lecture0.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "Lecture 0 - Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "The goal of this lecture is to give a basic "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's import `numpy` and `pyplot` package first\n",
      "\n",
      "[Gentle introduction to numpy library](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-2-Numpy.ipynb)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Drawing Samples from Distribution##"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`Dirichlet` distribution is a distribution over a multinomial distribution, which means a random sample (*\\theta*) drawn from K-dimensional `Dirichlet` can be used as a parameter of multinomial distribution. (i.e. *\\sum_i^K \\theta_i = 1, \\theta_i > 0* for all *i*)\n",
      "\n",
      "PDF of unsymmetric K-dim Dirichlet distribution (use different parameters for each dimension)\n",
      "\n",
      "$$Dir(\\vec\\theta | \\vec\\alpha) = \\frac{\\Gamma(\\sum^K \\alpha_i)}{\\prod^K \\Gamma(\\alpha_i)} \\prod^K \\theta_i^{\\alpha_i-1}$$\n",
      "\n",
      "PDF of symmetric Dirichlet distribution (use same parameter for every dimension)\n",
      "\n",
      "$$Dir(\\vec\\theta | \\alpha) = \\frac{\\Gamma(K \\alpha)}{\\Gamma(\\alpha)^K} \\prod^K \\theta_i^{\\alpha-1}$$\n",
      "\n",
      "Now, let's draw samples from Dirichlet distribution with `numpy` library"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# number of dimensions of Dirichlet distribution\n",
      "ndim = 5\n",
      "# number of samples drawn\n",
      "nsample = 10\n",
      "# parameter of dirichlet distribution\n",
      "alpha = [0.1] * ndim\n",
      "\n",
      "# drawing samples using numpy\n",
      "theta = np.random.dirichlet(alpha, size=nsample)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#plot samples using bar chart\n",
      "ndraws = 4\n",
      "plt.subplots(figsize=(12,3*ndraws/2))\n",
      "for i in xrange(ndraws):\n",
      "    plt.subplot(ndraws/2,2,i)\n",
      "    plt.bar(xrange(ndim), theta[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/arongdari/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/matplotlib/axes/_subplots.py:69: MatplotlibDeprecationWarning: The use of 0 (which ends up being the _last_ sub-plot) is deprecated in 1.4 and will raise an error in 1.5\n",
        "  mplDeprecation)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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BkiRJao4hWJIkSc0xBEuSJKk5hmBJkiQ1xxAsSZKk5hiCJUmS1BxDsCRJkppj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\nSWrO/wdiKYgRnUiTxQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10dd7ea10>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's compute the mean of one million samples from `Dir(0.1)`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# increase the sample size\n",
      "nsample = 1000000\n",
      "theta = np.random.dirichlet(alpha, size=nsample)\n",
      "np.mean(theta, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([ 0.20006261,  0.19972409,  0.20022272,  0.20010768,  0.1998829 ])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, let's compute the mean of one million samples from `Dir(1)`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha = [1]*ndim\n",
      "nsample = 1000000\n",
      "theta = np.random.dirichlet(alpha, size=nsample)\n",
      "np.mean(theta, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([ 0.20029273,  0.20002407,  0.19991972,  0.19992145,  0.19984203])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ndraws = 4\n",
      "plt.subplots(figsize=(12,3*ndraws/2))\n",
      "for i in xrange(ndraws):\n",
      "    plt.subplot(ndraws/2,2,i)\n",
      "    plt.bar(xrange(ndim), theta[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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U+3PQJO8Cfga4fBvXbjGsxeNHxpLOxCJYkobnOLBrZH8Xay26L9ENhvsEsKeq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\nYxEsSZKk5lgES5IkqTkWwZIkSWrO/w9Me2mc8HpfogAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10dd7e410>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's compute the mean of one million samples from `Dir(100)`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha = [100]*ndim\n",
      "nsample = 1000000\n",
      "theta = np.random.dirichlet(alpha, size=nsample)\n",
      "np.mean(theta, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([ 0.20001437,  0.19997349,  0.20001017,  0.200016  ,  0.19998597])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ndraws = 4\n",
      "plt.subplots(figsize=(12,3*ndraws/2))\n",
      "for i in xrange(ndraws):\n",
      "    plt.subplot(ndraws/2,2,i)\n",
      "    plt.bar(xrange(ndim), theta[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SpLvvT/KSqrpixr4A7B01G2BO08LxlUkenzh+Yjw3S5sfnaEvAHtHzQaY07Rw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\nAAzCMQAADMIxAAAM/x8Sn9TwxXcQBAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e99a410>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The averages of samples from different `Dirichlet` are almost identical, however, as the value of parameter decreases, the sparsity of samples increases."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Gaussian Mixture Model\n",
      "====================="
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this section, I will describe the collapsed Gibbs sampling algorithm for Gaussian mixture model (GMM) with known variance (assume we know the variance of each cluster).\n",
      "\n",
      "Generative process of GMM\n",
      "\n",
      "prior part\n",
      "$$\n",
      "\\mu_k \\sim N(\\mu_0, \\sigma_0) \\\\\n",
      "\\pi \\sim \\text{Dir} (\\alpha)\n",
      "$$\n",
      "\n",
      "for each data $i$\n",
      "$$\n",
      "z_i \\sim \\text{Mult}(\\pi)\\\\\n",
      "x_i \\sim N(\\mu_{z_i}, \\sigma)\n",
      "$$\n",
      "\n",
      "\n",
      "Let's start with generating 200 sample data set from 5 clusters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pi = np.array([0.2]*5)\n",
      "mu = [-5,-2.5,0,2.5,5]\n",
      "sigma = 1.\n",
      "K = 5\n",
      "\n",
      "\n",
      "num_data = 100\n",
      "x = np.zeros(num_data)\n",
      "z = np.zeros(num_data, dtype=int)\n",
      "for i in xrange(num_data):\n",
      "    z[i] = np.random.multinomial(1, pi).argmax()\n",
      "    x[i] = np.random.normal(mu[z[i]], sigma)\n",
      "    \n",
      "for k in xrange(K):\n",
      "    print 'clister', k, ' = ', np.mean(x[z == k]), ' num cases = ', np.sum(z==k)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "clister 0  =  -5.09849587101  num cases =  21\n",
        "clister 1  =  -2.36740367617  num cases =  17\n",
        "clister 2  =  0.214391568419  num cases =  26\n",
        "clister 3  =  3.05373272972  num cases =  22\n",
        "clister 4  =  4.39649752891  num cases =  14\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Collapsed Gibbs sampling for GMM\n",
      "--------------------------------\n",
      "\n",
      "\n",
      "$$\n",
      "p(z_i|z_{-i}, x, \\mu_0, \\alpha) \\propto p(x_i | z_i, x_{-i}, \\mu_0) p(z_i|z_{-i}, \\alpha)\n",
      "$$\n",
      "The first term of RHS is a conjugate posterior predictive distribution of normal-normal conjugacy, and the second term of RHS is a conjugate posterior predictive distribution of Dirichlet-multinomial conjugacy. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import norm\n",
      "from sklearn import metrics\n",
      "\n",
      "num_iter = 100\n",
      "\n",
      "s_z = np.zeros(num_data) - 1\n",
      "K = 5\n",
      "\n",
      "hyper_mu = 0.\n",
      "hyper_var = 1.\n",
      "known_var = 1.\n",
      "\n",
      "alpha = 1.\n",
      "\n",
      "rand_index_score = np.zeros(num_iter)\n",
      "trace = np.zeros([num_iter, K])\n",
      "\n",
      "for it in xrange(num_iter):\n",
      "    for i in xrange(num_data):\n",
      "        s_z[i] = -1\n",
      "        \n",
      "        prob = np.zeros(K)\n",
      "\n",
      "        for k in xrange(K):\n",
      "            sample_num = np.sum(s_z == k)\n",
      "            sample_sum = np.sum(x[s_z == k])\n",
      "            posterior_mean = (hyper_mu/hyper_var + sample_sum/known_var)/(1./hyper_var + sample_num/known_var)\n",
      "            posterior_variance = 1./(1./hyper_var + sample_num/known_var)\n",
      "            \n",
      "#            prob[k] = (sample_num+alpha) * norm.pdf(x[i], posterior_mean, posterior_variance)\n",
      "            prob[k] = norm.logpdf(x[i], posterior_mean, posterior_variance)\n",
      "            prob[k] += np.log((sample_num+alpha)/(num_data-1+alpha*K))\n",
      "            \n",
      "        prob -= prob.max()\n",
      "        prob = np.exp(prob)   \n",
      "        prob /= np.sum(prob)\n",
      "                \n",
      "        new_k = np.random.multinomial(1, prob).argmax()\n",
      "        \n",
      "        s_z[i] = new_k\n",
      "    \n",
      "    rand_index_score[it] = metrics.adjusted_rand_score(z, s_z)  \n",
      "    trace[it,:] = [np.sum(s_z == k) for k in xrange(K)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for k in xrange(K):\n",
      "    print np.mean(x[s_z == k]), np.sum(s_z == k)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "4.39330927614 21\n",
        "-5.13704960516 21\n",
        "-0.0275381820348 20\n",
        "2.26235708061 20\n",
        "-2.33804670059 18\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the rand index scores over iterations\n",
      "plot(rand_index_score)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10e2e1bd0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1138c0510>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the number of assigned data points for each cluster over iterations\n",
      "plot(trace)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[<matplotlib.lines.Line2D at 0x11513b250>,\n",
        " <matplotlib.lines.Line2D at 0x11513b4d0>,\n",
        " <matplotlib.lines.Line2D at 0x11513b710>,\n",
        " <matplotlib.lines.Line2D at 0x11513b8d0>,\n",
        " <matplotlib.lines.Line2D at 0x11513ba90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e2c31d0>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's change the prior distribution of normal from normal (unknown mean and known variance) to normal-inverse-gamma (unknown mean and variance)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import student-t distribution\n",
      "from scipy.stats import t\n",
      "\n",
      "num_iter = 100\n",
      "\n",
      "s_z = np.zeros(num_data) - 1\n",
      "K = 5\n",
      "\n",
      "hyper_mu = 0.\n",
      "hyper_var = 1.\n",
      "\n",
      "# inverse-gamma parameters\n",
      "ig_alpha = 1.\n",
      "ig_beta = 1.\n",
      "\n",
      "alpha = 1.\n",
      "\n",
      "rand_index_score = np.zeros(num_iter)\n",
      "trace = np.zeros([num_iter, K])\n",
      "\n",
      "for it in xrange(num_iter):\n",
      "    for i in xrange(num_data):\n",
      "        s_z[i] = -1\n",
      "        \n",
      "        prob = np.zeros(K)\n",
      "\n",
      "        for k in xrange(K):\n",
      "            sample_num = np.sum(s_z == k)\n",
      "            sample_sum = np.sum(x[s_z == k])\n",
      "            if sample_num != 0:\n",
      "                sample_mean = np.mean(x[s_z == k])\n",
      "            else:\n",
      "                sample_mean = 0\n",
      "            \n",
      "            posterior_mean = (hyper_mu*hyper_var+sample_num*sample_mean)/(hyper_var+sample_num)\n",
      "            posterior_var = hyper_var + sample_num\n",
      "            \n",
      "            posterior_alpha = ig_alpha + sample_num/2.0 \n",
      "            posterior_beta = ig_beta + 0.5 * np.sum((x[s_z==k]-sample_mean)**2) + 0.5*(sample_num*hyper_var)/(hyper_var + sample_num)\\\n",
      "                        *((sample_mean-hyper_mu)**2)\n",
      "                \n",
      "            # posterior predictive distribution follows student-t distribution\n",
      "            prob[k] = t.logpdf(x[i], df= 2.0*posterior_alpha, loc=posterior_mean, scale=posterior_beta*(posterior_var+1)/(posterior_var*posterior_alpha))\n",
      "            prob[k] += np.log((sample_num+alpha)/(num_data-1+alpha*K))\n",
      "            \n",
      "        prob -= prob.max()\n",
      "        prob = np.exp(prob)\n",
      "        prob /= np.sum(prob)\n",
      "                \n",
      "        new_k = np.random.multinomial(1, prob).argmax()\n",
      "        \n",
      "        s_z[i] = new_k\n",
      "    \n",
      "    rand_index_score[it] = metrics.adjusted_rand_score(z, s_z)  \n",
      "    trace[it,:] = [np.sum(s_z == k) for k in xrange(K)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the rand index scores over iterations\n",
      "plot(rand_index_score)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1151c6b90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1OcX167XIIFjO2oykEgYRaQGuA1YBy4HzReSY0D5nAUudc8uAjwBf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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11514dad0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the number of assigned data points for each cluster over iterations\n",
      "plot(trace)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1152b9e10>,\n",
        " <matplotlib.lines.Line2D at 0x1152bc0d0>,\n",
        " <matplotlib.lines.Line2D at 0x1152bc310>,\n",
        " <matplotlib.lines.Line2D at 0x1152bc4d0>,\n",
        " <matplotlib.lines.Line2D at 0x1152bc690>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ajpvDxIRquDFKoagfGjuERVi4ZWP+ILJGFkr9frj9dhXB/Nqv5X/v+HE4dkz/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\npaLe7m4nlAipoUq1xC+wLOq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b2t385Fz+qz4YD5JuaSqyvlr0otF5byfn7jnHiW0niKfi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kkqppQWIrSs0NBaYrtVZum+faSvvw29S18cayk5lgmYO1CuGimmY24lAgGx6Fzp1BbCFYzS5egy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\nwwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1151d9250>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for k in xrange(K):\n",
      "    print np.mean(x[s_z == k]), np.sum(s_z == k)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-0.508555963255 13\n",
        "0.134044712948 44\n",
        "0.391721675502 8\n",
        "-0.253489394291 18\n",
        "-0.639100806055 17\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    }
   ],
   "metadata": {}
  }
 ]
}