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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import pylab as pl\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a name='sections'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [What is IPython?](#ipython)\n",
      "- [Machine Learning](#machine learning)\n",
      "    - [Problem setting](#problem setting)\n",
      "    - [Data Representation in scikit-learn](#data representation)\n",
      "    - [Supervised vs. unsupervised learning](#supervised)\n",
      "    - [Supervised Learning: Classifying Digits](#supervised learning)\n",
      "- [Excerpt: Python is slow](#numpy)\n",
      "    - [Unsupervised Learning: Visualizing Digits](#unsupervised learning)\n",
      "- [Measuring Prediction Performance](#prediction performance)\n",
      "    - [The Importance of Splitting](#splitting)\n",
      "    - [Validation Metrics](#validation metrics)\n",
      "    - [Cross Validation](#cross validation)\n",
      "- [Overfitting and Underfitting](#overfitting underfitting)\n",
      "    - [Illustration of the Bias-Variance Tradeoff](#bias variance)\n",
      "    - [Detecting over-fitting](#detect overfitting)\n",
      "- [How do I choose what to do with my data set?](#flow chart)\n",
      "- [Showcasing sklearn algorithms](#showcasing)\n",
      "    - [Classify hand-written digits](#handwritten)\n",
      "        - [Visualizing the data](#visualizing)\n",
      "        - [Gaussian Naive Bayes Classification](#gaussian)\n",
      "        - [Quantitative Measurement of Performance](#quantitative1)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"ipython\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#What Is IPython?\n",
      "[[back to top]](#sections)\n",
      "\n",
      "##*\"Tools for the entire lifecycle of a scientific idea\"*\n",
      "\n",
      "- From **exploration** to **collaboration** to **publication** to **reproduction of results**.\n",
      "\n",
      "- Code + Description + Data + Visualization in one place = True Openness and Reproducibility!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src=\"images/ipkernel_clients.png\" width=\"40%\">\n",
      "\n",
      "Message passing is *kernel agnostic*\n",
      "\n",
      "Client view is *browser-based*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='machine learning'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Machine Learning\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Machine Learning is about building programs with **tunable parameters** (typically an\n",
      "array of floating point values) that are adjusted automatically so as to improve\n",
      "their behavior by **adapting to previously seen data.**\n",
      "\n",
      "Machine Learning can be considered a subfield of **Artificial Intelligence** since those\n",
      "algorithms can be seen as building blocks to make computers learn to behave more\n",
      "intelligently by somehow **generalizing** rather that just storing and retrieving data items\n",
      "like a database system would do."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='problem setting'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Problem setting\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In most ML applications, the data is in a 2D array of shape ``[n_samples x n_features]``,\n",
      "where the number of features is the same for each object, and each feature column refers\n",
      "to a related piece of information about each sample.\n",
      "\n",
      "Machine learning can be broken into two broad regimes:\n",
      "*supervised learning* and *unsupervised learning*.\n",
      "We\u2019ll introduce these concepts here, and discuss them in more detail below."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"data representation\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Data Representation in scikit-learn\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Data in scikit-learn is represented as a **feature matrix** and a **label vector**\n",
      "\n",
      "$$\n",
      "{\\rm feature~matrix:~~~} {\\bf X}~=~\\left[\n",
      "\\begin{matrix}\n",
      "x_{11} & x_{12} & \\cdots & x_{1D}\\\\\n",
      "x_{21} & x_{22} & \\cdots & x_{2D}\\\\\n",
      "x_{31} & x_{32} & \\cdots & x_{3D}\\\\\n",
      "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
      "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
      "x_{N1} & x_{N2} & \\cdots & x_{ND}\\\\\n",
      "\\end{matrix}\n",
      "\\right]\n",
      "$$\n",
      "\n",
      "$$\n",
      "{\\rm label~vector:~~~} {\\bf y}~=~ [y_1, y_2, y_3, \\cdots y_N]\n",
      "$$\n",
      "\n",
      "Here there are $N$ samples and $D$ features.\n",
      "Several example datasets are available in the ``sklearn.datasets`` module"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"supervised\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Supervised vs. Unsupervised Learning\n",
      "[[back to top]](#sections)\n",
      "\n",
      "The algorithms of machine learning are generally split into two basic categories: **Supervised** and **Unsupervised** learning.\n",
      "\n",
      "#### Supervised Learning\n",
      "**Supervised** learning concerns **labeled** data, and the construction of models that can be used to predict labels for new, unlabeled data.\n",
      "\n",
      "*Example:* given a set of *labeled* hand-written digits, create an algorithm which will predict the label of a new instance for which a label is not known.\n",
      "\n",
      "#### Unsupervised Learning\n",
      "**Unsupervised** learning concerns **unlabeled** data, and finding structure in the data such as clusters, important dimensions, etc."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"supervised learning\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Supervised Learning: Classifying Digits\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Let's get some digits data and show a quick classification example, using the simple-and-fast [Gaussian Naive Bayes estimator](https://en.wikipedia.org/wiki/Naive_Bayes_classifier)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets import load_digits\n",
      "digits = load_digits()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(8, 12, subplot_kw={'xticks':[], 'yticks':[]})\n",
      "\n",
      "for i in range(ax.size):\n",
      "    ax.flat[i].imshow(digits.data[i].reshape(8, 8),\n",
      "                      cmap=plt.cm.binary)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "output_type": "display_data",
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9oDa1nJ+f4+zsTIyBvb09JBIJvPvuu9jb21v7Hbrdbuzu7mIwGKBUKolxwLLQ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\nYIK/A/wfWQbVRvSKh2kAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fea7f805f10>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print digits.data.shape\n",
      "print digits.target.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1797, 64)\n",
        "(1797,)\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that the digits data has 1797 **samples** and 64 **features**: that is,\n",
      "observations of 64 measurements on each of 1797 different digits.\n",
      "\n",
      "In code, we usually denote these numbers ``n_samples`` and ``n_features``.\n",
      "\n",
      "Most machine learning algorithms implemented in scikit-learn expect data to be stored in a\n",
      "**two-dimensional array or matrix**.  The arrays can be\n",
      "either ``numpy`` arrays, or in some cases ``scipy.sparse`` matrices.\n",
      "The size of the array is expected to be `[n_samples, n_features]`\n",
      "\n",
      "- **n_samples:**   The number of samples: each sample is an item to process (e.g. classify).\n",
      "  A sample can be a document, a picture, a sound, a video, an astronomical object,\n",
      "  a row in database or CSV file,\n",
      "  or whatever you can describe with a fixed set of quantitative traits.\n",
      "- **n_features:**  The number of features or distinct traits that can be used to describe each\n",
      "  item in a quantitative manner.  Features are generally real-valued, but may be boolean or\n",
      "  discrete-valued in some cases.\n",
      "\n",
      "The number of features must be fixed in advance. However it can be very high dimensional\n",
      "(e.g. millions of features) with most of them being zeros for a given sample. This is a case\n",
      "where `scipy.sparse` matrices can be useful, in that they are\n",
      "much more memory-efficient than numpy arrays."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"numpy\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Excerpt: Python is slow\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# A silly function implemented in Python\n",
      "\n",
      "def func_python(N):\n",
      "    d = 0.0\n",
      "    for i in range(N):\n",
      "        d += (i % 3 - 1) * i\n",
      "    return d"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Use IPython timeit magic to time the execution\n",
      "%timeit func_python(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 3.45 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To compare to a compiled language, let's write the same function in fortran and use the ``f2py`` tool (included in NumPy) to compile it"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file func_fortran.f\n",
      "\n",
      "      subroutine func_fort(n, d)\n",
      "           integer, intent(in) :: n\n",
      "           double precision, intent(out) :: d\n",
      "           integer :: i\n",
      "           d = 0\n",
      "           do i = 0, n - 1\n",
      "                d = d + (mod(i, 3) - 1) * i\n",
      "           end do\n",
      "      end subroutine func_fort"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting func_fortran.f\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!f2py -c func_fortran.f -m func_fortran > /dev/null"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from func_fortran import func_fort\n",
      "%timeit func_fort(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 36.6 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fortran is about 100 times faster for this task!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Scientific computing? Use NumPy!\n",
      "\n",
      "A NumPy array in its simplest form is a Python object build around a C array. That is, it has a pointer to a *contiguous* data buffer of values. A Python list, on the other hand, has a pointer to a contiguous buffer of pointers, each of which points to a Python object which in turn has references to its data (in this case, integers).  This is a schematic of what the two might look like:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<img src=\"images/numpy.png\">"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### So Why Use Python?\n",
      "\n",
      "Given this inherent inefficiency, why would we even think about using Python? Well, it comes down to this: Dynamic typing makes Python **easier to use** than C.  It's extremely **flexible and forgiving**, this flexibility leads to **efficient use of development time**, and on those occasions that you really need the optimization of C or Fortran, **Python offers easy hooks into compiled libraries**. It's why Python use within many scientific communities has been continually growing. With all that put together, Python ends up being an extremely efficient language for the overall task of doing science with code."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### *Example:* given a set of *unlabeled* digits, determine which digits are related."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.naive_bayes import GaussianNB\n",
      "X = digits.data\n",
      "y = digits.target\n",
      "\n",
      "# Instantiate the estimator\n",
      "clf = GaussianNB()\n",
      "\n",
      "# Fit the estimator to the data, leaving out the last five samples\n",
      "clf.fit(X[:-5], y[:-5])\n",
      "\n",
      "# Use the model to predict the last several labels\n",
      "y_pred = clf.predict(X[-5:])\n",
      "\n",
      "print y_pred\n",
      "print y[-5:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[9 0 8 9 8]\n",
        "[9 0 8 9 8]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that this relatively simple model leads to a perfect classification of the last few digits!\n",
      "\n",
      "Let's use the model to predict labes for the full dataset, and plot the [**confusion matrix**](https://en.wikipedia.org/wiki/Confusion_matrix), which is a convenient visual representation of how well the classifier performs:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import metrics\n",
      "\n",
      "clf = GaussianNB()\n",
      "clf.fit(X, y)\n",
      "y_pred = clf.predict(X)\n",
      "\n",
      "def plot_confusion_matrix(y_pred, y):\n",
      "    plt.imshow(metrics.confusion_matrix(y, y_pred),\n",
      "               cmap=plt.cm.binary, interpolation='nearest')\n",
      "    plt.colorbar()\n",
      "    plt.xlabel('true value')\n",
      "    plt.ylabel('predicted value')\n",
      "    \n",
      "print \"classification accuracy:\", metrics.accuracy_score(y, y_pred)\n",
      "plot_confusion_matrix(y, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "classification accuracy: 0.827490261547\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rjogkSZyDW9CkzMN9+5PQPTcRId7d0iDBrQN7qDAOy6twHHCuuyqJSFIkObg1Am8APgK0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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fea7a4facd0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interestingly, there is confusion between some values.  In particular, the number **2** is often mistaken for the number **8** by this model!  But for the vast majority of digits, we can see that the classification looks correct.\n",
      "\n",
      "Let's use the ``metrics`` submodule again to print the accuracy of the classification:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print metrics.accuracy_score(y, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.827490261547\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have an 82% accuracy rate with this particular model.\n",
      "\n",
      "But there's a problem: we are testing the model on the data we used to train the model. This is generally not a good approach to model validation!  Because of the nature of the Naive Bayes estimator, it's alright in this case, but we'll see later examples where this approach causes problems."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"unsupervised learning\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Unsupervised Learning: Visualizing Digits\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Now let's say you'd want to visualize the relationship between the digits samples.  There are 1700 samples in 64 dimensions: if we could simply draw a 64-dimensional scatter-plot, we'd be able to see the relationships.  Unfortunately, most humans can't visualize more than 3 dimensions, so we have to project the data.\n",
      "\n",
      "Let's try a random projection solution first:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(0)\n",
      "proj = np.random.normal(size=(X.shape[1], 2))\n",
      "X_rand = np.dot(X, proj)\n",
      "\n",
      "fig, ax = plt.subplots()\n",
      "im = ax.scatter(X_rand[:, 0], X_rand[:, 1], c=y)\n",
      "fig.colorbar(im);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0a9f2ur0TKjcGSsLofnb1pbjy/jM+3evNhvUbeGFsVRRFwSfYSJ1ugaxbv5bO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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fea7a2b1710>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's now use an unsupervised learning approach to visualize this same data.  We'll reduce the dimensionality of the data using [Principal Component Analysis (PCA)](https://en.wikipedia.org/wiki/Principal_component_analysis):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.decomposition import PCA\n",
      "\n",
      "# instantiate the model\n",
      "model = PCA(n_components=2)\n",
      "\n",
      "# fit the model: notice we don't pass the labels!\n",
      "model.fit(X)\n",
      "\n",
      "# transform the data to two dimensions\n",
      "X_PCA = model.transform(X)\n",
      "print \"shape of result:\", X_PCA.shape\n",
      "\n",
      "# plot the results along with the labels\n",
      "fig, ax = plt.subplots()\n",
      "im = ax.scatter(X_PCA[:, 0], X_PCA[:, 1], c=y)\n",
      "fig.colorbar(im);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "shape of result: (1797, 2)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iUuTz9ZLdXkXw9Akr/SsFVWW32nXgVsNqK7oHVY6yFEcFFMjpHKYrr+x3kvzb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\nbddpvGvC3wvWIcDjF31eCNS8w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6wRO1+eR/7pLMwmE7bMAlZUHEx2bg7+wkLKju/Glmfn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\nLfX5iSayc0TzBnDilKG9PtbfKOcydBzM/dLgI2jTujHVb6jF0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AmvMmGCvD5x4gQOh4O4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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fea78a41b90>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We've reduced the dimensionality to two in a way that takes into account the structure of the data.\n",
      "By comparison, a random projection does not conserve this structure:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"prediction performance\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Measuring Prediction Performance\n",
      "\n",
      "An important piece of the learning task is the measurement of prediction performance, also known as **model validation**.  We'll go into detail about this, but first motivate the approach with an example."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"splitting\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Importance of Splitting\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Above we looked at a *confusion matrix*, which can be computed based on the results of any model. Let's look at another classification scheme here, the [*K-Neighbors Classifier*](https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.neighbors import KNeighborsClassifier\n",
      "from sklearn import datasets\n",
      "\n",
      "digits = datasets.load_digits()\n",
      "X, y = digits.data, digits.target\n",
      "\n",
      "clf = KNeighborsClassifier(n_neighbors=1)\n",
      "clf.fit(X, y)\n",
      "y_pred = clf.predict(X)\n",
      "\n",
      "print \"classification accuracy:\", metrics.accuracy_score(y, y_pred)\n",
      "plot_confusion_matrix(y, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "classification accuracy: 1.0\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fea7a261c90>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our classifier gives perfect results!  Have we settled on a perfect classification scheme?\n",
      "\n",
      "**No!**  The *K*-neighbors classifier is an example of an instance-based classifier, which memorizes the input data and compares any unknown sample to it.  To accurately measure the performance, we need to use a separate *validation set*, which the model has not yet seen.\n",
      "\n",
      "Scikit-learn contains utilities to split data into a training and validation set:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cross_validation import train_test_split\n",
      "\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)\n",
      "print X_train.shape, X_test.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1257, 64) (540, 64)\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf = KNeighborsClassifier(n_neighbors=1)\n",
      "clf.fit(X_train, y_train)\n",
      "y_pred = clf.predict(X_test)\n",
      "\n",
      "print \"classification accuracy:\", metrics.accuracy_score(y_test, y_pred)\n",
      "plot_confusion_matrix(y_test, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "classification accuracy: 0.985185185185\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7fea7a2caf50>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"validation metrics\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Validation Metrics\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Above, we used perhaps the most simple evaluation metric, the number of matches and mis-matches.  But this is not always sufficient.  For example, imagine you have a situation where you'd like to identify a rare class of event from within a large number of background sources (an example of this is finding objects that are in the foreground and objects that are in the background).  This \"number of matches\" metric can break down:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Generate an un-balanced 2D dataset\n",
      "np.random.seed(0)\n",
      "X = np.vstack([np.random.normal(0, 1, (950, 2)),\n",
      "               np.random.normal(-1.8, 0.8, (50, 2))])\n",
      "y = np.hstack([np.zeros(950), np.ones(50)])\n",
      "\n",
      "plt.scatter(X[:, 0], X[:, 1], c=y, edgecolors='none',\n",
      "            cmap=plt.cm.Accent)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "<matplotlib.collections.PathCollection at 0x7fea7a4ad6d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HFjxESAhxZPAIYTHM6tzVCZvEgijw1fBX8nFICLGrfRdjoTE2Fm+k39+fsFGb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UCpgIuIBKoWBfxJYAm4rga/S0REqrTZAt4KHADO1yCLU2NjY64jVEU5ayuEnCFkBOV0YbMF/DXg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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fea7a47b210>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The problem here is that we might not care how well we can classify the **background**, but might instead be concerned with successfully pulling-out an uncontaminated set of **foreground** sources.  We can get at this by computing statistics such as the **precision**, the <a href=\"https://en.wikipedia.org/wiki/Recall_(information_retrieval)\">**recall**</a>, and the [**f1 score**](https://en.wikipedia.org/wiki/F1_score).\n",
      "\n",
      "We'll use  a [*Support Vector Machine*](https://en.wikipedia.org/wiki/Support_vector_machine), and see how well the model can classify this data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import metrics\n",
      "from sklearn.svm import SVC\n",
      "\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)\n",
      "clf = SVC().fit(X_train, y_train)\n",
      "y_pred = clf.predict(X_test)\n",
      "\n",
      "print \"accuracy:\", metrics.accuracy_score(y_test, y_pred)\n",
      "print \"precision:\", metrics.precision_score(y_test, y_pred)\n",
      "print \"recall:\", metrics.recall_score(y_test, y_pred)\n",
      "print \"f1 score:\", metrics.f1_score(y_test, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "accuracy: 0.968\n",
        "precision: 0.833333333333\n",
        "recall: 0.625\n",
        "f1 score: 0.714285714286\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Whatever these values mean, they're indicating that this is not doing as well as the accuracy says it does.\n",
      "\n",
      "These are ways of taking into account not just the classification results, but the results **relative to the true category**.\n",
      "\n",
      " $$ {\\rm accuracy} \\equiv \\frac{\\rm correct~labels}{\\rm total~samples} $$\n",
      "\n",
      " $$ {\\rm precision} \\equiv \\frac{\\rm true~positives}{\\rm true~positives + false~positives} $$\n",
      "\n",
      " $$ {\\rm recall} \\equiv \\frac{\\rm true~positives}{\\rm true~positives + false~negatives} $$\n",
      "\n",
      " $$ F_1 \\equiv 2 \\frac{\\rm precision \\cdot recall}{\\rm precision + recall} $$\n",
      "\n",
      "The **accuracy**, **precision**, **recall**, and **f1-score** all range from 0 to 1, with 1 being optimal.\n",
      "Here we've used the following definitions:\n",
      "\n",
      "- *True Positives* are those which are labeled ``1`` which are actually ``1``\n",
      "- *False Positives* are those which are labeled ``1`` which are actually ``0``\n",
      "- *True Negatives* are those which are labeled ``0`` which are actually ``0``\n",
      "- *False Negatives* are those which are labeled ``0`` which are actually ``1``\n",
      "\n",
      "So the precision says, that all the lables, that're labeled as 1, out of 83% are actually correct.\n",
      "\n",
      "The recall says, out of all the things we're looking for this algorithm does find only 63% and it does find this things with a precision about 84%.\n",
      "\n",
      "In the end it turns out, depending on the problem itself, it is not so clear whether you're more interested in the overall precision or in the recall.\n",
      "\n",
      "That is why the $F_1$ comes into play, combining those two metrics\n",
      "\n",
      "We can quickly compute a summary of these statistics using scikit-learn's provided convenience function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print metrics.classification_report(y_test, y_pred,\n",
      "                                    target_names=['background', 'foreground'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "             precision    recall  f1-score   support\n",
        "\n",
        " background       0.97      0.99      0.98       234\n",
        " foreground       0.83      0.62      0.71        16\n",
        "\n",
        "avg / total       0.97      0.97      0.97       250\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This tells us that, though the overall correct classification rate is 97%, we only correctly identify 67% of the desired samples, and those that we label as positives are only 83% correct!  This is why you should make sure to carefully choose your metric when validating a model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"excersice\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Excersise\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compare the *K Neighbors Classifier*, the *Gaussian Naive Bayes Classifier*, and the *Support Vector Machine Classifier* on this toy dataset, using their default parameters.  Which is most accurate?  Which is most precise?  Which has the best recall?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Equal Interface"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One of the reason the *scikit-learn* interface is really nice is, because the interface is designed in such a way, that for every *machine learning* model (algorithm), it has for all the different models a uniform interface:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn import metrics\n",
      "from sklearn.svm import SVC\n",
      "\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)\n",
      "\n",
      "for Model in [SVC, KNeighborsClassifier, GaussianNB]:\n",
      "    clf = Model().fit(X_train, y_train)\n",
      "    y_pred = clf.predict(X_test)\n",
      "    \n",
      "    print Model\n",
      "    print \"accuracy:\", metrics.accuracy_score(y_test, y_pred)\n",
      "    print \"precision:\", metrics.precision_score(y_test, y_pred)\n",
      "    print \"recall:\", metrics.recall_score(y_test, y_pred)\n",
      "    print \"f1 score:\", metrics.f1_score(y_test, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'sklearn.svm.classes.SVC'>\n",
        "accuracy: 0.968\n",
        "precision: 0.833333333333\n",
        "recall: 0.625\n",
        "f1 score: 0.714285714286\n",
        "<class 'sklearn.neighbors.classification.KNeighborsClassifier'>\n",
        "accuracy: 0.96\n",
        "precision: 0.714285714286\n",
        "recall: 0.625\n",
        "f1 score: 0.666666666667\n",
        "<class 'sklearn.naive_bayes.GaussianNB'>\n",
        "accuracy: 0.976\n",
        "precision: 0.857142857143\n",
        "recall: 0.75\n",
        "f1 score: 0.8\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"cross validation\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Cross-Validation\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Using the simple train/test split as above can be useful, but there is a disadvantage: **You're ignoring a portion of your dataset**.  One way to address this is to use cross-validation.\n",
      "\n",
      "The simplest cross-validation scheme involves running two trials, where you split the data into two parts, first training on one, then training on the other:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X1, X2, y1, y2 = train_test_split(X, y, test_size=0.5)\n",
      "print X1.shape\n",
      "print X2.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(500, 2)\n",
        "(500, 2)\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y2_pred = SVC().fit(X1, y1).predict(X2)\n",
      "y1_pred = SVC().fit(X2, y2).predict(X1)\n",
      "\n",
      "print np.mean([metrics.precision_score(y1, y1_pred),\n",
      "               metrics.precision_score(y2, y2_pred)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.794117647059\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is known as <a href=\"https://en.wikipedia.org/wiki/Cross-validation_(statistics)#2-fold_cross-validation\">**two-fold**</a> cross-validation, and is a special case of *K*-fold cross validation.\n",
      "\n",
      "Because it's such a common routine, scikit-learn has a K-fold cross-validation scheme built-in:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cross_validation import cross_val_score\n",
      "\n",
      "# Let's do a 2-fold cross-validation of the SVC estimator\n",
      "print cross_val_score(SVC(), X, y, cv=2, scoring='precision')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.90909091  0.76190476]\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It's also possible to use ``sklearn.cross_validation.KFold`` and ``sklearn.cross_validation.StratifiedKFold`` directly, as well as other cross-validation models which you can find in the ``cross_validation`` module."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"overfitting underfitting\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Overfitting, Underfitting and Model Selection\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Now that we've gone over the basics of metrics, validation, and cross-validation, it's time to go into even more depth regarding model selection.\n",
      "\n",
      "The issues associated with validation and \n",
      "cross-validation are some of the most important\n",
      "aspects of the practice of machine learning.  Selecting the optimal model\n",
      "for your data is vital, and is a piece of the problem that is not often\n",
      "appreciated by machine learning practitioners.\n",
      "\n",
      "Of core importance is the following question:\n",
      "\n",
      "**If our estimator is underperforming, how should we move forward?**\n",
      "\n",
      "- Use simpler or more complicated model?\n",
      "- Add more features to each observed data point?\n",
      "- Add more training samples?\n",
      "\n",
      "The answer is often counter-intuitive.  In particular, **Sometimes using a\n",
      "more complicated model will give _worse_ results.**  Also, **Sometimes adding\n",
      "training data will not improve your results.**  The ability to determine\n",
      "what steps will improve your model is what separates the successful machine\n",
      "learning practitioners from the unsuccessful."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"bias variance\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Illustration of the [Bias-Variance Tradeoff](https://en.wikipedia.org/wiki/Bias%E2%80%93variance_dilemma)\n",
      "[[back to top]](#sections)\n",
      "\n",
      "For this section, we'll work with a simple 1D regression problem.  This will help us to\n",
      "easily visualize the data and the model, and the results generalize easily to  higher-dimensional\n",
      "datasets.  We'll explore a simple [**linear regression**](https://en.wikipedia.org/wiki/Linear_regression) problem.\n",
      "This can be accomplished within scikit-learn with the `sklearn.linear_model` module.\n",
      "\n",
      "We'll create a simple nonlinear function that we'd like to fit"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def test_func(x, err=0.5):\n",
      "    y = 10 - 1. / (x + 0.1)\n",
      "    if err > 0:\n",
      "        y = np.random.normal(y, err)\n",
      "    return y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's create a realization of this dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def make_data(N=40, error=1.0, random_seed=1):\n",
      "    # randomly sample the data\n",
      "    np.random.seed(1)\n",
      "    X = np.random.random(N)[:, np.newaxis]\n",
      "    y = test_func(X.ravel(), error)\n",
      "    \n",
      "    return X, y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X, y = make_data(40, error=1)\n",
      "plt.scatter(X.ravel(), y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "<matplotlib.collections.PathCollection at 0x7fb0aeab1210>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EkxmF3gnYAnyL+7BFgIeB90rNo0IXESmnUDjK5XxU6CIi5WT2US4iImIiFbqI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\nIiIiIiIiIiJitv8HZ9r2iVPpPesAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0b963cc10>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now say we want to perform a regression on this data.  Let's use the built-in linear regression function to compute a fit:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X_test = np.linspace(-0.1, 1.1, 500)[:, None]\n",
      "\n",
      "from sklearn.linear_model import LinearRegression\n",
      "model = LinearRegression()\n",
      "model.fit(X, y)\n",
      "y_test = model.predict(X_test)\n",
      "\n",
      "plt.scatter(X.ravel(), y)\n",
      "plt.plot(X_test.ravel(), y_test)\n",
      "print \"mean squared error:\", metrics.mean_squared_error(model.predict(X), y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean squared error: 1.78514645061\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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o0V+5775hHD/+KHa98jCgHGXK9KJly285+2z/xi8i/qOEHuTmzp3GBRcsJjr6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\niIiIiIiIiIiIiIiIiIiISKD9Px0yfg76kWI1AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0b9622d90>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have fit a straight line to the data, but clearly this model is not a good choice.  We say that this model is **biased**, or that it **under-fits** the data.\n",
      "\n",
      "Let's try to improve this by creating a more complicated model.  We can do this by adding degrees of freedom, and computing a [*polynomial regression*](https://en.wikipedia.org/wiki/Polynomial_regression) over the inputs.  Let's make this easier by creating a quick PolynomialRegression estimator:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class PolynomialRegression(LinearRegression):\n",
      "    \"\"\"Simple Polynomial Regression to 1D data\"\"\"\n",
      "    def __init__(self, degree=1, **kwargs):\n",
      "        self.degree = degree\n",
      "        LinearRegression.__init__(self, **kwargs)\n",
      "        \n",
      "    def fit(self, X, y):\n",
      "        if X.shape[1] != 1:\n",
      "            raise ValueError(\"Only 1D data valid here\")\n",
      "        Xp = X ** (1 + np.arange(self.degree))\n",
      "        return LinearRegression.fit(self, Xp, y)\n",
      "        \n",
      "    def predict(self, X):\n",
      "        Xp = X ** (1 + np.arange(self.degree))\n",
      "        return LinearRegression.predict(self, Xp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we'll use this to fit a quadratic curve to the data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = PolynomialRegression(degree=2)\n",
      "model.fit(X, y)\n",
      "y_test = model.predict(X_test)\n",
      "\n",
      "plt.scatter(X.ravel(), y)\n",
      "plt.plot(X_test.ravel(), y_test)\n",
      "print \"mean squared error:\", metrics.mean_squared_error(model.predict(X), y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean squared error: 0.919717192242\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i8Hhu2yDcHz/hSa7EHwpcjTVew4G117UBq65rN1fiH4X1izoOa0zJ\ncqw5nJK9F5ZH+eu2WxQubbvFTegdz/HYAaxkvx+oChwsoF0o1s/Qj4CFxYzDE/7EOkh7Ug1O/zQu\nqE313Pv8gSvxg3Uw5V2sOty5fuL5mivxN8YqBYBVw+2CVR5Y5PXoCudK/HuxyixpuZe1WAnRHxK6\nK/G3BP6dez0R+BWoj/Vrw9/587brKlu33Rc5faT8cfI/KBoETAcm+CqocwjB+pDWxupXX9hB0Rb4\n14EVV+KviVUnbeHTyFzjSvx5TcW/erm4Ev8lwAqsA5AOrANgDX0X4jm5Ev8rwNO51ytjJfzzfRSf\nK2rj2kFRf9t2T6pNwfHbvu2ej/XhPbvbYjXg89zrrbBmatyC1ZUrAevbxy5dsHra/MzpaYDvyr2c\n9Hru4z9g/Xz2J4XF/x7WgayT7/V3vg6wEK68/yf5W0IH1+J/BKuny1bs76Z7tsLir4g1d9MPWPEP\n9HWA5/AJVm0/E+uX0G2UrG23sPj9fdsVEREREREREREREREREREREREREREREREREbv9P00cnM2v\n+8asAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0ae078e10>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This reduces the [*mean squared error*](https://en.wikipedia.org/wiki/Mean_squared_error), and makes a much better fit.  What happens if we use an even higher-degree polynomial?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = PolynomialRegression(degree=30)\n",
      "model.fit(X, y)\n",
      "y_test = model.predict(X_test)\n",
      "\n",
      "plt.scatter(X.ravel(), y)\n",
      "plt.plot(X_test.ravel(), y_test)\n",
      "plt.ylim(-4, 14)\n",
      "print \"mean squared error:\", metrics.mean_squared_error(model.predict(X), y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "mean squared error: 0.375554333023\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Lii3bDJojrviRpG7fsmV6To/bbrO+zYQJ46hVawJLly6gcuVyJCauITIykgED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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0aea8d8d0>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When we increase the degree to this extent, it's clear that the resulting fit is no longer reflecting the true underlying distribution, but is more sensitive to the noise in the training data. For this reason, we call it a **high-variance model**, and we say that it **over-fits** the data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name=\"detect overfitting\"/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Detecting over-fitting\n",
      "[[back to top]](#sections)\n",
      "\n",
      "Clearly, computing the error on the training data is not enough (we saw this previously).  But computing this *training error* can help us determine what's going on: in particular, comparing the training error and the validation error can give you an indication of how well your data is being fit.\n",
      "\n",
      "Let's do this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "degrees = np.arange(1, 30)\n",
      "\n",
      "X, y = make_data(100, error=1.0)\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)\n",
      "\n",
      "training_error = []\n",
      "test_error = []\n",
      "mse = metrics.mean_squared_error\n",
      "\n",
      "for d in degrees:\n",
      "    model = PolynomialRegression(d).fit(X_train, y_train)\n",
      "    training_error.append(mse(model.predict(X_train), y_train))\n",
      "    test_error.append(mse(model.predict(X_test), y_test))\n",
      "    \n",
      "# note that the test error can also be computed via cross-validation\n",
      "plt.plot(degrees, training_error, label='training')\n",
      "plt.plot(degrees, test_error, label='test')\n",
      "plt.legend()\n",
      "plt.xlabel('degree')\n",
      "plt.ylabel('MSE')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "<matplotlib.text.Text at 0x7fb0b9622a50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Yzv772bz0zUt8uutTNhZs5GDpQaprqj17QD+w4/AOhswews4jO/n+nu+VDERs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\niIiIiIiIiIiIiIiIiIiI7/1/Y6EDBHhpl3sAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0ade70a50>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is a typical bias/variance plot.\n",
      "\n",
      "On the **Left Side** of the plot, we have a **high-bias** model, characterized by the training and test data showing equally bad performance.  This shows that the model is **under-fitting** the data, because it does equally poorly on both known and unknown values.\n",
      "\n",
      "On the **Right Side** of the plot, we have a **high-variance model**, characterized by a divergence of the training and test data.  Here the model is **over-fitting** the data: in other words, the particular noise distribution of the input data has too much effect on the result.\n",
      "\n",
      "The optimal model here will be around the point where the **test** error is minimized."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='flow chart'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# How do I choose what to do with my data set?\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<img src=\"images/ml_map.png\">"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='showcasing'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Showcasing sklearn algorithms\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='handwritten'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Classify hand-written digits\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets import load_digits\n",
      "digits = load_digits()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# copied from notebook 02A_representation_of_data.ipynb\n",
      "fig = plt.figure(figsize=(6, 6))  # figure size in inches\n",
      "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n",
      "\n",
      "# plot the digits: each image is 8x8 pixels\n",
      "for i in range(64):\n",
      "    ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n",
      "    ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')\n",
      "    \n",
      "    # label the image with the target value\n",
      "    ax.text(0, 7, str(digits.target[i]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Tpk1oaWlBIBDAww8/jDfeeANLly697v8zE79W9NhpmZmZWL16NebOnYtBgwYh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0af1a3610>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='visualizing'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Visualizing the Data\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A good first-step for many problems is to visualize the data using one of the\n",
      "[*Dimensionality Reduction*](https://en.wikipedia.org/wiki/Dimensionality_reduction) techniques we saw earlier.  We'll start with the\n",
      "most straightforward one, Principal Component Analysis (PCA).\n",
      "\n",
      "PCA seeks orthogonal linear combinations of the features which show the greatest\n",
      "variance, and as such, can help give you a good idea of the structure of the\n",
      "data set.  Here we'll use `RandomizedPCA`, because it's faster for large `N`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.decomposition import RandomizedPCA\n",
      "pca = RandomizedPCA(n_components=2)\n",
      "proj = pca.fit_transform(digits.data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n",
      "_ = plt.colorbar()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uu1xhYcq4oNQafawjGn3ZpUfsM3XKFMWEezW6mUvtU31q2bSBcnJy9MZrr6lW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W6vQ4/tbKLF6qSFZ9soGO2W121R6yZo3RJUtwa6qS06k462rkLRkXatWbOmuN2cnBzFlgjV0gWm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\no9FoNBqNRqPRaDQajUaj0Wg0mkuN/wf8pLr1Gao0EAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0af1aa790>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we see that the digits do cluster fairly well, so we can expect even\n",
      "a fairly naive classification scheme to do a decent job separating them.\n",
      "\n",
      "A weakness of PCA is that it produces a linear dimensionality reduction:\n",
      "this may miss some interesting relationships in the data.  If we want to\n",
      "see a nonlinear mapping  of the data, we can use one of the several\n",
      "methods in the `manifold` module.  Here we'll use Isomap (a concatenation\n",
      "of Isometric Mapping) which is a manifold learning method based on\n",
      "graph theory:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.manifold import Isomap\n",
      "iso = Isomap(n_neighbors=5, n_components=2)\n",
      "proj = iso.fit_transform(digits.data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n",
      "_ = plt.colorbar()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dgDvefVoQM+t3vHo3J+W3gzg2DKAoMQu7EC9yj8Tg7OcBajXGK9lEbt1O8+bN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mHRpBEdHf1Q98Zro8ZxQV+NO7U2cCd+NYkhXXl+0LD72pQoUYL+zzyNZVMzbGEl0Zz4GA6Mhcim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\nY0QVur1RzQw+98zLB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       "text": [
        "<matplotlib.figure.Figure at 0x7fb0aebd2d50>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='gaussian'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Gaussian Naive Bayes Classification\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For most classification problems, it's nice to have a simple, fast, go-to\n",
      "method to provide a quick baseline classification.  If the simple and fast\n",
      "method is sufficient, then we don't have to waste CPU cycles on more complex\n",
      "models.  If not, we can use the results of the simple method to give us\n",
      "clues about our data.\n",
      "\n",
      "One good method to keep in mind is Gaussian Naive Bayes.  It is a *generative*\n",
      "classifier which fits an axis-aligned multi-dimensional Gaussian distribution to\n",
      "each training label, and uses this to quickly give a rough classification.  It\n",
      "is generally not sufficiently accurate for real-world data, but can perform surprisingly well."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.naive_bayes import GaussianNB\n",
      "from sklearn.cross_validation import train_test_split"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# split the data into training and validation sets\n",
      "X_train, X_test, y_train, y_test = train_test_split(digits.data, digits.target)\n",
      "\n",
      "# train the model\n",
      "clf = GaussianNB()\n",
      "clf.fit(X_train, y_train)\n",
      "\n",
      "# use the model to predict the labels of the test data\n",
      "predicted = clf.predict(X_test)\n",
      "expected = y_test"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot the digits again with the predicted labels to get an idea of\n",
      "how well the classification is working:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(6, 6))  # figure size in inches\n",
      "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n",
      "\n",
      "# plot the digits: each image is 8x8 pixels\n",
      "for i in range(64):\n",
      "    ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n",
      "    ax.imshow(X_test.reshape(-1, 8, 8)[i], cmap=plt.cm.binary,\n",
      "              interpolation='nearest')\n",
      "    \n",
      "    # label the image with the target value\n",
      "    if predicted[i] == expected[i]:\n",
      "        ax.text(0, 7, str(predicted[i]), color='green')\n",
      "    else:\n",
      "        ax.text(0, 7, str(predicted[i]), color='red')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Gi7++3vg/RtevX+9kmKZk987G7Ntn476X70NS5yQE+wYNvxho/U0rEm+FVkDe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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fb0ae958150>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>\n",
      "<a name='quantitative1'/>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Quantitative Measurement of Performance\n",
      "[[back to top]](#sections)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We'd like to measure the performance of our estimator without having to resort\n",
      "to plotting examples.  A simple method might be to simply compare the number of\n",
      "matches:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "matches = (predicted == expected)\n",
      "print matches.sum()\n",
      "print len(matches)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "376\n",
        "450\n"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "matches.sum() / float(len(matches))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "0.83555555555555561"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that nearly 1500 of the 1800 predictions match the input.  But there are other\n",
      "more sophisticated metrics that can be used to judge the performance of a classifier:\n",
      "several are available in the ``sklearn.metrics`` submodule."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "\n",
      "\n",
      "def css_styling():\n",
      "    styles = open(\"styles/custom.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunss.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-weight: bold;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsx.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-style: oblique;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunsi.otf');\n",
        "    }\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        font-weight: bold;\n",
        "        font-style: oblique;\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunso.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:800px;\n",
        "        margin-left:16% !important;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: Helvetica, serif;\n",
        "    }\n",
        "    h4{\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\n",
        "       }\n",
        "    div.text_cell_render{\n",
        "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
        "        line-height: 145%;\n",
        "        font-size: 130%;\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
        "    }\n",
        "    .prompt{\n",
        "        display: None;\n",
        "    }\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 22pt;\n",
        "        color: #4057A1;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "    \n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }  \n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<IPython.core.display.HTML at 0x7f033457b7d0>"
       ]
      }
     ],
     "prompt_number": 5
    }
   ],
   "metadata": {}
  }
 ]
}

bypass 1.0, Devloped By El Moujahidin (the source has been moved and devloped)
Email: contact@elmoujehidin.net bypass 1.0, Devloped By El Moujahidin (the source has been moved and devloped) Email: contact@elmoujehidin.net