP4fOND2wfaoigK/8vM\n5M20NL729uZhZ+cG7zdmJpP0490Ut8okyHkeDjMmUlIC44ZASgocPgweHhceR7m+nGd/fpbDpw6z\ne9RuAtoHNN0khRDiOiKhWAghmpih1EDCkwlUJFagOazBztOOSqORZ5KSOFJczIGQELxatKj/ZpOJ\nsqUzibV6D4dWPmj+cwrLlu2Jj4cBA+CWW2D/frC1vfA44nPjCVsbRnDHYCLGR+BgfRE9noUQ4gYl\nNcVCCNGEyhPLie4TjYWdBSEHQrDztCO9spLbjx2jzGjksEbTcCD+4w9ynvXmWMdZdPabjs+wP7Bs\n2Z716+H222HKFFi8+OIC8Xe/f8ftS2/nhZteYPljyyUQCyHEBchKsRBCNJGzP5wlcWIinu960ml8\nJ8zMzPi1oIARcXG85OrKS25umNVXP1xWhvHd6ZywmE9h/1YE9YnAwTEYgwFeew3WrIGtWyE09MJj\nqNBXMHnbZHan7Wbn4zsJ6hjU9BMVQojrkIRiIYT4h0wGE2nT08hZmUPPLT1x7O2Ioih8nJHBRxkZ\nfOfry51t2tR/89atlM8cj+6VMuw970cbuBxLy5acOQNDhoCVFURGqseuXUhSXhJha8PwdvYmckIk\njjYNt4gWQghRm4RiIYT4B6rPVhM7LBYAbaQW63bWlBmNjIuP50RFBeEaDe711TucPg2TJ5NjvocT\n71fh6T2bTp0mYGZmxuHDMHgwPPEEzJwJFhYXHsca3Rqe/flZZvabydOhT9e/Ii2EEKJBEoqFEOIy\nFR8pRjdIR4eRHfB8xxMzCzNOlJfTX6ejV8uW7A8JwfbvidZkggULML4zneTZ7hR0b0lgwDZatgxB\nUWD+fHjrLbV2+JFHLjyGKkMVL/3yEltPbGXbiG1oXbTNM1khhLjOSSgWQohLpCgKpxeeJnV6Kj0W\n9qDdY+0A+CkvjzHx8cz08OApF5e6q7XHj8PEiZS31xO7pj12bbqj9V6MpaUj5eXw9NMQHQ0HDoCX\n14XHkVqQStjaMNxbuRM1IYrWthfRwUMIIUS95PQJIYS4BMYKIwljEzj1xSlC9ofQ7rF2mBSFmWlp\nTExIYGNAAE937lw7EJeVwauvwj33cOaFII7+N4NOns/i57caS0tHkpPVo9YMBvX84YsJxBvjN3LT\n4psYGTiS9YPXSyAWQoh/6IKheNu2bfj4+ODl5cXs2bPrXM/NzeX+++8nODiYgIAAvvnmm+YYpxBC\n/OsqUio4estRTJUmNIc1tOjRgkK9nkdjYtiRn0+EVsstrVrVvunnnyEgAFN2Bkk7/kOK504CA7fS\nufOzmJmZ8dNPcPPNMG4crFgB9vaNj6HaWM2U7VOYvG0ym4dtZnKfyVI/LIQQTcBMURSloYtGoxFv\nb2927txJ586d6dWrF6tWrcLX17fmOzNmzKCqqor333+f3NxcvL29ycnJwdKydmWGmZkZjbxKCCGu\nanlb84gfHU+X17vQ+Tl1JVhXVkb/mBjuc3Li427dsDY/b50hKwsmT4boaCrmv0ms0xfY2Ljh7f01\nVlatMRrh7bdhyRJYvRpuvfXCY0gvSmfw2sG0s2/HsseW4WTn1HwTFkKIa9jl5M5GV4qPHDlC9+7d\n8fDwwMrKiqFDh7Jp06Za3+nUqRPFxcUAFBcX07Zt2zqBWAghrlWKSSFtZhoJTybgv94f1+ddMTMz\nY+2ZM/Q7dow3unThCy+vc4HYaIR58yAoCHr04Ozed4lu8TIdOozE3389Vlatyc+Hhx+GPXvU49Yu\nJhD/lPgTvRb1YqDvQDYN3SSBWAghmlij6TUzMxM3N7eaX7u6uhIeHl7rO+PHj+fOO+/ExcWFkpIS\n1qxZ0zwjFUKIK0yfryfu8TiMxUa0kVpsOtlgMJl4LTWVtWfPsj0wEE3Lludu+HMjHZaWmHbvINnm\nG/IyptGz5xYcHXsDcPQoDBwI/fvDBx+o5xA3Ogajnjd+fYOVMSvZMHgDt7pfRIIWQghxyRoNxRdT\npzZr1iyCg4PZs2cPycnJ3HPPPRw/fpyW5/9G8acZM2bU/Hu/fv3o16/fJQ9YCCGuhJKjJegG6nB+\nzJmus7tibmVObnU1Q2NjMTczI1Krpe1fibasDGbMgGXLYNYsKobfSWzcMKyVTmi10VhZqY07vvkG\nXnkFvvpKPYf4QjKLMxm6fij2VvZET4imnX27ZpuvEEJcy/bs2cOePXv+0TMaDcWdO3cmIyOj5tcZ\nGRm4urrW+s7Bgwd5/fXXAejWrRuenp4kJCQQWk8/0vNDsRBCXK2yl2WT/HIy3b/oToehHQCIKilh\nYEwMwzp04F1PTyz+WjT4+Wd45hm47Tb44w9yLcJJOHoz7u7/xdX1RczMzKiqghdegN27Ye9e8PO7\n8Bi2n9jOqI2jeK73c0y7fRrmZnJYkBBCNOTvi60zZ8685Gc0GopDQ0NJSkoiLS0NFxcXVq9ezapV\nq2p9x8fHh507d3LrrbeSk5NDQkICXbt2veSBCCHEv81UZeLE5BMU/FpA8J5g7P3VoyC+OX2aV1JS\n+F+PHgxs9+dq7Xkb6Vi0CNNd/UhJmcbZs2sJCNhIq1Y3A5CRoZZLuLpCRAQ4XqDzstFkZMaeGXx9\n7Gu+H/Q9/Tz6NeOMhRBC/KXRUGxpacmXX37Jfffdh9FoZNy4cfj6+rJgwQIAJk6cyGuvvcaYMWMI\nCgrCZDIxZ84cnJxkA4gQ4tpSmVGJbpAOGxcbtEe0WLaypNpk4sUTJ9hZUMDe4GD87O3VjXT/+59a\nLvHUU7BsGZVmZ4k91hdLy7aEhkZjZdUWgF27YORIePFFtWziQhVpp0tOM3zDcMzNzImeEE0Hhw7N\nP3EhhBDABY5ka9IXyZFsQoirVMGuAuJGxuE62RW3V90wMzMjq6qKMJ0OZysrlvv60srSEo4dUzfS\nWVvDggXg50de3k/Ex4/Dze0l3NxewszMHEWBOXPgs8/gu+/gzjsvPIZfU39l5IaRTNBOYHrf6ViY\nW1z4JiGEEPW6nNwpZ6cJIW5YiqKQMSeDU5+dwneFL23uUjfE7S8sZEhsLE+7uPBaly6Yl5fDtGnq\nRrr334cxYzBhJDV5KmfOrCQgYD2tWqmnQhQXw+jRkJkJR47AeQf41MtoMjJr3yzmRc5j+WPLuafb\nPc08ayGEEPWRUCyEuCEZig3Ej46nKrMKzRENtm62KIrCvKws3k5L4xsfHx5o2xa2bIFJk+D22yEm\nBtq3p7LyFLGxQ7G0bIlWG4W1tVpnrNPBgAHqyvCqVWBj0/gYzpSdYeSGkVQZq4iaEIVLS5crMHMh\nhBD1ke3MQogbTpmujKheUVh3sCbktxBs3WypMBoZHR/PgqwsDmo0PFBVBWFhakHw4sXw7bfQvj15\neduIigqlbduH6Nnzp5pAvHo19OunLijPn3/hQPzbyd/QLNAQ6hLKrid2SSAWQoh/mawUCyFuKGdW\nnyFpUhJdP+xKp9GdAEirqGCATodPixYcCgrCftGicxvpli8HOztMJgNpaW+Rnb0Mf/81tG7dFwC9\nHl59FTZtgl9+gZCQxt9vUkzMOTCHzw5/xtJHl/KA1wPNPGMhhBAXQ0KxEOKGYNKbSHk1hdxNuQT+\nEkjLELXB0M78fEbGxTHV3Z0XcnMxu+02sLWF334DX18AqqqyiI0djrm5NaGh0VhbtwcgO1ttwuHg\noLZrvtDBO3nleTyx8QkKKwuJGB+BW6sLFBwLIYS4YqR8Qghx3avKruL4XccpTyhHG6mlZUhLFEVh\nTno6T8TH872nJ5M//xyz++9XV4f37KkJxPn5O4iKCqVNm7sIDNxaE4j374fQULjrLrXs+EKB+GDG\nQUIWhODn7MeeUXskEAshxFVGVoqFENe1wv2FxA6NxWW8C12md8HM3IwSg4Ex8fFkVFVxpKAA1+HD\noW9f+OMPaK+GXkUxkpY2k9Onl+Dr+x1t2tzx5+fwxRfw3nuwdCk8+GDj71cUhU8OfcLsA7NZ/Mhi\nHvF+pLmnLIQQ4jJIKBZCXJcURSHzi0xOvncSn6U+tH1QbaiRWF5O/5gYbrG0ZMWcOdhGR6sb6e6+\nu+beqqps4uKGA2ZotVHY2HQEoKwMJkyA2Fg4dAgu1LyzoKKA0ZtGc7rkNEfGH8GjtUczzVYIIcQ/\nJeUTQojrjrHMSNyIOLKXZqM5pKkJxD/m5nLb0aNMTkxk0X33Yevtra4OnxeICwp+JSpKS6tWfQkK\n+qUmECclQZ8+YGUFBw5cOBBHZEagWajBo5UH+8ful0AshBBXOVkpFkJcV8oTy9EN1OGgdSDkYAgW\ndhaYFIUZaWksTU/nxy++oM+ZM7U20oFaLnHy5HtkZf0PH5/lODmdC8qbNsH48fD222pDu8baNSuK\nwpdHvuSd395h/kPzGeg3sDmnK4QQoolIKBZCXDdyN+WSMD4Bz3c86TShE2ZmZhTo9YyMiaE0JYXI\nadPoMHWq2nLO/NxflFVXnyEubgQmkx6tNhIbG/XMYKMR3nxTPaJ482a46abG319UWcSTm58kOT+Z\nQ+MO0c2pWzPOVgghRFOSUCyEuOYpRoXU6ankrMih5+aeON7kCMAfpaX0P3KE/+zYwZzTp7E6cADa\ntat1b2HhXmJjR9Cx42g8PGZgbq7+WMzNhWHD1GAcGVmz/65BR08fJWxtGPd2u5dv+3+LraVts8xV\nCCFE85BQLIS4plWfrSZueByKSUEbqcW6vTUA38fH81xqKp999x0jxo5Vey+fR1FMpKd/QGbmF/j4\nfIOT03011yIiYNAgGDpUPWXCspGflIqisCBqAdN3T+eLB75gaMDQZpmnEEKI5iWhWAhxzSo+Uowu\nTEeH4R3weMcDc0tzDAYD//3hBzYajexMTydo8WK1Gcd5qqvPEhf3OCZTGRpNBLa2rjXXFi2C116D\n//0PBl6gHLikqoSJWyYScyaG/WP24+3s3RzTFEIIcQVIKBZCXHMUReH0otOkvp5Kj4U9aNdfLYk4\nExXFkKNHsVEUIm65BaehdVdtCwv3Exc3jA4dRuLh8U5NuURFBUyapB61tm8f+Pg0PoY/cv4gbG0Y\nt7vfTviT4dhZ2TX5PIUQQlw5EoqFENcUY4WRpGeTKA4vJmR/CC28W0BpKUc+/ZRBvr484ezMzEce\nwcK89omTimIiI+NDMjI+xcfna9q2Pdd1Iy1NXRXu3h2OHFHbNjdEURSWHlvKqzte5ZP7PuGJoCea\naaZCCCGuJAnFQohrRkVqBbqBOux62KEJ12DpYAmbN7NkzRqmDR/Owh49eKxb3RMf9Po84uJGYTDk\no9VGYGt7rsXy9u3wxBMwdSpMntz4cWtl1WU88/MzRGRG8NuY3/Br59cc0xRCCPEvkOYdQohrQt7W\nPKL7RNPhiQ74rfLDsjCbqrAwnoqO5qOxY/mtb996A3FR0SEiIzXY2/sSHLy3JhCbTPDuuzBmDKxd\nCy++2Hggjj0bS+/FvVEUhYjxERKIhRDiOiMrxUKIq5piUjj57kmyFmThv86f1re0hC++4NSXXzLo\no4/o7OHBET8/Wv7tiAhFUTh16hPS0+fg7b0YZ+f/1FwrLITHH4f8fPW4NReXxsfw7fFvmfLLFD64\n6wPGhozFrLH0LIQQ4pokoVgIcdXSF+iJezwOQ6EBbaQWm9M66DOR3/z8GLp4Mc916cJUd/c6IVWv\nLyA+fjTV1dlotUewte1Sc+3332HAAHjwQVi/HqytG35/hb6C57c+z2/pv7HriV0EdghsrqkKIYT4\nl0n5hBDiqlRyrISo0CjsutsRvLk7Nh9OQ3ngAeZOnUrYhAl8ExDAtC5d6gTi4uIjREVpsLPrSkjI\nvlqBeMUKuOsumDkT5s5tPBAn5iXSZ0kfSvWlRI6PlEAshBDXOVkpFkJcdbKXZ5P8UjLd53ang304\nBN1F+T33MGHbNnRGI4f9/fG0q30Emlou8Tnp6bPo0WMB7dr1r7lWXQ0vvQTbtsGuXRB4gXy7OmY1\nk7ZO4p073mGidqKUSwghxA1AQrEQ4qphqjJx4sUTFOwsIGhVRxzmPQ06HSnLljHAwYGetrYc6NGD\nFhYWte7T6wtJSBhLVVUGGk04dnaeNdcyMyEsDJyd1U51rVs3/P5KQyVTtk/hl+Rf2D5yO5pOmuaa\nqhBCiKuMlE8IIa4KlacqOfp/R6nKrEI7LgKHYX0gMJDte/dys7U14zp1YrmPT51AXFwcSVSUBhsb\nV0JC9tcKxHv2QK9e8NBDsHFj44E4OT+ZW7++lTNlZ4iaECWBWAghbjCyUiyE+NcV7C4gbngcnQeB\n+8GnMNvmgLJvH+/b2fFlSgpr/f3p+7dEqygKmZlfcfLk23h5zaN9+0HnXYNPPoEPP4Tly+Heext/\n/4a4DTy15Smm953OpN6TpFxCCCFuQBKKhRD/GkVRyPgwg4yP0/G97Tec1nwOc+ZQPHw4oxMSOJ2X\nR4RWS2cbm1r3GQxFJCSMp6LiBCEhB2nRonvNtZISGDsWUlMhPBy6dPn7W8+pNlbz6o5X2ZSwiS3D\nt9C7c+/mmqoQQoirnIRiIcS/wlBsIH5MPFV/ZKO1eAVbx2DQ6Yi3s6P/0aP0a92aVX5+2PytXXNJ\nSTQ63WCcnO7Fx2c5Fha2Ndfi46F/f7jtNti/H2xt//7Wc9IK0xiybggd7DsQNSEKJzun5pqqEEKI\na4DUFAshrriy2DKiNOFYRe8mRHkB2+8+gaVL+UFR6HvsGK+4uTG/R49agVgtl/gfv/9+H127vkeP\nHvNqBeL16+H229VTJhYtajwQ/5jwI70X9Waw32A2Dd0kgVgIIYSsFAshrqwz32eT9GQMXVlAp1cC\nYGo0Rmtr3kxJYUVODj/17EkvR8da9xgMJSQmTqCsLJaQkAO0aNHjvGvw2muwZg1s3QqhoQ2/W2/U\n89qu11itW83GoRu5xe2W5pqmEEKIa4yEYiHEFWHSm0gZc4jctTkE9lxLy+/eBW9v8vV6hv/+O9WK\nQoRWS/u/ddQoLT2OThdG69Z3oNEcxsLi3PnEZ87AkCFgZaW2a3Z2bvj9p4pPMWTdEFrZtCJ6YjTO\nLRr5shBCiBuOlE8IIZpd1Yl8jntuoHxtBNpPy2kZsRK8vTlWUkJoVBQB9vb8EhhYKxArikJW1iKO\nH78bD4+38PZeUCsQHz4MWi3cequ6QtxYIN52YhuhC0N52OthtgzfIoFYCCFEHbJSLIRoVkXvb0Y3\nXU+ngFN4RI3ArEM7AL7LyWHyiRN80b07Qzt0qHWPwVBKYuJTlJUdJzh4H/b2PjXXFAXmz4cZM2Dx\nYnjkkYbfbTAZeGv3Wyw7vow1YWvo26Vvc0xRCCHEdUBCsRCiWSjp6WQ+vISTsVp83nGi7bQBAOhN\nJl5JTmZLXh6/BgXR08Gh1n2lpTHExobh6HgLGk04FhYtaq6Vl8PTT0N0NBw4AF5eDb8/qySL4euH\nY2VhRfTEaNrbt2+WeQohhLg+SPmEEKJpGQwYZ88lzmsZp8/2QvP7/9F2Wj8Acqqrufv4cZIqKojU\nausE4tOnl3L8+B24u0/Dx2dJrUCcnAy33KJurDt8uPFAvCtlF6ELQ7nT8062jdgmgVgIIcQFmSmK\nolyRF5mZcYVeJYT4t0RFUf7Ea+hOjsXhbg96rAzFooXalvlwURFhsbGM69iRNz08MD+va5zRWEZi\n4rOUlETg778We3u/Wo/96ScYMwamT4dJk6ChhnNGk5F3fnuHhVEL+bb/t9zV9a5mm6oQQoir1+Xk\nTimfEEL8cyUlMH06ud8kkWB6FY85Prg87VLTLnlhVhZvpKayxNub//xtR1xZWSw6XRgtW4ai1R7B\nwsK+5prRCG+/DUuWwA8/qJvqGpJTmsOIDSMwmAxETYiiU8tOzTJVIYQQ1ycJxUKIf2bjRpRJz5Pa\n9mVy7AcRsL4nrfq0AqDSaOS5Eyc4WFTE/pAQerRoUevW7OxvSU6eQteuc+jUaUyta/n5MGKEWkcc\nGQkdOzY8hL1pexm+YThjgscwo98MLM3lR5sQQohLI79zCCEuT3o6PPcc1bpTxHVajtKyNdodfli3\nV49Vy6isZKBORxdbW8I1Ghwsz/24MRrLSUp6jqKiAwQF/YqDQ89aj46OhoEDYcAA+OAD9Rzi+pgU\nEx/s/4C54XP55rFvuL/7/c02XSGEENc32WgnhLg0BgN8+iloNBR3/D+iqr/A4U43An8JrAnEewoK\n6B0dTVi7dqzx86sViMvK4omOvgmTqQqtNrJOIP7mG7jvPpg9Gz7+uOFAnFuey0MrH+LnpJ+JnBAp\ngVgIIcQ/IivFQoiLFxkJEyZAmzZkTd5B6ufl9PifF+0GqmcPK4rCp6dOMSc9nRW+vtzt5FTr9pyc\nlZw48QKenrPo1OnJmppjgKoqeOEF2LMH9u4Fv9p77Wo5kH6AYeuHMSxgGO/e+S5WFg0kZyGEEOIi\nSSgWQlxYcbF69MPq1Rjf+4ikA6EUrywmeF8w9j7qxrgyo5EnExJILC8nXKuli61tze1GYwUnTkym\nsHA3QUE7cXAIqvX4jAy1XMLNDY4cAUfH+oehKAofH/qYDw9+yJJHlvBwj4ebbcpCCCFuLFI+IYRo\nmKKoxz74+0NpKRVbj3J0ng/GMiOaI5qaQJxcUcHN0dHYmJmxPySkViAuL08iOvpmDIaiP8slcxin\nLQAAIABJREFUagfiXbugVy8YNAjWrWs4EOdX5PPo94+yLnYdR548IoFYCCFEk5KVYiFE/f7cSEdi\nIqxYQX5lT+Luj8N9qjuuk11rSh9+zstjTHw8b3l48LSLS62SiDNnVpOUNAkPj7dxcXmq1jVFUeuG\nP/8cVq6EO+9seCjhp8IZsm4I/X36s27wOqwtrJtt2kIIIW5MEoqFELUZDDB3LsyaBZMno3y/mpMf\nZZM1Px7/tf607tsaAJOi8N7Jk/wvK4sNAQHc2qpVzSOMxkqSk6eQn/8LgYG/0LJlSK1XFBWpzTgy\nM9VyCTe3+oeiKApzw+fy3r73WPDwAvr79m+2aQshhLixSSgWQpwTEaFupHNygkOH0LfzIH5wPPp8\nPdpILTYuNgAUGQw8ERdHnl5PpFZLJxubmkdUVCSj0w3Gzq4roaFRWFq2qvUKnU49au2uu2DVKjjv\n1loKKwsZ9+M4Thae5PCTh+napmuzTVsIIYSQmmIhhLqR7vnn4T//gSlTYOdOSss7ERUahW1XW4J3\nB9cE4tiyMnpHReFmY8OvwcG1AvHZs+uJjr6Zjh3H4Oe3pk4g/v576NcPXnsN5s1rOBBHn45Gu1BL\nJ4dOHBh7QAKxEEKIZicrxULcyP7aSPf883D//eoybtu2ZK/IJvnFZLp/3p0OwzvUfH3dmTM8nZTE\nR926Meq8FnMmUxXJya+Ql7eFnj1/xtExtNZr9Hp49VX48UfYsQOCgxsajsL8yPm8tectvnzgS4YE\nDGmWaQshhBB/J6FYiBtVejpMmgRJSepOt759MVWbODEpkYLtBQT9GoRDTwcAjIrC6ykpfH/mDNsD\nA9G0bFnzmIqKVGJjh2Bj44pWG42VVetarzl9GgYPVk+ViIyENm3qH05xVTETNk8gLjeOA2MP0KNt\nj2abuhBCCPF3Uj4hxI3GYIBPPgGNBnr3hmPHoG9fKk9Vcuz/jlGVUYU2UlsTiHOrq7n/99+JLCkh\nUqutFYjPnt1IdPRNtG8/HH//9XUC8f79EBoKd98Nmzc3HIiPZx8ndGEojjaOHB53WAKxEEKIK05W\nioW4kfy1ka5tWzh0CLy8ACjYU0Dc8Dg6P9cZ9/+6Y2auHp0WXVLCQJ2OIe3a8a6nJ5bm6p+jTaZq\nUlKmcvbsBnr23Iyj4021XqMo8MUX8N57sHQpPPhg/cNRFIUlR5cwbdc0Pr3vU0YGjmy+uQshhBCN\nkFAsxI2guBhefx3WroWPPoIRI8DMDEVRyPg4g4yPMvD91hene861ZV6enc1LycnM9/JiUPv2NZ9X\nVp5EpxuCtXV7QkOjsbKq3cq5rAzGj4e4ODV3d21gj1xZdRlP//Q00aej+W30b/i2822WqQshhBAX\nQ8onhLieKQqsXw9+flBRoW6kGzkSzMwwlBjQhek4u/os2nBtTSCuNpmYlJjIuydPsic4uFYgzs3d\nQlRUb9q3DyMgYFOdQJyUBH36gLU1HDzYcCDWndHRa1EvLMwtCH8yXAKxEEKIf52sFAtxvTp5Ut1I\nl5ysHgh8++01l8riytAN0NGqbyt8V/hiYWsBwOmqKsJ0OpysrIjQamllqf6IMJn0pKa+xpkzawgI\n2EirVjfXed2mTeoK8dtvw8SJcF7zulqWHVvGyzteZs7dcxgTMqbp5y2EEEJcBgnFQlxvDAa1d/L7\n78OLL6orxdbn2iKfWXuGpGeS6Dq7K53Gdqr5/GBREYN1Oia6uPB6ly6Y/5lqKysziI0diqVl6z/L\nJdrWep3RCNOnw4oV6ma6m2qXF9co15fz3M/PcSDjALtH7SagfUDTz10IIYS4TBKKhbieHDmiLtM6\nO8Phw9C9e80lk8FEytQUctfnErgtkJZa9RQJRVGYn5XFjLQ0vvHx4cG250JvXt5W4uPH4Ob2Im5u\nr2BmVrviKjcXhg1Tg3FkJJxXaVFLQm4Cg9YOIrBDIJETInGwdmj6uQshhBD/wAVrirdt24aPjw9e\nXl7Mnj273u/s2bOHkJAQAgIC6NevX1OPUQhxIUVF8Nxz8Oij8PLL8MsvtQJxdU41x+8+TllMGdpI\nbU0grjAaGZuQwPysLA6GhNQEYpPJQErKNBITJ+Dvvw539//WCcQREaDVqv/88kvDgXjlHyu5belt\nPNf7OVb0XyGBWAghxFXJTFEUpaGLRqMRb29vdu7cSefOnenVqxerVq3C1/fcppjCwkJuvfVWtm/f\njqurK7m5uTg7O9d90Z873YUQTeivjXSTJ8MDD8Ds2eBUe/Nb0cEidIN1dBrbCY+3PDCzUMsiTlZW\nMjAmBq8WLVjs7Y29hVpXXFWVSWzsMMzNW+Dr+y3W1u3qvHLxYrVV84IFMGBA/UOrNFQyedtkdqXu\nYs2gNYR0Cmn6+QshhBD1uJzc2Wj5xJEjR+jevTseHh4ADB06lE2bNtUKxStXrmTgwIG4uroC1BuI\nhRDNIC1N3UiXklJnIx2oZRGZX2Vy8u2TeH/tjfPD5/7f3FVQwIjYWF51d+dFV1fM/qwfzs/fTnz8\naDp3noS7+7Q6q8MVFeorDx9WG3N4e9c/tBP5JwhbG0Z3p+5Ejo+klW2rJp26EEII0dQaLZ/IzMzE\nzc2t5teurq5kZmbW+k5SUhL5+fnccccdhIaG8u233zbPSIUQKr1ePWs4NBRuvlntSPe3QGwsMxL3\neBynF51Gc0hTE4gVReHD9HRGxsWxys+PKW5uf/5p2khq6nTi48fh5/c9Xbq8XicQp6XBbbdBaSmE\nhzcciNfFruPmJTczLmQcawatkUAshBDimtDoSrFZQ2cqnUev1xMdHc2uXbsoLy/n5ptvpk+fPnj9\n2SnrfDNmzKj59379+kn9sRCXKjxc3UjXvn2djXR/KT9Rjm6ADocgBzSHNFi0UMsiSg0GxiYkkFpZ\nyRGNBjdbWwCqqk4TFzccMzNLQkOjsLbuUOeZ27fDE0/A1KlqpUZ9PxqqDFW8suMVtiRuYeuIrYS6\nhDbt3IUQQogG7Nmzhz179vyjZzQaijt37kxGRkbNrzMyMmrKJP7i5uaGs7MzdnZ22NnZ0bdvX44f\nP37BUCyEuARFRWpHuvXr4eOP1SMf6kmmuZtzSRiXgMcMD1yedqn5g21SeTn9Y2K4ydGRfcHB2P5Z\nP1xQsIu4uMdxcXnqz9Vhi1rPM5lg1iyYN09thte3b/3DSy1IZci6Ibi0dCFqQhRt7No07fyFEEKI\nRvx9sXXmzJmX/IxGyydCQ0NJSkoiLS2N6upqVq9ezSOPPFLrO48++ij79+/HaDRSXl5OeHg4fn5+\nlzwQIUQ9FAXWrQN/f6iuVjvSDR9eJxArRoWUN1JIeiaJgE0BdH6mc00g3pyby61Hj/K8qyuLvb2x\ntbD4s1xiBnFxj+PruwIPjzfrBOLCQvUwi61b1ePWGgrEm+I30WdJH4YFDOOHIT9IIBZCCHFNanSl\n2NLSki+//JL77rsPo9HIuHHj8PX1ZcGCBQBMnDgRHx8f7r//fgIDAzE3N2f8+PESioVoCn9tpEtN\nhe+/Vwt666HP0xM7PBalWkEbqcW6g9qow6QozExL4+vsbH4MCKBPK7W2t7o6h9jYEYAJrTYaG5uO\ndZ75++/qqRIPPlin98e59xr1TN05lXVx69g0dBN9XPs01cyFEEKIK67RI9ma9EVyJJsQF0evh88+\nU49XmzJFPXe4vlQKFEcWoxuko/3g9njO8sTcUv3Ln0K9npFxcRQbjazx86OjjQ0ABQV7iIsbQadO\n4/DweKvO6jConelefFEdwogR9Q8xoyiDIeuG4GTnxLLHltG2Rdv6vyiEEEL8C5r8SDYhxBV2+LC6\nka5DhwY30v0la3EWqdNS8ZrvRftB5zpnxJSW0l+n40EnJz7q1g0rc3MUxcTJk7PIyvoKH59lODnd\nW+d51dVqBt++HXbtgsDA+t/7c9LPjN00lik3T+HlW17G3OyCPYCEEEKIq56EYiGuBkVFajeMDRvg\nk09g6ND6j3gAjJVGkiYlUXywmOB9wdj72NdcW33mDJOSkvi0WzdGdlTLIqqrzxAXNxKTqQqtNgob\nG5c6z8zMhLAwtTt0RAS0bl33vQaTgem/TmfFHytYN3gdt7nXX84hhBBCXItkiUeIf5OiqMc6+PmB\nwQCxsQ2eLAFQebKSo7cdxVhsRBOuqQnEBpOJl0+cYFpKCjsCA2sCcWHhb0RGamjZshdBQbvqDcR7\n9kCvXvDww7BxY/2BOLM4kzuX3Ul0djRRE6IkEAshhLjuyEqxEP+WtDR49lk4eRLWrIFbb2306/m/\n5BP3RBzur7rj+uK5LnRnq6sZEhuLlZkZEVotba2sUBQT6emzOXXqc3x8vqFt2/vrPE9R1EXpDz+E\n5cvh3roVFQD8kvwLozaO4tlez/La7a9JuYQQQojrkoRiIa608zfSvfQS/PBDgxvpABSTQvr76WR+\nlYn/an9a/9+5pdzI4mIG6nSM7NCBtz09sTAzo7o6l/j4JzAYitFqI7G1da3zzJISGDtWzeXh4dCl\nS933Gk1GZu6dyZKjS1g5YCV3eN7RFLMXQgghrkoSioW4kv7aSNexo5pGu3Vr9Ov6Qj3xT8Sjz9Wj\njdBi09mm5trXp0/z35QUFvboQf927QAoKjpAbOww2rcfhqfnu5ibW9V5Znw89O+vnvC2bx/82diu\nluzSbIavHw5A1IQoOjrUPbZNCCGEuJ7I34MKcSUUFsIzz6hpdOpU2LbtgoG49PdSokKjsPWwJXhP\ncE0grjaZeDoxkTnp6fwWHEz/du3+LJf4kJiYAXh5zaNbt9n1BuL16+H229UF6kWL6g/Eu1N3o12o\n5Tb329jx+A4JxEIIIW4IslIsRHP6ayPdiy+qO9liY6HNhTu+Za/IJvnFZLp92o2OI8+F0syqKgbp\ndHS0tuaIVoujpSV6fT7x8aPQ63PRaiOwtXWv8zyDQT3cYs0atUNdaGjdd5oUE7P2zeKriK9Y9tgy\n7u3WQJGxEEIIcR2SUCxEc0lNVTfSpadf1EY6AFO1ieSXksnbmkfQriAcAh1qru0rLGRobCzPdu7M\nVHd3zM3MKCo6TGzsUNq1G4i//3rMzevWJufkqCe8WVmp7Zqdneu+92zZWUb+MJIKfQWR4yPp7Nj5\nH01dCCGEuNZI+YQQTU2vhzlz1HPO+vaF6OiLCsRVmVUc63eMypOVaCO1NYFYURS+OHWKQTodX/v4\n8FqXLpgBGRmfEBPzKF5en9O9+8f1BuLDh9VV4VtvVVeI6wvE+9P3o1moQdNRw6+jfpVALIQQ4oYk\nK8VCNKVDh9SNdC4ucOQIdO16UbcV7CkgbngcnZ/tjPs0d8zM1ePWyo1GnkpM5PfSUg5pNHS1s0Ov\nLyA+fgzV1afRaMKxs/Oo8zxFgfnzYcYMWLwYHnmk7jtNiokPD3zIJ4c/YemjS3nQ68F/MHEhhBDi\n2iahWIimUFioFu1u3Kge/jtkSIMNOM6nKAqnPjlF+ofp+C73xelep5prqRUVDNDp8GvRgoMaDS0s\nLCgujiA2djBt2z6Kv/+aeleHy8vhqafg2DE4cAC8vOq+N688j1EbR5FXkUfE+AjcW9WtQxZCCCFu\nJFI+IcQ/oSiwerXakc5kAp2u0RbN5zOUGIgdHEvOqhy04dpagfiX/Hz6REczumNHVvj6YmduzqlT\nc/njj4fo1u1jvLw+qzcQJyfDzTeD0aguWtcXiA+fOoxmoQbvtt7sHb1XArEQQgiBrBQLcflSU9Vj\n1k6dgnXr4JZbLvrWsrgydAN0tLqtFSH7Q7CwtQDUlePZ6enMzcxkjb8//9e6NXp9IQkJ46isPIlG\ncxg7u/pLMrZsURtyvPmmur/v77lcURQ+O/wZ7+9/n4X/WchjPo9d9tSFEEKI642EYiEulV5/rj/y\nK6/AlCnq0Q4X6cy6MyQ9nYTn+564POlS83mJwcDo+Hgyq6o4otHgamtLSUk0Ol0Ybds+iJ/fSszN\nbeo8z2iEt9+GJUvU6o36snlBRQFjfxzLqeJThD8Zjmcbz8uauhBCCHG9klAsxKW4zI10ACaDidRp\nqZxZe4aeW3viGOpYcy2hvJzHYmLo26oVK/38sDYzIzNzHmlpM/Dy+or27cPqfWZ+PowYodYRR0aq\njfL+LjIrksFrB/Nwj4f5fuD32FjWDdZCCCHEjU5CsRAXo7AQpk2DTZvg009h8OCLqhv+S3VONbFD\nYzGzNkMbqcXa+Vw98MazZ5mQmMgsT0+edHHBYCgmNmE8FRWJhIQcoEWLegqDUU96GzgQBgyADz6o\nu1itKArzIuYxY+8M5j04jzD/+oO1EEIIISQUC9E4RVEbb7z4Ijz6qNqRrnXrS3pE0aEiYgfH0nF0\nRzxmeGBmoYZpo6LwVmoqy3Ny2NKzJ70dHSkpOUZsbBht2tyNj88hLCzq6cMMLF0Kr74KX32l5vO/\nK64q5skfnyQpP4lD4w7R3an7JU9dCCGEuJFIKBaiISkp6ka6zMxL3kgH6kpt1rws0mam4b3EG+f/\nnOucka/XMyIujgqjkUitlnZWVmRlLSA19Q26d59Lhw7D6n1mVRU8/zzs3av+4+dX9zvHso8RtjaM\nuzzv4tC4Q9ha1h+shRBCCHGOhGIh/k6vh48/ho8+uqyNdADGciOJExMpPV5KyMEQWnRvUXPteGkp\nA2JieNTZmTldu4KpjLi40ZSVxRASsp8WLbzrfWZ6OgwaBG5uajmzo2Pt64qisCh6Ea//+jpz75/L\nsJ71B2shhBBC1CWhWIjzHTyobqRzdb3kjXR/qUiuIGZADPY97dEc1mDRwqLm2sqcHF44cYK53bsz\nrEMHSkt/R6cbTOvWt6PRhGNhYVfvM3ftUjfUvfQSvPxy3XLm0upSJm6ZyO85v7NvzD58nH0uedxC\nCCHEjUxCsRAABQXqRrrNm9WNdGFhl7SR7i+5W3JJGJuAx1seuDzjgtmfz9CbTLyaksLm3Fx2BQXR\n096erKzFpKZOo1u3T+nYcWS9z1MUmD0bPv8cVq6EO++s+52YMzGErQ3jFtdbCH8ynBZWLep+SQgh\nhBCNklAsbmx/daSbMgUee0ztSHeJG+kAFKNC2sw0spdmE7AxgFa3tKq5llNdzRCdjhYWFkRotTia\nVxMfP4qSkmiCg3/D3t633mcWFcHo0XD6tLpo7eZW9ztLjy7l1Z2v8tE9HzEqeNQlj1sIIYQQKgnF\n4sb110a6rCxYv17tj3wZ9Hl6YkfEYqo0qcetdTh33Fp4cTFhOh2jO3bkLQ8PKstjidKF4ejYB632\nCBYW9a/qxsSoR63dfTd8/z3Y/O1o4XJ9Oc/+/CyHTx1m96jdBLQPuKyxCyGEEEJl/m8PQIgrTq9X\nD/bt3VutR4iKuuxAXBJVQlRoFA49HQjaGVQrEC/KyuI/f/zBF15evO3pyZnsZRw71g83t1fx8fm6\nwUD8/fdwxx3w+uswb17dQBx3No7ei3pjMBmIGB8hgVgIIYRoArJSLG4sBw6oG+nc3CAiAjwvv93x\n6a9Pk/LfFLzme9F+UPuaz6tMJp5LSmJ/URH7QkLobgPx8WMoLg4nOHgP9vb+9T5Pr1fPHv7xR9ix\nA4KD637nu9+/Y/L2ybx/1/uMCxlXU7P8d4mJibRp04Z27drVfFZWVsaJEyfo2bMn5uaX/+fhsrIy\n9u3bh5+fH+7u7pf9HL1eT0xMDP7+/qSmpuLk5FRrvEIIIcSVJKFY3BgKCmDqVNiy5R9tpAMwVho5\n8fwJivYVEfxbMPa+9jXXTlVWMlCnw83GhnCNBvOqJKKiwmjZUoNGcwRLS4d6n3n6tNqEw9FRbdfc\npk3t6xX6CiZvm8zutN3sfHwnQR2DGhzfDz/8wPDh47G2tiA5WYezs3o+cq9e/UhJSefZZ8fx8cez\nLmvuAP7+vTl5MhMLC4Xo6H0EBgZe1nOGDh3HTz9tx9vbg8TEZGxsLElJicXJyemyxyaEEEJcLimf\nENc3RYFVq8DfHywt1Y10l9ii+XyVJys5dvsxDAUGNEc0tQLx3sJCekdHM6BdO9b6+1OW+z3HjvXF\nze1FfHyWNRiI9++H0FC1fnjz5rqBOCkviZuX3ExRVRGREyIbDcQAJ0+eRFG6UV1toKioqObzjIxU\nDAYNJ06kXdbcQT0LOTs7A+iFotiQlZV12c9KTk5Frw8hM/MUitKdqqpqiouLL/t5QgghxD8hK8Xi\n+pWcrG6ky86GDRugT59/9Lj8HfnEPR6H28tuuL3kVlO6oCgKn586xQfp6Xzr68udrexITJxAYeFv\nBAXtwsGh/pVURYG5c2HWLLVt84MP1v3OGt0anv35WWb2m8nToU83WC5xvqeffhpzc3O6du1Kt27d\naj7fs2c7O3bsYOzYsZf3HwAwMzNj375dzJkzh759p3Pfffdd9rN++GE5q1at4pFHPmLXrl10794d\nDw+Py36eEEII8U+YKYqiXJEXmZlxhV4lbnTV1WpHuo8/hv/+FyZPvuSOdOdTTArpH6ST+UUmvit9\naXPHuaXccqOR8QkJxJWXs8Hfn/ZKOjpdGPb2AfTosQBLy5b1PrOsDMaPh7g49eCLv/cIqTJU8dIv\nL7H1xFbWDFqD1kV72eMXQgghbjSXkztlpVhcX/7aSOfurhbn/sOVR32hnvhR8ejP6tFGarHpfO4o\niJSKCvrHxBDk4MCBkBCKc9dw9MTzeHq+R6dO4xvZBAcDB4JWqzbQs/tbE7uUghQGrx2Meyt3oiZE\n0dr20s9NFkIIIcSlkZpicX0oKIAJE9R64bfegp9++seBuPSPUqJ7RWPjZkPwnuBagXhrXh43R0cz\nwcWFpT08yEieRFramwQG7sDFZUKDgXjTJrjtNpg0SS2Z+Hsg/iHuB/os7sPjgY+zfvB6CcRCCCHE\nFSIrxeLapijqwb5TpqjdLmJjoVWrC993ATkrczjxwgm6fdKNjo93rPncpCjMOnmS+VlZrPf3R2Od\ny9Gjt2Bn54VWG4WlpWO9zzMaYfp0WLFC3Ux30021r1cbq/nvjv/yQ/wPbB62mZtcb6r3OUIIIYRo\nHhKKxbXr/I10GzfWTZqXwVRtIvnlZPJ+ziNoZxAOQedOjCgyGBgVF8dZvZ4IrRbLoh85qnsWD48Z\nuLg0vAnu7FkYPhxMJrWio3372tdPFp5kyLohtLNvR/TEaJzs5EgyIYQQ4kqT8glx7amuVo9suOkm\nuOceNWk2QSCuyqri2B3HqEytRBuhrRWI48rK6B0VhYuNDbsCfSk9+RIpKVMJDNxK587PNBiIjxxR\nj1vTamH79rqBeEviFnov7s1A34FsGrpJArEQQgjxL5GVYnFt2b9f3Ujn4dEkG+n+UvhbIbHDYnF5\n2oUur3XBzPxcyN1w9ixPJSYyu2tXhrauIObY7djadiE0NBpLy/pLNRQFFi1SWzUvWKBWdpxPb9Tz\nxq9vsDJmJRsGb+BW91ubZB5CCCGEuDwSisW1IT9f7Uj300/w+efq8Q2X2YDjfIqicOrTU6TPTsd3\nuS9O951bqTUqCm+kprIyJ4efe/akS9VOoqOfokuXN+jc+bkGV4crKtSNdIcPqxne27v29cziTIau\nH4q9lT3RE6JpZy+tjYUQQoh/m5RPiKubosDKlWpHOmtrdSPdoEFNEogNpYb/b+/O46quEv+Pv1hV\nJJFCFIVEEBXEhcUcG/NXTVY6X8l9NzO3nNE2S5smy0ktbdqsHMctx9TMrdRMcclQcwEF0wQLNwYX\nRAUxcGG59/P746Z4R7mgcgXk/Xw8Po9H3PPh3HMex5NvP4/zOYek3kmkL0wnPDbcKhBn5OfTYd8+\n4n77jbiwZnikj+Pw4dE0a7YaX9/niwzEKSmW3SUuXIDY2OsD8bpD64icFUmHhh1Y02+NArGIiEg5\noSfFUn4dOgQjRsDp06X2It0VF365QGLXRGq0qUHYtjCcqjpdLduTnU23xES616rFmz4O/Jr4KK6u\ndYmISMDFxbPIOtetg6efhr/9DV54wTq3m8wmxseM5/OfPmdRt0U87P9wqfVFREREbp9CsZQ/eXnw\nz3/CRx9Zlky88MJtnUj3v84sP0Pyc8k0eLcBdYfUtSqbf+oULx8+zLSgIB513MHePcO4//7X8PV9\nscinw2YzTJoE06fD0qXQrp11eVp2Gn2/7ouTgxMJwxKo7V671PoiIiIipUOhWMqXKy/SNWgA8fFQ\nv36pVW0uMHP09aOcXnKaZmuaUaNV4Z7C+WYzow8fZm1mJpuahVDt9EQOnllOaOhKPDz+UGSdWVkw\nYIBlyfPu3VDXOmOz6egm+n/dn+ERw3mj3Rs4OTrduCIREREpUwrFUj5kZsLYsbB2reVFuq5dS2Xd\n8BV5p/NI6p2Eg7MDEbsjcPVyvVp2KjeXHklJ1HR2ZltTL44ndwQXLyIjE3BxKXqLtL17Le/7/fnP\nsHy5ZcnzFSaziUlbJzF993Tmd5nPYwGPlVpfREREpPTpRTspW4YBCxdaXqSrWhUSE0ttZ4krzu88\nT3xkPDUerEHztc2tAvGO8+dplZDAY56efO7zXw7ufRAvr66Ehq60GYgXLIDHHoO337Zk+GsD8ekL\np3ly4ZN8f/R74ofFKxCLiIhUAHpSLGXnyot0Z87AypXwwAOlWr1hGJz890lS3kqh8ezGeEV5WZXN\nOHmSN1NS+LxRAMG/fcyhg4sIDf0aD4+i9wzOy7OcKL1uHWzaBM2aWZdv+e8W+i7vy9MtnubtR97G\n2VFTTEREpCLQ39hy5+XlwXvvwccfF27V4Fy6fxRNF00kj0gmJyGHsG1huAW5XS27bDLxl4MHifvt\nN7Y09ebikR5ccL6HiIgEXF29iqzzxAnLbnDe3rBrF9SsWVhmNsxM+XEKU2OnMvepuXQI6lCq/RER\nERH7UiiWO2vrVsuLdAEBpf4i3RWXDl9if7f9VG9anfCd4ThVL3y5LfXyZbolJhJQtSrr/E+TkhiF\nr++L3H//GBwcil5NFBMDfftaDuV47TVwvObWjIsZDPhmAOdzz7Nr6C78PPxKvU8iIiL03rV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ZcyGbhiIGcunGFx98XUr1n/DvRARERE7mZaUyx2d+hCJkv2DCbM+Ik/hG/Cq0ZYsb9z7hwMGABZ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\nUygWERERkUpPoVhEREREKr3/D7PxWqeq3B2SAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5b99410>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "...we can see that our estimates do not vary as much.  How different are the two sets of coefficients?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate DF from coefficients\n",
      "ridge_v_reg=DataFrame({'ridge':[x[0] for x in ridge_coef_list],\n",
      "                       'reg':[x[0] for x in reg_coef_list]})\n",
      "\n",
      "#Set plot size\n",
      "plt.rcParams['figure.figsize']=12,8\n",
      "\n",
      "#Generate boxplot\n",
      "ridge_v_reg.boxplot()\n",
      "plt.title('Ridge vs. OLS Coefficients');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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M1157bZvPNXiFOkmSOP/886Nfv355w/Tq1atj7733jlwuF3Pnzo0kSbYK0xERb7zxhq41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\n4o0PnZxIEgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5f149d0>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The boxplot above captures the essence of the implications of the ridge technique.  We know that the train target and train data have a 1-to-1 direct (that is, with no proportional scaling) mapping.  Therefore, the population parameter is 1.  OLS, our BLUE estimator, shows a median estimate that is very close to this value.  There is, however, relatively substantial variation around the median estimate.\n",
      "\n",
      "The ridge regression shows dramatically less variation around its median estimate, *but the estimate is quite biased*.  The ridge median estimate is quite close to half the magnitude of the true population parameter.  The `alpha` parameter in the **Ridge** object determines how much we would like to suppress variance in the estimate."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Sparsity"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In many cases there are large differences in coverage of the parameter space across dimensions.  Looking again at the diabetes data, let us consider fitting just two of the 11 available dimensions.  (Two dimensions are chosen to aid in visual pedagogy.  The intuition from this example scales to higher dimensions.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Create filter for the first two dimensions\n",
      "indices = (0, 1)\n",
      "\n",
      "#Redefine train and test components\n",
      "diab2_X_train = diabetes.data[:-20, indices]\n",
      "diab2_X_test = diabetes.data[-20:, indices]\n",
      "diab2_y_train = diabetes.target[:-20]\n",
      "diab2_y_test = diabetes.target[-20:]\n",
      "\n",
      "#Fit new regression model\n",
      "ols = linear_model.LinearRegression()\n",
      "ols.fit(diab2_X_train,diab2_y_train)\n",
      "\n",
      "#Define function plot 3-D figures from different angles\n",
      "def plot_figs(fig_num, elev, azim,clf):\n",
      "    #Generate figure object\n",
      "    fig=plt.figure(fig_num, figsize=(4,3))\n",
      "    plt.clf()\n",
      "    #Generate 3-D axes\n",
      "    ax=Axes3D(fig,elev=elev,azim=azim)\n",
      "    #Plot data points\n",
      "    ax.scatter(diab2_X_train[:,0],diab2_X_train[:,1],diab2_y_train,c='k')\n",
      "    #Plot coefficient surface\n",
      "    ax.plot_surface(np.array([[-.1, -.1], [.15, .15]]),\n",
      "                    np.array([[-.1, .15], [-.1, .15]]),\n",
      "                    clf.predict(np.array([[-.1, -.1, .15, .15],\n",
      "                                          [-.1, .15, -.1, .15]]).T\n",
      "                                ).reshape((2, 2)),\n",
      "                    alpha=.5)\n",
      "    #Set labels\n",
      "    ax.set_xlabel('X_1')\n",
      "    ax.set_ylabel('X_2')\n",
      "    ax.set_zlabel('Y')\n",
      "    \n",
      "#Plot three views of the data\n",
      "plot_figs(1,43.5,-110,ols)\n",
      "plot_figs(3,-.5,0,ols)\n",
      "plot_figs(2,-.5,90,ols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ip0rYekQMcYW40XE+8MAD7Nixg7q6OgBGjhxJdXW1EpcTdawaGhqor68nHA6z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       "text": [
        "<matplotlib.figure.Figure at 0x5a89e50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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66g2nVMjcOhzWcNlsNrp06cKFCxdITk6mY8eO5OfnS0XBAQEB5OfnA3UfvO7d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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5f36750>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g84PD++G+nfdp4Gdg/7/8pQKA+wdp4O/33nsfTie/n0vYX+x87ts5buC13W6H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\nBwkXQRCK4/8DaScawT8yRHgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5a89f10>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When looking at the target plotted against two dimensions, data coverage looks pretty good.  If we were to estimate the impact of `X1`, we would be able to capture enough variation in the target and the data to capture a meaningful estimate.  Along the `X2` dimension, however, estimation becomes more difficult.  `X2` is binary, and either of the available values is associated with a number of target values.  Furthermore, the central tendencies of the target conditioned on both `X2` values are very similar.  The `X2` dimension can be referred to as non-informative.\n",
      "\n",
      "The tutorial recommends the [Lasso](http://en.wikipedia.org/wiki/Least_squares#Lasso_method) approach for such situations.  It is not yet clear to me why this method would be preferrable to simply dropping the variable from the model.  Perhaps this can be a topic for a future Notebook."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Classification"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For classification, linear regression is not an appropriate tool because it would give too much weight to extreme values (data that is 'far from the decision frontier').  The conventional approach for categorical responses in a machine learning context is the same one used in classical econometrics:  logistic regression.\n",
      "\n",
      "$$y = \\text{sigmoid}(X \\beta - \\text{offset}) + \\epsilon = \\frac{1}{1 + exp(-X \\beta + \\text{offset})} + \\epsilon$$\n",
      "\n",
      "[Support Vector Machines](http://en.wikipedia.org/wiki/Support_vector_machine) (SVMs) are an alternative method of deterministic classification.  In a nutshell, they look for samples of the data that enable the building of a plane that maximizes the margin between two classes.\n",
      "\n",
      "Finally, [kernel classification](http://en.wikipedia.org/wiki/Kernel_trick) is a variant of SVM that provides flexibility in capturing classes that are not linearly separable in the feature space."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Model Selection:  Choosing Estimators and Their Parameters"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The goal in machine learning is to maximize *predictive* accuracy.  When performing an analysis, the goal is to avoid overfitting the data and to acquire the best estimate of the underlying population parameter possible.  If do not split the data into training and test cases, the threat of overfitting looms large.\n",
      "\n",
      "Let us look again at the SKL's digit data.  Here we will find the score after one train/test split."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Extract data and target from the digits Bunch object\n",
      "X_digits=digits.data\n",
      "y_digits=digits.target\n",
      "\n",
      "#Create a support vector machine object\n",
      "svc=svm.SVC(C=1,kernel='linear')\n",
      "\n",
      "#Fit the data and extract the score\n",
      "svc.fit(X_digits[:-100],y_digits[:-100]).score(X_digits[-100:],y_digits[-100:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "0.97999999999999998"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To increase the predictive accuracy, we can simply increase the number times we train and test.  Splitting the data into groups for this process is called **KFold** cross-validation.  When we get multiple scores, we have a better sense of the accuracy of our model.\n",
      "\n",
      "We can fold the data and target above into three groups."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Fold the data into three groups\n",
      "X_folds=np.array_split(X_digits,3)\n",
      "y_folds=np.array_split(y_digits,3)\n",
      "\n",
      "X_folds"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "[array([[  0.,   0.,   5., ...,   0.,   0.,   0.],\n",
        "       [  0.,   0.,   0., ...,  10.,   0.,   0.],\n",
        "       [  0.,   0.,   0., ...,  16.,   9.,   0.],\n",
        "       ..., \n",
        "       [  0.,   0.,   5., ...,  16.,  11.,   2.],\n",
        "       [  0.,   0.,   6., ...,   0.,   0.,   0.],\n",
        "       [  0.,   0.,   0., ...,  12.,   0.,   0.]]),\n",
        " array([[  0.,   0.,   1., ...,  16.,  16.,   8.],\n",
        "       [  0.,   0.,  10., ...,  16.,  16.,   9.],\n",
        "       [  0.,   0.,   6., ...,  16.,  15.,   3.],\n",
        "       ..., \n",
        "       [  0.,   1.,  13., ...,   0.,   0.,   0.],\n",
        "       [  0.,   1.,   7., ...,  12.,   2.,   0.],\n",
        "       [  0.,   0.,  13., ...,   0.,   0.,   0.]]),\n",
        " array([[  0.,   0.,   0., ...,   9.,   0.,   0.],\n",
        "       [  0.,   0.,   7., ...,   8.,   0.,   0.],\n",
        "       [  0.,   0.,  12., ...,   0.,   0.,   0.],\n",
        "       ..., \n",
        "       [  0.,   0.,   1., ...,   6.,   0.,   0.],\n",
        "       [  0.,   0.,   2., ...,  12.,   0.,   0.],\n",
        "       [  0.,   0.,  10., ...,  12.,   1.,   0.]])]"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's explore the distribution of scores we get when testing across these three groups.  With each scoring iteration, we are pulling $\\frac{2}{3}$ as the train set, and testing against the remaining $\\frac{1}{3}$.  When scores are consistently high across groups, it gives us confidence in the predictive accuracy of our model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Create container for scores\n",
      "score_list=[]\n",
      "\n",
      "#For three iterations\n",
      "for i in range(3):\n",
      "    #...create a list copy of data and target...\n",
      "    X_train=list(X_folds)\n",
      "    y_train=list(y_folds)\n",
      "    #...pull out test set arrays from a third of the folded data and target...\n",
      "    X_test=X_train.pop(i)\n",
      "    y_test=y_train.pop(i)\n",
      "    #...combine the remaining two thirds into the training set...\n",
      "    X_train=np.concatenate(X_train)\n",
      "    y_train=np.concatenate(y_train)\n",
      "    #...fit and score the data for the given split...\n",
      "    score=svc.fit(X_train,y_train).score(X_test,y_test)\n",
      "    #...and capture the score\n",
      "    score_list.append(score)\n",
      "    \n",
      "#Plot scores\n",
      "plt.rcParams['figure.figsize']=8,6\n",
      "Series(score_list).plot(kind='bar',title='KFold Cross-Validation Scores - k=3')\n",
      "print '**Scores**\\n',score_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "**Scores**\n",
        "[0.93489148580968284, 0.95659432387312182, 0.93989983305509184]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wjTwXOgDMc6EDIBJc6AAJheELAECctTt8KyoqNGTIEBUWFmrBggWtnvfaa68p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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x63db590>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is a bit of a pain to write each time, so SKL has implemented some convenience functions.  In this case, once the **KFold** object has been generated, the relevant information can be extracted succinctly with a list comprehension."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate KFold object\n",
      "k_fold=cross_validation.KFold(len(X_digits),n_folds=3)\n",
      "\n",
      "#Capture scores from same model\n",
      "new_score_list=[svc.fit(X_digits[train],y_digits[train]).score(X_digits[test],y_digits[test]) for train,test in k_fold]\n",
      "\n",
      "#Plot scores\n",
      "Series(new_score_list).plot(kind='bar',title='KFold Cross-Validation Scores - k=3')\n",
      "print '**Scores**\\n',score_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "**Scores**\n",
        "[0.93489148580968284, 0.95659432387312182, 0.93989983305509184]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wjTwXOgDMc6EDIBJc6AAJheELAECctTt8KyoqNGTIEBUWFmrBggWtnvfaa68p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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x616e8d0>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In fact, if we are concerned only with the scores themselves, there is a method dedicated to this task."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Capture scores\n",
      "even_newer_scores=list(cross_validation.cross_val_score(svc, X_digits, y_digits, cv=k_fold, n_jobs=-1))\n",
      "\n",
      "#Plot scores\n",
      "Series(even_newer_scores).plot(kind='bar',title='KFold Cross-Validation Scores - k=3')\n",
      "print '**Scores**\\n',even_newer_scores"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "**Scores**\n",
        "[0.93489148580968284, 0.95659432387312182, 0.93989983305509184]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wjTwXOgDMc6EDIBJc6AAJheELAECctTt8KyoqNGTIEBUWFmrBggWtnvfaa68p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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6194890>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In addition to `KFold(n,k)`, there are other cross-validation generators as well:\n",
      "\n",
      "+ `StratifiedKFold(y,k)`:  preserves class ratios/label distribution within each fold\n",
      "+ `LeaveOneOut(n)`:  pops just one observation out instead of evenly split folds\n",
      "+ `LeaveOneLabelOut(labels)`:  pops out a group based upon a categorical identifier"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Grid-Search & Cross-Validated Estimators"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This all well and good, but this all occurs after we have developed our parameter estimates.  What if we want to employ these techniques to help us identify the appropriate estimate?"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Grid-Search"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It turns out SKL provides a class designed to pick the parameter estimates that maximize the cross-validation score.  Going back to the SVM example, one of the parameters of interest is the kernel coefficient.  We can feed a **GridSearchCV** object with a list of possible values for $\\gamma$ (the kernel coefficient), and extract which is optimal (based upon the resultant cross-validation score)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Define parameter input dictionary\n",
      "gamma_dict=dict(gamma=np.logspace(-6,2,10))\n",
      "\n",
      "#Instantiate GridSearchCV object\n",
      "gscv=grid_search.GridSearchCV(estimator=svc,param_grid=gamma_dict,n_jobs=-1)\n",
      "\n",
      "#Fit data\n",
      "gscv.fit(X_digits[:1000],y_digits[:1000])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "GridSearchCV(cv=None,\n",
        "       estimator=SVC(C=1, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=0.0,\n",
        "  kernel='linear', 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={'gamma': array([  1.00000e-06,   7.74264e-06,   5.99484e-05,   4.64159e-04,\n",
        "         3.59381e-03,   2.78256e-02,   2.15443e-01,   1.66810e+00,\n",
        "         1.29155e+01,   1.00000e+02])},\n",
        "       pre_dispatch='2*n_jobs', refit=True, score_func=None, scoring=None,\n",
        "       verbose=0)"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From here, we can ask all kinds of questions.  \n",
      "\n",
      "+ What was the best score?\n",
      "+ What was the best value of $\\gamma$?\n",
      "+ What did the distribution of scores look like?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Extract best score\n",
      "print '***Best Score***\\n',gscv.best_score_\n",
      "\n",
      "#Extract best gamma value\n",
      "print '\\n***Best Gamma Value***\\n',gscv.best_estimator_.gamma\n",
      "\n",
      "#Create containers for gamma, mean, and std\n",
      "gamma_list=[]\n",
      "mean_list=[]\n",
      "std_list=[]\n",
      "\n",
      "#For each value of gamma...\n",
      "for i in range(len(gscv.grid_scores_)):\n",
      "    #...capture gamma, mean, and std\n",
      "    gamma_list.append(gscv.grid_scores_[i].parameters['gamma'])\n",
      "    mean_list.append(gscv.grid_scores_[i].cv_validation_scores.mean())\n",
      "    std_list.append(gscv.grid_scores_[i].cv_validation_scores.std())\n",
      "\n",
      "#Generate DF from extracted data\n",
      "gamma_performance=DataFrame({'gamma':gamma_list,\n",
      "                             'mean':mean_list,\n",
      "                             'std':std_list})\n",
      "print '\\n***Gamma Performance***'\n",
      "gamma_performance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "***Best Score***\n",
        "0.989\n",
        "\n",
        "***Best Gamma Value***\n",
        "1e-06\n",
        "\n",
        "***Gamma Performance***\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/choct155/analysis/Anaconda/lib/python2.7/site-packages/pandas/core/config.py:570: DeprecationWarning: height has been deprecated.\n",
        "\n",
        "  warnings.warn(d.msg, DeprecationWarning)\n",
        "/home/choct155/analysis/Anaconda/lib/python2.7/site-packages/pandas/core/config.py:570: DeprecationWarning: height has been deprecated.\n",
        "\n",
        "  warnings.warn(d.msg, DeprecationWarning)\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>gamma</th>\n",
        "      <th>mean</th>\n",
        "      <th>std</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td>   0.000001</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>   0.000008</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>   0.000060</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>   0.000464</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>   0.003594</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td>   0.027826</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
        "      <td>   0.215443</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td>   1.668101</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
        "      <td>  12.915497</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9</th>\n",
        "      <td> 100.000000</td>\n",
        "      <td> 0.988992</td>\n",
        "      <td> 0.007494</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "        gamma      mean       std\n",
        "0    0.000001  0.988992  0.007494\n",
        "1    0.000008  0.988992  0.007494\n",
        "2    0.000060  0.988992  0.007494\n",
        "3    0.000464  0.988992  0.007494\n",
        "4    0.003594  0.988992  0.007494\n",
        "5    0.027826  0.988992  0.007494\n",
        "6    0.215443  0.988992  0.007494\n",
        "7    1.668101  0.988992  0.007494\n",
        "8   12.915497  0.988992  0.007494\n",
        "9  100.000000  0.988992  0.007494"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To be perfectly honest, I don't know why the scores don't vary with $\\gamma$.  I will have to get into the weeds a bit more with SVM to understand if this is really an issue.\n",
      "\n",
      "In any case, we can also run two cross-validation loops in parallel:  one for gamma selection and one measuring predictive performance.  The result are unbiased estimates of scores on new data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cross_validation.cross_val_score(gscv, X_digits, y_digits)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([ 0.97996661,  0.98163606,  0.98330551])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Cross-Validate Estimators"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It turns out it's more efficient to perform cross-validation on an algorithm-by-algorithm basis.  Consequently, some estimators have their own specific cross-validation method.  For example, **lasso** objects can be cross validated with `LassoCV`."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Unsupervised Learning"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unsupervised learning differs from supervised learning in that there is no training set.  One of the primary functions that I need in my research is data-defined classification, so this is right up my alley."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "K-Means Clustering"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This technique basically amounts to least squares optimization in the local neighborhood.  The data are split into a pre-specified number of neighborhoods ($S$) such that the within neighborhood sum of squared residuals is minimized.\n",
      "\n",
      "$$\\text{argmin}_S \\sum_{i=1}^k \\sum_{x_i \\in S_i} \\lvert\\lvert x_j - \\mu_i \\rvert\\rvert^2$$\n",
      "\n",
      "The local neighborhood size is defined by the number $k$ and the minimized sum of all squared residuals.  (Note that K-Means is subject to convergence on local optima.  [Bisecting K-Means](http://minethedata.blogspot.com/2012/08/bisecting-k-means.html) has emerged as a technique to provide more reliable convergence to the global maximum.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Define variables\n",
      "X_iris=iris.data\n",
      "y_iris=iris.target\n",
      "\n",
      "#Create kmeans object\n",
      "k_means = cluster.KMeans(n_clusters=3)\n",
      "\n",
      "#Fit the data to the kmeans object\n",
      "k_means.fit(X_iris)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "KMeans(copy_x=True, init='k-means++', max_iter=300, n_clusters=3, n_init=10,\n",
        "    n_jobs=1, precompute_distances=True, random_state=None, tol=0.0001,\n",
        "    verbose=0)"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How does the classification compare with the target?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(k_means.labels_[::10])\n",
      "print(y_iris[::10])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1 1 1 1 1 0 0 0 0 0 2 2 2 2 2]\n",
        "[0 0 0 0 0 1 1 1 1 1 2 2 2 2 2]\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, we can plot these classes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate plot figure\n",
      "fig=plt.figure()\n",
      "\n",
      "#Generate 3D axes\n",
      "ax=Axes3D(fig,rect=[0,0,.95,1],elev=40,azim=133)\n",
      "\n",
      "#Plot the figure\n",
      "ax.scatter(X_iris[:, 3], X_iris[:, 0], X_iris[:, 2], c=k_means.labels_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "<mpl_toolkits.mplot3d.art3d.Patch3DCollection at 0x7372250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tAsbKzDC16KU58zxvydhWoy2qR1/zeteYvpZFUUQoFNL18/sBv8TNmLUA2HU+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\npxQKharFi91or5teZpRXri3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vSZKgvuqBCudz5gUX4E9XX40JnZ3IyTLyo0djxowZtqfK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\nQiEo9xGCQqFITr169bBhwwbMmTMHCxYsQFJSEs6fP2+zoVmtVgQFBYFlW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       "text": [
        "<matplotlib.figure.Figure at 0x708db50>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Principal Component Analysis"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Dimensionality reduction is a common problem.  In the context of my research, I need a method to compare fiscal portfolios.  Each function in an expenditure vector is a different dimension.  If I want to compare one budget to all others in a set, this gets to be a bit onerous.  Reducing the dimensions for comparisons makes it easier to do this.\n",
      "\n",
      "In many cases, dimensionality reduction techniques seek to change the basis for an observation space.  Think of it as shifting the axis in such a way as to better explain the variation along the axes themselves.  Principal component analysis is one such technique.\n",
      "\n",
      "Below we will create a 3D data set that has only two useful dimensions and explore a PCA decomposition."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate data set\n",
      "x1=np.random.normal(size=100)\n",
      "x2=np.random.normal(size=100)\n",
      "x3=x1+x2\n",
      "\n",
      "#Concatenate vectors into 3D matrix\n",
      "X=np.c_[x1,x2,x3]\n",
      "\n",
      "#Generate PCA object\n",
      "pca=decomposition.PCA()\n",
      "\n",
      "#Fit the data\n",
      "pca.fit(X)\n",
      "\n",
      "#Check variance contributions\n",
      "pca_df=DataFrame({'var':pca.explained_variance_,\n",
      "                  'var_ratio':pca.explained_variance_ratio_})\n",
      "\n",
      "pca_df"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/choct155/analysis/Anaconda/lib/python2.7/site-packages/pandas/core/config.py:570: DeprecationWarning: height has been deprecated.\n",
        "\n",
        "  warnings.warn(d.msg, DeprecationWarning)\n",
        "/home/choct155/analysis/Anaconda/lib/python2.7/site-packages/pandas/core/config.py:570: DeprecationWarning: height has been deprecated.\n",
        "\n",
        "  warnings.warn(d.msg, DeprecationWarning)\n"
       ]
      },
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>var</th>\n",
        "      <th>var_ratio</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 2.693144e+00</td>\n",
        "      <td> 7.482004e-01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 9.063516e-01</td>\n",
        "      <td> 2.517996e-01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 9.908170e-33</td>\n",
        "      <td> 2.752655e-33</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "            var     var_ratio\n",
        "0  2.693144e+00  7.482004e-01\n",
        "1  9.063516e-01  2.517996e-01\n",
        "2  9.908170e-33  2.752655e-33"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As can be seen, the third dimension adds an exceedingly small amount of variation in the data set.  Here is the original data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Generate plot figure\n",
      "fig1=plt.figure(1)\n",
      "fig2=plt.figure(2)\n",
      "fig3=plt.figure(3)\n",
      "\n",
      "#Generate 3D axes\n",
      "ax1=Axes3D(fig1,rect=[0,0,.95,1],elev=0,azim=0)\n",
      "ax2=Axes3D(fig2,rect=[0,0,.95,1],elev=90,azim=90)\n",
      "ax3=Axes3D(fig3,rect=[0,0,.95,1],elev=40,azim=133)\n",
      "\n",
      "#Plot data\n",
      "ax1.scatter(x1, x2, x3, c='k', marker='o', alpha=.4)\n",
      "ax2.scatter(x1, x2, x3, c='k', marker='o', alpha=.4)\n",
      "ax3.scatter(x1, x2, x3, c='k', marker='o', alpha=.4)\n",
      "\n",
      "#Label axes\n",
      "ax1.set_xlabel('x1')\n",
      "ax1.set_ylabel('x2')\n",
      "ax1.set_zlabel('x3')\n",
      "ax2.set_xlabel('x1')\n",
      "ax2.set_ylabel('x2')\n",
      "ax2.set_zlabel('x3')\n",
      "ax3.set_xlabel('x1')\n",
      "ax3.set_ylabel('x2')\n",
      "ax3.set_zlabel('x3')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "<matplotlib.text.Text at 0x8f27910>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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y8vKc3keiQsMQU+AqKyv1Ft9FRUXYunUrRkdHlx1igNkJjL29vbDZbNA0DdFoFOl0Wt//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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xab2fcd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1NVO6n8uXL6O9vR2lpaVwOp3o6uqC1WpFeXk55s2bB6vVOqXz5gpJkjA8PAxN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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xab2fc10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p0V5U6+kGKuUtl8uRi5duzku35zxqwqyOcttc4tb3wv5GPEi+mTD8JW74LRTs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\n7xQbDA1uzswAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xab2d950>"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What does the new basis look like?  To do this, we need to generate a plane along the two major dimensions of variation.  Let's see what the components look like first.  The plots below plot the first, second, and third components in red, green, and blue respectively."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print pca.components_\n",
      "\n",
      "#Generate new plot figure\n",
      "fig1 = plt.figure(1)\n",
      "fig2 = plt.figure(2)\n",
      "fig3 = plt.figure(3)\n",
      "\n",
      "#Generate 3D axes\n",
      "ax1 = Axes3D(fig1, rect=[0, 0, .95, 1], elev=0, azim=0)\n",
      "ax2 = Axes3D(fig2, rect=[0, 0, .95, 1], elev=90, azim=90)\n",
      "ax3 = Axes3D(fig3, rect=[0, 0, .95, 1], elev=40, azim=133)\n",
      "\n",
      "#Plot components\n",
      "ax1.scatter(pca.components_[0][0],pca.components_[0][1],pca.components_[0][2],c='r', marker='o', alpha=.4,s=1000)\n",
      "ax1.scatter(pca.components_[1][0],pca.components_[1][1],pca.components_[1][2],c='g', marker='o', alpha=.4,s=1000)\n",
      "ax1.scatter(pca.components_[2][0],pca.components_[2][1],pca.components_[2][2],c='b', marker='o', alpha=.4,s=1000)\n",
      "\n",
      "ax2.scatter(pca.components_[0][0],pca.components_[0][1],pca.components_[0][2],c='r', marker='o', alpha=.4,s=1000)\n",
      "ax2.scatter(pca.components_[1][0],pca.components_[1][1],pca.components_[1][2],c='g', marker='o', alpha=.4,s=1000)\n",
      "ax2.scatter(pca.components_[2][0],pca.components_[2][1],pca.components_[2][2],c='b', marker='o', alpha=.4,s=1000)\n",
      "\n",
      "ax3.scatter(pca.components_[0][0],pca.components_[0][1],pca.components_[0][2],c='r', marker='o', alpha=.4,s=1000)\n",
      "ax3.scatter(pca.components_[1][0],pca.components_[1][1],pca.components_[1][2],c='g', marker='o', alpha=.4,s=1000)\n",
      "ax3.scatter(pca.components_[2][0],pca.components_[2][1],pca.components_[2][2],c='b', marker='o', alpha=.4,s=1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.48653174  0.32459427  0.81112602]\n",
        " [ 0.65570842 -0.74920306 -0.09349464]\n",
        " [-0.57735027 -0.57735027  0.57735027]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 109,
       "text": [
        "<mpl_toolkits.mplot3d.art3d.Patch3DCollection at 0xab25d50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Y1BHT1N5wWHZenobddJNuqax09CJpJAYhBgCQNAUFBSqYMkWha67RoUOHdOTwYe3cs0fh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\ngUBAubm5jj7F9kSGYeiDDz7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hBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAA\nuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIh\nBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAA\nuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIh\nBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAA\nuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIh\nBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuBIhBgAAuNL/BxVxX0tpmHG/AAAAAElF\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9841610>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QJK1YsULz5s3rtUxJSYlGjBihnTt3SpI2btyoCRMmpDQngOS66KJKBYPvpXSd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\n4MGDdkQFgE8sPkqUl5cnSer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       "text": [
        "<matplotlib.figure.Figure at 0xa3dd150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8MTRJttPpQBRFtNvtmc87rxiGgW63i263i0qlgna7nVlTPgohNBoNp+dMv9+H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\nc1MmL5a7ZJ0dkUHjL9I+njT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TJ/BQtYpbPvABNBoNDIdDrKyswLIsLC4uxiZe2DykrCHx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\nf/7hhx9+QKVSkZSUNKaxhRDe8z9MYNeinPAnsQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb064890>"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It may be easier to perceive these points in space with an animation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import animation\n",
      "from JSAnimation.IPython_display import display_animation\n",
      "\n",
      "#Generate new plot figure\n",
      "fig = plt.figure()\n",
      "\n",
      "#Generate axis object\n",
      "ax = Axes3D(fig)\n",
      "\n",
      "#Define function to initialize animation\n",
      "def init():\n",
      "    #Plot components\n",
      "    ax.scatter(pca.components_[0][0],pca.components_[0][1],pca.components_[0][2],c='r', marker='o', alpha=.4,s=1000)\n",
      "    ax.scatter(pca.components_[1][0],pca.components_[1][1],pca.components_[1][2],c='g', marker='o', alpha=.4,s=1000)\n",
      "    ax.scatter(pca.components_[2][0],pca.components_[2][1],pca.components_[2][2],c='b', marker='o', alpha=.4,s=1000)\n",
      "\n",
      "#Define iterator function    \n",
      "def animate_components(i):\n",
      "    ax.view_init(elev=30,azim=i)\n",
      "\n",
      "#Generate animation    \n",
      "anim=animation.FuncAnimation(fig, animate_components,init_func=init,frames=90, interval=10,blit=True)\n",
      "\n",
      "display_animation(anim)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Define the Animation class */\n",
        "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
        "    this.img_id = img_id;\n",
        "    this.slider_id = slider_id;\n",
        "    this.loop_select_id = loop_select_id;\n",
        "    this.interval = interval;\n",
        "    this.current_frame = 0;\n",
        "    this.direction = 0;\n",
        "    this.timer = null;\n",
        "    this.frames = new Array(frames.length);\n",
        "\n",
        "    for (var i=0; i<frames.length; i++)\n",
        "    {\n",
        "     this.frames[i] = new Image();\n",
        "     this.frames[i].src = frames[i];\n",
        "    }\n",
        "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
        "    this.set_frame(this.current_frame);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.get_loop_state = function(){\n",
        "    var button_group = document[this.loop_select_id].state;\n",
        "    for (var i = 0; i < button_group.length; i++) {\n",
        "        var button = button_group[i];\n",
        "        if (button.checked) {\n",
        "            return button.value;\n",
        "        }\n",
        "    }\n",
        "    return undefined;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.set_frame = function(frame){\n",
        "    this.current_frame = frame;\n",
        "    document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
        "    document.getElementById(this.slider_id).value = this.current_frame;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.next_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.previous_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.first_frame = function()\n",
        "  {\n",
        "    this.set_frame(0);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.last_frame = function()\n",
        "  {\n",
        "    this.set_frame(this.frames.length - 1);\n",
        "  } \n",
        "\n",
        "  Animation.prototype.slower = function()\n",
        "  {\n",
        "    this.interval /= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.faster = function()\n",
        "  {\n",
        "    this.interval *= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_forward = function()\n",
        "  {\n",
        "    this.current_frame += 1;\n",
        "    if(this.current_frame < this.frames.length){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.first_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.last_frame();\n",
        "        this.reverse_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.last_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_reverse = function()\n",
        "  {\n",
        "    this.current_frame -= 1;\n",
        "    if(this.current_frame >= 0){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.last_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.first_frame();\n",
        "        this.play_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.first_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.pause_animation = function()\n",
        "  {\n",
        "    this.direction = 0;\n",
        "    if (this.timer){\n",
        "      clearInterval(this.timer);\n",
        "      this.timer = null;\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.play_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = 1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.reverse_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = -1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
        "  }\n",
        "</script>\n",
        "\n",
        "<div class=\"animation\" align=\"center\">\n",
        "    <img id=\"_anim_imgJOZGVJEOGTNUWDNK\">\n",
        "    <br>\n",
        "    <input id=\"_anim_sliderJOZGVJEOGTNUWDNK\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animJOZGVJEOGTNUWDNK.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.slower()\">&#8211;</button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "rV+/blxKMZUnLgAAAABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "RK5CYII=\n",
        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "AABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "Rpcle+Mf8wvgJ16zo/4BtQAAAABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+H\n",
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        "FnSONdiL8Qci0lzwpOM5sQAAAABJRU5ErkJggg==\n",
        "\"></button>\n",
        "    <button onclick=\"animJOZGVJEOGTNUWDNK.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_selectJOZGVJEOGTNUWDNK\" class=\"anim_control\">\n",
        "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
        "  </form>\n",
        "</div>\n",
        "\n",
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_imgJOZGVJEOGTNUWDNK\";\n",
        "    var slider_id = \"_anim_sliderJOZGVJEOGTNUWDNK\";\n",
        "    var loop_select_id = \"_anim_loop_selectJOZGVJEOGTNUWDNK\";\n",
        "    var frames = new Array(0);\n",
        "    \n",
        "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkAAAAGwCAYAAABB4NqyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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