slice_sampling_dirichlet_process.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A (definitely buggy) implementation of a MDP Splice Sampler from Walker 2007. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are probably a bunch of bugs. Please report them :D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import math\n",
    "from sklearn.mixture import GMM\n",
    "import scipy.stats as stats\n",
    "from scipy.stats import gamma, norm, uniform\n",
    "from functools import partial\n",
    "from scipy.special import gamma\n",
    "%matplotlib inline\n",
    "def lambda_to_std(_lambda): #function for converting lambdas given in the Walker paper for usage in generation of random variates\n",
    "    return 1/(np.sqrt(_lambda))\n",
    "    \n",
    "def count_unique(val, vec): #simple function to count unique occurrences \n",
    "    counter = 0\n",
    "    for _val in vec:\n",
    "        if val == _val:\n",
    "            counter += 1\n",
    "    return counter \n",
    "\n",
    "\n",
    "def movingaverage(interval, window_size): #plotting auxiliary function \n",
    "    window = np.ones(int(window_size))/float(window_size)\n",
    "    return np.convolve(interval, window, 'same')\n",
    "\n",
    "def runningMeanFast(x, N): #plotting auxiliary function\n",
    "    return np.convolve(x, np.ones((N,))/N)[(N-1):]\n",
    "    \n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we want to generate the test data, Gaussian Mixture Models that Walker uses. Let $$f(y) = \\frac{1}{3} N(y \\mid -4, 1) + \\frac{1}{3} N(y \\mid 0, 1) + \\frac{1}{3} N(y \\mid 8, 1) $$ \n",
    "We can use sci-kit learn's GMM library to simulate the draws as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7ffa035f9bd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEZCAYAAACU3p4jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nd6JlXjbyCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa0e2e3a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm = GMM(3, n_iter=1)\n",
    "gmm.means_ = np.array([[-4], [0], [8]])\n",
    "gmm.covars_ = np.array([[1], [1], [1]]) ** 2\n",
    "gmm.weights_ = np.array([0.334, 0.333, 0.333])\n",
    "Y = gmm.sample(50)\n",
    "Y = Y.flatten()\n",
    "plt.clf()\n",
    "plt.hist(Y, bins= 35)\n",
    "plt.title('Simulated Distribution of Y')\n",
    "plt.xlabel('Y value')\n",
    "plt.ylabel('Counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will walk through a single round of the Splice Sampling. First, we need to initalize values for our latent variables.\n",
    "\n",
    "Let's walk through the initialization of variables for the $\\theta = (\\mu_j, \\sigma^2)$ first. Walker describes the conditional distributions for $\\mu_j$ and $\\lambda_j$ as follows:\n",
    "\n",
    "$$f(\\mu_j \\mid \\ldots) = N\\left( \\frac{\\xi_j \\lambda_j}{m_j \\lambda_j + s},  \\frac{1}{m_j \\lambda_j + s} \\right)$$\n",
    "\n",
    "Walker gives prior values for $\\mu_j \\sim N(0, 1/s)$, and $\\lambda \\sim N(\\epsilon, \\epsilon)$. The values for his particular example are $\\epsilon = 0.5$ and $s = 0.1$. We will initalize these below. \n",
    "\n",
    "There is also a prior on $c$ ($\\alpha$ in previous schemes), it is given as $c \\sim Gamma(a = 0.1, b = 0.1)$. We will declare those as well. \n",
    "\n",
    "Finally, using the notation from Escobar and West (1995), which Walker references for inference of $c$, we need to initalize a latent variable $\\nu$ (which is $\\eta$ in their notation) to assist with inference of $c$. Escobar and West don't really reference how $\\nu$ is initalized, but we know it's distributed according to $\\nu \\sim Beta(c+1, n)$, where $n$ is the number of observed values in $Y$, so we will just randomly initalize a value from this distribution.\n",
    "\n",
    "I'll also initalize $c$ as 1. Again, it's possible to alternatively specify it as being drawn from $Gamma(0.1,0.1)$, that alternative is commented out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "epsilon = 0.5\n",
    "s = 0.1\n",
    "s_inv = 1/s\n",
    "s_sqrt = np.sqrt(s_inv) #easier for generation with numpy.random.normal later, since we have to specify the standard deviation\n",
    "a = 0.1 \n",
    "b = 0.1 \n",
    "c = 1\n",
    "#c = np.random.gamma(0.1, 0.1)\n",
    "nu = np.random.beta(c+1, len(Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we initalize our weights $w$, our cluster assiginments (and total number of clusters) $z$, our stick breaking measures $v$, and our initial $\\theta = (\\mu, \\lambda)$. There are several ways to initalize $w$ and $k$. It's not specificed in Walker how they chose these initial values. I'll start with $k = 1$ and $w$ drawn randomly from $Beta(1, c)$. \n",
    "\n",
    "First stick-breaking value $v_0$ is equal to $w_0$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#initalize first weights\n",
    "w = []\n",
    "w.append(np.random.beta(1, c))\n",
    "\n",
    "v = []\n",
    "v.append(w[0])\n",
    "#initalize first mu (cluster mean)\n",
    "mus = []\n",
    "mus.append(np.random.normal(0, s_sqrt))\n",
    "\n",
    "#initalize first lambda (inverse sigma^2)\n",
    "lambdas = []\n",
    "lambdas.append(np.random.gamma(epsilon,1/epsilon))\n",
    "stds = [] #to keep track of actual sigma generated\n",
    "stds.append(lambda_to_std(lambdas[0]))\n",
    "z = np.zeros(len(Y)) #cluster assignments\n",
    "u = np.zeros(len(Y))\n",
    "active_ks = []\n",
    "total_ks = []\n",
    "total_cs = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One particular problem I had is with the parameterization of $Gamma$ in the Walker paper. \n",
    "\n",
    "The Gamma distribution can be parameterized either with a shape parameter $k$ and a scale parameter $\\theta$, or alternatively with a shape parameter $\\alpha = k$ and a rate parameter $\\beta = 1 / \\theta$. \n",
    "\n",
    "In Bayesian settings (according to wikipedia), the shape and rate $(\\alpha, \\beta)$ parameterization is most often used. However, Escobar and West (1995) use  $(k, \\theta)$, shape and scale, instead.  \n",
    "\n",
    "For reasons that will be clear in a few minutes, I'll assume that Walker uses the $Gamma(\\alpha, \\beta)$ parameterization, and Escobar and West uses $Gamma(k, \\theta)$. \n",
    "\n",
    "Note that numpy.random.gamma uses the $k, \\theta$ notation, so i'll be inverting most of the 2nd parameters in Walker."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One iteration of slice sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do the first step of slice sampling. We first want to initalize our auxiliary variable $u$. Recall the step for generating this is given below:\n",
    "\n",
    "For $i=1 \\dots n$, pick $u_i \\sim U(0,w_{k_i})$, choose $u^* = min\\{u_1 \\dots u_n\\}$\n",
    "\n",
    "Where $n$ is the number of observations in $Y$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0084831435529\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEKCAYAAAD3tSVSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIS9JDTPkJalh/x/bBMyqcMggEgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa03404250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "    u = np.zeros(len(Y))\n",
    "    for idx, val in enumerate(Y):\n",
    "        cluster_label = int(z[idx]) #vector z holds all the current cluster assignments indexed 0...k-1\n",
    "        u[idx] = np.random.uniform(0, w[cluster_label]) #we can fetch the current w_k from the w vector, with same indexing scheme as k\n",
    "    #min u \n",
    "    u_star = np.min(u)\n",
    "    plt.hist(u, bins=25)\n",
    "    plt.title('Distribution of u')\n",
    "    print u_star"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's do the next step, which is: \n",
    "\n",
    "Create new components through stick breaking until we have $k^*$\n",
    "\n",
    "To do this, we can re-formulate the equation:\n",
    "$$\\sum_{j=1}^{k^*} w_j > 1-u^*$$\n",
    "\n",
    "We can re-arrange to derive, $\\beta^*$, which is $1 - \\sum_{j=1}^{k^*} w_j$. Now we see that the above condition is now:\n",
    "\n",
    "$$u^* > \\sum_{j=1}^{k^*} w_j$$\n",
    "$$u^* > \\beta^*$$\n",
    "So while this above expression is not true, we need to generate more components $k$ until we reach $k^*$.\n",
    "\n",
    "For each new $k$ that is generated, we can draw the corresponding $\\theta = (u, \\sigma^2)$ values straight from the priors specified earlier\n",
    "\n",
    "The stick-breaking lengths corresponding to each new segment is  generated as \n",
    "\n",
    "$$v_{k} = Beta(1, c)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "    beta_star = 1 - np.sum(w)\n",
    "\n",
    "    while (beta_star >= u_star): #generate a new k while this condition is true\n",
    "        _vk = np.random.beta(1, c)\n",
    "        beta_k = _vk * beta_star\n",
    "        \n",
    "        #append beta_k to the weights\n",
    "        w.append(beta_k)\n",
    "            \n",
    "        #append _vk to v\n",
    "        v.append(_vk)\n",
    "        \n",
    "        #append new mu to mus \n",
    "        mus.append(np.random.normal(0, s_sqrt)) #draw from our prior N(0, 1/s)\n",
    "        \n",
    "        #append new lambda to lambda\n",
    "        new_lambd = np.random.gamma(epsilon, 1/epsilon) #draw from Gamma(epsilon, epsilon)\n",
    "        lambdas.append(new_lambd)\n",
    "\n",
    "        \n",
    "        #finally update beta_star\n",
    "        beta_star = beta_star*(1 -_vk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that $\\beta^*$ is now below $u^*$. \n",
    "\n",
    "Additionally, we can inspect the number of instantiated components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta star is 0.00723562694353\n",
      "u star is 0.0084831435529\n",
      "Number of instianted components is  12\n",
      "sample means for each new cluster\n",
      "[3.492266298341146, -1.3646793921728757, 1.2455967035219233, -3.004244525275804, -0.7536826018453914, 6.110083861132122, 1.1252617123250122, -4.016293364696706, -2.227040515635054, -0.7604725536515271, -2.3670532248556673, -0.3419210395158843]\n",
      "lambdas for each new cluster\n",
      "[3.4345549702195637, 0.23871155605118105, 3.027268816411562, 0.003181411490288357, 0.057300934106158954, 0.02540565665622101, 3.4984740178777405, 1.125634821233331, 1.303443874982055, 0.35296367601129747, 2.002011176727681, 0.3827998157092762]\n",
      "Sigma (translated lambda)\n",
      "[0.53959108303488057, 2.0467428321026926, 0.57474407963608243, 17.729238296788047, 4.1775258805120616, 6.2738594866053212, 0.53463904647809823, 0.94254314735205402, 0.87589860001920239, 1.6831971731006614, 0.7067515199234734, 1.6162708486473381]\n"
     ]
    }
   ],
   "source": [
    "print \"Beta star is\", beta_star\n",
    "print \"u star is\" , u_star\n",
    "print \"Number of instianted components is \" , len(w)\n",
    "print \"sample means for each new cluster\"\n",
    "print mus\n",
    "print \"lambdas for each new cluster\"\n",
    "print lambdas\n",
    "#convert lambdas to sigmas\n",
    "sigma = [lambda_to_std(x) for x in lambdas]\n",
    "print \"Sigma (translated lambda)\"\n",
    "print sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the optimal number of potential components $k^*$, we can start assigning our observed points in $Y$ to these clusters. \n",
    "\n",
    "This is given by the following equation: \n",
    "\n",
    "$$ p(\\delta_i  = k| y_i, u_i, w, \\theta) \\propto  1{\\{k:w_k > u^* \\}}P(y_i|\\theta_k)$$\n",
    "\n",
    "It's perhaps easier to express this as:\n",
    "\n",
    "$$ p(\\delta_i  = k| y_i, u_i, w, \\theta) \\propto \\begin{cases} N(y_{i} \\mid \\theta_k) & \\text{if } w_k \\geq u_{i} \\\\ 0 & \\text{otherwise} \\end{cases}$$\n",
    "\n",
    "We'll use the scipy normal distribution to generate the pdf for each $Y_{i}$ for each cluster. We can then renormalize these weights and draw from this discrete distribution use scipy custom r.v. object. These assignments will form the new $z$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  3.  3.  0.  1.  0.  3.  0.  0.  0.  0.  0.  3.  0.  0.  3.  0.\n",
      "  0.  0.  0.  0.  0.  0.  3.  0.  0.  2.  0.  3.  3.  0.  1.  0.  0.  0.\n",
      "  3.  3.  0.  0.  3.  0.  3.  0.  0.  0.  2.  2.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "    assert len(w) == len(mus)\n",
    "    assert len(w) == len(lambdas)\n",
    "    \n",
    "    #now we get the cluster assignments z for each observation\n",
    "    for y_idx , y_val in enumerate(Y):\n",
    "        z_probs = np.zeros(len(w)) #initalize placeholder for new zs\n",
    "        for cluster_idx, mu in enumerate(mus):\n",
    "            if w[cluster_idx] > u[y_idx]:\n",
    "                z_probs[cluster_idx] = norm.pdf(y_val, loc = mu, scale = lambda_to_std(lambdas[cluster_idx]))\n",
    "            else:\n",
    "                z_probs[cluster_idx] = 0\n",
    "        #sample cluster assignments\n",
    "        norm_z_probs = z_probs / np.sum(z_probs) #normalize and feed into a discrete r.v.\n",
    "        z_sampler = stats.rv_discrete(name = \"z_sampler\", values = (np.arange(len(z_probs)), norm_z_probs))\n",
    "        z_assignment = z_sampler.rvs()\n",
    "        z[y_idx] = z_assignment #grab z_assignment\n",
    "        #print \"%i\\t%0.03f\\t%0.03f\\t%0.03f\\t%i\"%(y_idx, y_val, mu_)\n",
    "    \n",
    "    z_ints = [int(x) for x in z] #make z ints for easier use in future \n",
    "    print z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see how the cluster assignments turned out. We don't expect these to be great. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7ffa02e72690>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEZCAYAAABrUHmEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02cc5e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(z, Y)\n",
    "plt.title('Cluster assignment vs Y value')\n",
    "plt.xlabel('Cluster assignment')\n",
    "plt.ylabel('Y value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we observe here, we only used 4 of the 12 total possible $k^*$. This is perhaps a downside of $Y$, in the sense that our \"dynamic truncation\" is potentially causing us to waste computational resources to sample $w_k$ and calculate $p(\\delta_{i} \\mid \\ldots)$ for a large number of clusters that we may not necessarily care about."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's update our $\\theta$. This involves updating $\\mu$ and $\\lambda$. We know that the updates (from Walker section 4) to be:\n",
    "\n",
    "$$f(\\mu_j \\mid \\ldots) = N\\left( \\frac{\\xi_j \\lambda_j}{m_j \\lambda_j + s},  \\frac{1}{m_j \\lambda_j + s} \\right)$$\n",
    "Where,\n",
    "$$\\xi_j = \\sum_{k_{i} = j} y_{i}$$\n",
    "$$m_j = \\sum_{k_{i} = j} 1$$\n",
    "\n",
    "The updates for $\\lambda_j$ is as follows:\n",
    "$$f(\\lambda_j \\mid \\ldots) = Gamma(\\epsilon + m_j/2 , \\epsilon + d_j/2)$$\n",
    "where,\n",
    "$$d_j = \\sum_{k_{i} = j } (y_{i} - \\theta_j)^2$$\n",
    "\n",
    "I'm unsure why Walker used $\\theta_j$ instead of $\\mu_j$ here...as I'm unsure of how to incorporate $\\theta = (\\mu, \\lambda)$ information. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "    z_ints = [int(x) for x in z] #make z ints for easier use in future \n",
    "    \n",
    "    #perform necessary updates for means and lambdas for each cluster \n",
    "    new_mus = []\n",
    "    new_lambdas = []\n",
    "    new_z = np.zeros(len(Y))\n",
    "    active_cluster = 0\n",
    "    count_dict = {}\n",
    "    \n",
    "    for cluster_idx in range(len(w)):\n",
    "        #update means\n",
    "        cur_lambda = lambdas[cluster_idx]    \n",
    "        eta = 0\n",
    "        m = 0\n",
    "        y_k = []\n",
    "        for y_idx, z_val in enumerate(z_ints):\n",
    "            if z_val == cluster_idx:\n",
    "                m += 1\n",
    "                eta += Y[y_idx]\n",
    "                y_k.append(Y[y_idx])\n",
    "                new_z[y_idx] = active_cluster\n",
    "        \n",
    "        if m == 0: #if un-utilized cluster, skip and don't add weights/means\n",
    "            continue\n",
    "        else:\n",
    "            count_dict[active_cluster] = m\n",
    "            active_cluster += 1        \n",
    "            _mean = (eta * cur_lambda)/(m * cur_lambda + s)\n",
    "            _variance = 1 / (m * cur_lambda + s)\n",
    "            new_mu = np.random.normal(_mean, np.sqrt(_variance)) #draw new mu from N()\n",
    "            #mus[cluster_idx] = new_mu\n",
    "            new_mus.append(new_mu)\n",
    "            #update lambda\n",
    "            d = 0\n",
    "            for val in y_k:\n",
    "                d += (val - new_mu) ** 2 #calculate d_j\n",
    "            \n",
    "            _alpha = epsilon + m/2\n",
    "            _beta = epsilon + d/2\n",
    "            new_lambda = np.random.gamma(_alpha, 1/_beta) #draw new lambda from Gamma\n",
    "            #lambdas[cluster_idx] = new_lambda\n",
    "            #print \"added at %i\"%(cluster_idx)\n",
    "            new_lambdas.append(new_lambda)\n",
    "            #stds.append(lambda_to_std(new_lambda))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.3544130789819926, -1.5534969741568005, 0.34127649059096954, 0.7196369554569925]\n",
      "[0.029671530632143384, 1.6119451373185545, 7.391632465468197, 0.024707462351632955]\n",
      "[5.8053716107400453, 0.78763475552697926, 0.36781532306968484, 6.3618866773241036]\n"
     ]
    }
   ],
   "source": [
    "#inspect the new valeus\n",
    "print new_mus\n",
    "print new_lambdas\n",
    "print [lambda_to_std(x) for x in new_lambdas]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's update our $v_{k}$ and $w_{k}$ vectors. We know that \n",
    "\n",
    "$$v_k \\mid c, \\delta \\sim Beta(1+n_k, c + \\sum_{l=k+1}^{k^*} n_l)$$\n",
    "\n",
    "and\n",
    "\n",
    "$$w_k = v_k \\prod \\limits_{l=1}^{k-1}(1-v_l)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New weights are\n",
      "[0.743327730846943, 0.06775591025456462, 0.03563452743135215, 0.12976241475948386]\n",
      "They sum up to\n",
      "0.976480583292\n"
     ]
    }
   ],
   "source": [
    "    k = active_cluster \n",
    "    vks = []\n",
    "    #print count_dict\n",
    "    for cluster_idx in range(k):\n",
    "        n_k = count_dict[cluster_idx]\n",
    "        n_j = 0\n",
    "        #print range(cluster_idx + 1, k )\n",
    "        for i in range(cluster_idx+1, k):\n",
    "            n_j += count_dict[i]\n",
    "        vks.append(np.random.beta(1 + n_k, c + n_j))\n",
    "        \n",
    "    #update weights w_k\n",
    "    new_w = []\n",
    "    old_vks = []\n",
    "    for cluster_idx in range(k):\n",
    "        if cluster_idx == 0:\n",
    "            new_w.append(vks[cluster_idx])    \n",
    "            old_vks.append(1-vks[cluster_idx])\n",
    "        else:\n",
    "            #print cluster_idx\n",
    "            vj = 1 \n",
    "            for i in range(cluster_idx):\n",
    "                #print i\n",
    "                #print old_vks\n",
    "                vj *= old_vks[i]\n",
    "            new_w.append(vks[cluster_idx] * vj)\n",
    "            old_vks.append(1-vks[cluster_idx]) \n",
    "    print \"New weights are\"\n",
    "    print new_w\n",
    "    print \"They sum up to\"\n",
    "    print sum(new_w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we update $c$. I utilize the derivation from Escobar and West (1995) that Walker references (http://www.cs.berkeley.edu/~jordan/courses/281B-spring04/readings/escobar-west.pdf). This is equations 13 and 14 in their paper. Walker's updates for alpha wasn't terribly clear; however, their implementation is also included, but commented out. \n",
    "\n",
    "The full derivation is in that paper. For our purposes, we introduce a new latent variable $\\nu \\sim Beta(c + 1, n)$ that assists with updates on $c$. This $\\nu$ is $\\eta$ in Escobar and West. We derive equation 13 from Escobar and West:\n",
    "\n",
    "$$p(c \\mid \\nu, k ) \\sim \\pi_{n} G(a + k, b - \\log(\\eta)) + (1 - \\pi_{n}) G(a+ k - 1, b - \\log(\\eta)) $$\n",
    "\n",
    "where \n",
    "$$\\frac{\\pi_n}{1-\\pi_n} = \\frac{a + k -1}{n (b - \\log(\\eta))}$$\n",
    "\n",
    "Gamma here is parameterized by $(k, \\theta)$.\n",
    "\n",
    "$\\nu$ is updated as \n",
    "\n",
    "$$p(\\nu \\mid \\ldots) \\sim Beta(c + 1, n)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New value of c is  1.89279828311\n"
     ]
    }
   ],
   "source": [
    "    new_nu = np.random.beta(c + 1, len(Y)) #update nu    \n",
    "    \n",
    "    pi_n_ratio = (a + k - 1) / (len(Y) * (b - np.log10(new_nu))) #calculate ratios for c update\n",
    "    pi_1 = pi_n_ratio / (1 + pi_n_ratio)\n",
    "    pi_2 = 1 - pi_1\n",
    "    #new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, 1/ b-np.log10(new_nu))\n",
    "    new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    #new_c = ((c**k )* gamma(c) * np.random.gamma(a, b)) / (gamma(c + len(Y)))   #alternative update scheme from Walker  \n",
    "    \n",
    "    #store results\n",
    "    active_ks.append(k)\n",
    "    total_ks.append(len(w))\n",
    "    total_cs.append(new_c)\n",
    "    \n",
    "    #end of gibbs cycle, update all the variables for next round\n",
    "    mus = new_mus\n",
    "    lambdas = new_lambdas\n",
    "    z = new_z \n",
    "    c = new_c\n",
    "    nu = new_nu\n",
    "    v = vks \n",
    "    w = new_w\n",
    "    print \"New value of c is \", c\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running Slice Sampler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've completed a successful Gibbs cycle, we can run it for a short amount of time (100 or so iterations) to see what happens to all our values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On iteration 50\tBeta_star is 0.050418\tU-star is 0.000910\tActive ks 8\tAlpha is 13.598403\n",
      "\n",
      "[0.3845356029744349, 0.09653542119618165, 0.14560807779770366, 0.14935927965916357, 0.10392166700250499, 0.01161791062745882, 0.02547069229859097, 0.03253304033885927]\n"
     ]
    }
   ],
   "source": [
    "for cur_iter in range(99):\n",
    "    #print \"Starting iter %i\"%(cur_iter)\n",
    "    u = np.zeros(len(Y))\n",
    "    #grab u \n",
    "    for idx, val in enumerate(Y):\n",
    "        cluster_label = int(z[idx])\n",
    "        u[idx] = np.random.uniform(0, w[cluster_label])\n",
    "    \n",
    "    #min u \n",
    "    u_star = np.min(u)\n",
    "    \n",
    "    #find k_star and initalize components until we have enough\n",
    "    beta_star = 1 - np.sum(w)\n",
    "    if cur_iter > 1 and cur_iter % 50 == 0:\n",
    "        print \"On iteration %i\\tBeta_star is %0.06f\\tU-star is %0.06f\\tActive ks %i\\tAlpha is %0.06f\\n\"%(cur_iter, beta_star, u_star, active_ks[-1], total_cs[-1])\n",
    "        print w\n",
    "    while (beta_star >= u_star):\n",
    "        _vk = np.random.beta(1, c)\n",
    "        beta_k = _vk * beta_star\n",
    "        \n",
    "        #append beta_k to the weights\n",
    "        w.append(beta_k)\n",
    "            \n",
    "        #append _vk to v\n",
    "        v.append(_vk)\n",
    "        \n",
    "        #append new mu to mus \n",
    "        mus.append(np.random.normal(0, s_sqrt))\n",
    "        \n",
    "        #append new lambda to lambda\n",
    "        new_lambd = np.random.gamma(epsilon, 1/epsilon)\n",
    "        lambdas.append(new_lambd)\n",
    "\n",
    "        \n",
    "        #finally update beta_star\n",
    "        beta_star = beta_star*(1 -_vk)\n",
    "    \n",
    "    assert len(w) == len(mus)\n",
    "    assert len(w) == len(lambdas)\n",
    "    \n",
    "    #now we get the cluster assignments z for each observation\n",
    "    for y_idx , y_val in enumerate(Y):\n",
    "        z_probs = np.zeros(len(w))\n",
    "        for cluster_idx, mu in enumerate(mus):\n",
    "            if w[cluster_idx] > u[y_idx]:\n",
    "                z_probs[cluster_idx] = norm.pdf(y_val, loc = mu, scale = lambda_to_std(lambdas[cluster_idx]))\n",
    "            else:\n",
    "                z_probs[cluster_idx] = 0\n",
    "        #sample cluster assignments\n",
    "        norm_z_probs = z_probs / np.sum(z_probs)\n",
    "        z_sampler = stats.rv_discrete(name = \"z_sampler\", values = (np.arange(len(z_probs)), norm_z_probs))\n",
    "        z_assignment = z_sampler.rvs()\n",
    "        z[y_idx] = z_assignment\n",
    "        #print \"%i\\t%0.03f\\t%0.03f\\t%0.03f\\t%i\"%(y_idx, y_val, mu_)\n",
    "    \n",
    "    z_ints = [int(x) for x in z] #make z ints for easier use in future \n",
    "    \n",
    "    #perform necessary updates for means and lambdas for each cluster \n",
    "    new_mus = []\n",
    "    new_lambdas = []\n",
    "    new_z = np.zeros(len(Y))\n",
    "    active_cluster = 0\n",
    "    count_dict = {}\n",
    "    \n",
    "    for cluster_idx in range(len(w)):\n",
    "        #update means\n",
    "        cur_lambda = lambdas[cluster_idx]    \n",
    "        eta = 0\n",
    "        m = 0\n",
    "        y_k = []\n",
    "        for y_idx, z_val in enumerate(z_ints):\n",
    "            if z_val == cluster_idx:\n",
    "                m += 1\n",
    "                eta += Y[y_idx]\n",
    "                y_k.append(Y[y_idx])\n",
    "                new_z[y_idx] = active_cluster\n",
    "        \n",
    "        if m == 0:\n",
    "            continue\n",
    "        else:\n",
    "            count_dict[active_cluster] = m\n",
    "            active_cluster += 1        \n",
    "            _mean = (eta * cur_lambda)/(m * cur_lambda + s)\n",
    "            _variance = 1 / (m * cur_lambda + s)\n",
    "            new_mu = np.random.normal(_mean, np.sqrt(_variance))\n",
    "            #mus[cluster_idx] = new_mu\n",
    "            new_mus.append(new_mu)\n",
    "            #update lambda\n",
    "            d = 0\n",
    "            for val in y_k:\n",
    "                d += (val - new_mu) ** 2\n",
    "            \n",
    "            _alpha = epsilon + m/2\n",
    "            _beta = epsilon + d/2\n",
    "            new_lambda = np.random.gamma(_alpha, 1/_beta)\n",
    "            #lambdas[cluster_idx] = new_lambda\n",
    "            #print \"added at %i\"%(cluster_idx)\n",
    "            new_lambdas.append(new_lambda)\n",
    "            stds.append(lambda_to_std(new_lambda))\n",
    "            \n",
    "    #update the stick breaking lengths v_k \n",
    "    k = active_cluster \n",
    "    vks = []\n",
    "    #print count_dict\n",
    "    for cluster_idx in range(k):\n",
    "        n_k = count_dict[cluster_idx]\n",
    "        n_j = 0\n",
    "        #print range(cluster_idx + 1, k )\n",
    "        for i in range(cluster_idx+1, k):\n",
    "            n_j += count_dict[i]\n",
    "        vks.append(np.random.beta(1 + n_k, c + n_j))\n",
    "        \n",
    "    #update weights w_k\n",
    "    new_w = []\n",
    "    old_vks = []\n",
    "    for cluster_idx in range(k):\n",
    "        if cluster_idx == 0:\n",
    "            new_w.append(vks[cluster_idx])    \n",
    "            old_vks.append(1-vks[cluster_idx])\n",
    "        else:\n",
    "            #print cluster_idx\n",
    "            vj = 1 \n",
    "            for i in range(cluster_idx):\n",
    "                #print i\n",
    "                #print old_vks\n",
    "                vj *= old_vks[i]\n",
    "            new_w.append(vks[cluster_idx] * vj)\n",
    "            old_vks.append(1-vks[cluster_idx])   \n",
    "    \n",
    "    #lastly, update c (alpha) and nu (Escobar & West 1995, section 6)\n",
    "    #update c\n",
    "    new_nu = np.random.beta(c + 1, len(Y))    \n",
    "    \n",
    "    pi_n_ratio = (a + k - 1) / (len(Y) * (b - np.log10(new_nu)))\n",
    "    pi_1 = pi_n_ratio / (1 + pi_n_ratio)\n",
    "    pi_2 = 1 - pi_1\n",
    "    #new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    #new_c = np.random.gamma(a+k, b - np.log10(new_nu))\n",
    "    #new_c = ((c**k )* gamma(c) * np.random.gamma(0.1,10)) / (gamma(c + len(Y)))      \n",
    "    \n",
    "    #store results\n",
    "    active_ks.append(k)\n",
    "    total_ks.append(len(w))\n",
    "    total_cs.append(new_c)\n",
    "    \n",
    "    #end of gibbs cycle, update all the variables for next round\n",
    "    mus = new_mus\n",
    "    lambdas = new_lambdas\n",
    "    z = new_z \n",
    "    c = new_c\n",
    "    nu = new_nu\n",
    "    v = vks \n",
    "    w = new_w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot our current sampling iteration and how our $k$ is changing with MCMC iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEZCAYAAABmTgnDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzDI5WZiZWSYnCzMzy+RkYWZmmf4/eM4VCS0l4KwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa02992390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "plt.scatter(z , Y)\n",
    "plt.title('Representative Clustering')\n",
    "plt.xlabel('Cluster Index')\n",
    "plt.ylabel('Y value')\n",
    "plt.savefig('rep_clustv2.png',dpi=450)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7ffa0304f1d0>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEZCAYAAACU3p4jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nd6JlXjbyCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa03072c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "plt.hist(Y, bins= 35)\n",
    "plt.title('Simulated Distribution of Y')\n",
    "plt.xlabel('Y value')\n",
    "plt.ylabel('Counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like our sampler is getting the left cluster...confused. The right-most cluster is being resolved well. Or I have a bug somewhere. Who knows?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEZCAYAAACTsIJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\njuPkwhWD4ziOkwtXDI7jOE4u/h9Z3q+ZXDTewgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa028ccf90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "plt.clf()\n",
    "#plt.scatter(np.arange(len(active_ks)), active_ks)\n",
    "\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(total_ks, 10), 'b-', label='Moving average total k')\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(active_ks, 10), 'r-', label='Moving average realized k')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Clusters')\n",
    "plt.xlim((0,100))\n",
    "plt.legend(prop={'size':8})\n",
    "plt.title('Moving average of clusters vs. Gibbs Iterations')\n",
    "plt.savefig('var_c4.png', dpi=500)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's run this some more and see what happens.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On iteration 50\tBeta_star is 0.146247\tU-star is 0.000839\tActive ks 7\tAlpha is 5.304842\n",
      "\n",
      "[0.14870448606103684, 0.11762895681644388, 0.05165514858264237, 0.3304961515122182, 0.12557321635594695, 0.044896521253519533, 0.03479835679248947]\n",
      "On iteration 100\tBeta_star is 0.104520\tU-star is 0.002113\tActive ks 8\tAlpha is 4.512718\n",
      "\n",
      "[0.3420658160041864, 0.08272812177075652, 0.242193770146681, 0.11430588690408333, 0.04614446523521093, 0.03974835830903283, 0.02101916090084772, 0.007274666794291189]\n",
      "On iteration 150\tBeta_star is 0.114541\tU-star is 0.001020\tActive ks 9\tAlpha is 6.851666\n",
      "\n",
      "[0.2788750012601663, 0.08864130669213524, 0.24320516455637603, 0.012134613726573564, 0.0646604283344759, 0.04357066414763661, 0.05832974001603898, 0.031093226419411115, 0.06494928334397465]\n",
      "On iteration 200\tBeta_star is 0.048501\tU-star is 0.000195\tActive ks 10\tAlpha is 5.659168\n",
      "\n",
      "[0.3200902529171862, 0.10874595494321883, 0.1603071559915094, 0.008594813996052324, 0.06627439071206073, 0.04303467273271218, 0.09447900352450644, 0.053179250263304764, 0.0056358511532849775, 0.09115805340957815]\n",
      "On iteration 250\tBeta_star is 0.029166\tU-star is 0.001034\tActive ks 12\tAlpha is 13.152175\n",
      "\n",
      "[0.30034609373324456, 0.37846119144883705, 0.03915089555918336, 0.014624824930502819, 0.012940312836399449, 0.03722284884151371, 0.048481337597952076, 0.00856414188149011, 0.06703963786249949, 0.018964440824250087, 0.026334406971255657, 0.018704092576142427]\n",
      "On iteration 300\tBeta_star is 0.022058\tU-star is 0.002656\tActive ks 7\tAlpha is 5.079953\n",
      "\n",
      "[0.4073468788930519, 0.1960514014183512, 0.19819517061378356, 0.08761454535831584, 0.048030478038501107, 0.014089317531557028, 0.026613728480920057]\n",
      "On iteration 350\tBeta_star is 0.038625\tU-star is 0.000560\tActive ks 8\tAlpha is 8.424209\n",
      "\n",
      "[0.270314235787276, 0.3632043244745519, 0.11700207564796167, 0.07979279606182628, 0.0472266345788716, 0.03754496094530863, 0.02295198822966522, 0.023337681557210697]\n",
      "On iteration 400\tBeta_star is 0.150064\tU-star is 0.002319\tActive ks 12\tAlpha is 6.797050\n",
      "\n",
      "[0.2594723386218089, 0.05659153615669444, 0.05663393910473922, 0.07904413211553128, 0.06726343770704493, 0.02601261958389306, 0.047115656343615954, 0.06006631552212519, 0.08128689793842303, 0.08965711511966362, 0.02176336002773371, 0.005028715657646546]\n",
      "On iteration 450\tBeta_star is 0.116781\tU-star is 0.000803\tActive ks 11\tAlpha is 6.251462\n",
      "\n",
      "[0.253649327750209, 0.3499851095394016, 0.005194428607522486, 0.01559794379515953, 0.0759325834273817, 0.04793532558236075, 0.007504842392947708, 0.026441196010203092, 0.05822724863859534, 0.032534679004281045, 0.010216423962261854]\n",
      "On iteration 500\tBeta_star is 0.055941\tU-star is 0.002491\tActive ks 8\tAlpha is 9.415275\n",
      "\n",
      "[0.07367761017736059, 0.0353047832078843, 0.14030664740798415, 0.06347424566010788, 0.2654779881802823, 0.19501677976408036, 0.12162273488328551, 0.049177772069600306]\n",
      "On iteration 550\tBeta_star is 0.130157\tU-star is 0.001302\tActive ks 9\tAlpha is 5.540745\n",
      "\n",
      "[0.23094504373282176, 0.014052984406293795, 0.0970996291303056, 0.3021565103497201, 0.06512920139230245, 0.0843603110998065, 0.04202292263859886, 0.009627576833087544, 0.024448746242917856]\n",
      "On iteration 600\tBeta_star is 0.057117\tU-star is 0.000210\tActive ks 13\tAlpha is 17.562018\n",
      "\n",
      "[0.34973861292570296, 0.11935761173038412, 0.14144316335804474, 0.03698683170245606, 0.07450114443640307, 0.0782419563841671, 0.03535842922427643, 0.034074389415147316, 0.004522504036645929, 0.04618383471090341, 0.014507106248179498, 0.0056734750630716025, 0.002293793307186205]\n",
      "On iteration 650\tBeta_star is 0.096426\tU-star is 0.000135\tActive ks 10\tAlpha is 11.643206\n",
      "\n",
      "[0.3117885143638336, 0.28333428784590275, 0.041024160320252, 0.09252352944972222, 0.0776686939638518, 0.010082054922068135, 0.029607735748966232, 0.026993067539650445, 0.020989251999285547, 0.009562569378205916]\n",
      "On iteration 700\tBeta_star is 0.173598\tU-star is 0.000068\tActive ks 12\tAlpha is 11.902394\n",
      "\n",
      "[0.2314453483945379, 0.04942827853404409, 0.06351935834540495, 0.15920804014573303, 0.026491667504105323, 0.04335650543543267, 0.06912520592443289, 0.11709250892489514, 0.02489797558478751, 0.021584473976566248, 0.01983316135910866, 0.00041919627044261735]\n",
      "On iteration 750\tBeta_star is 0.087437\tU-star is 0.001577\tActive ks 13\tAlpha is 7.363003\n",
      "\n",
      "[0.31740687792703587, 0.05134471735708992, 0.17929988485312456, 0.040227674940490725, 0.031422705141392254, 0.06096231188890163, 0.014948400230119235, 0.06286621687965047, 0.04437904223775548, 0.0029224517656886804, 0.010364559483651694, 0.06368347299164241, 0.03273470383750487]\n",
      "On iteration 800\tBeta_star is 0.106511\tU-star is 0.000870\tActive ks 9\tAlpha is 5.049801\n",
      "\n",
      "[0.34672582233672167, 0.10639110738673564, 0.11377304982574989, 0.06204781394247675, 0.0952019634351445, 0.15318246845241232, 0.008618445350269646, 0.0030144417964303575, 0.0045335552740530605]\n",
      "On iteration 850\tBeta_star is 0.079352\tU-star is 0.000619\tActive ks 13\tAlpha is 8.830380\n",
      "\n",
      "[0.25959278806448366, 0.12372686068787489, 0.034463845493167285, 0.10080268219903814, 0.039711620857379774, 0.08476079331053418, 0.0287174998816951, 0.06518351208146468, 0.0169270374502308, 0.041257153350397376, 0.06334606364320075, 0.0102994313755432, 0.05185890694996459]\n",
      "On iteration 900\tBeta_star is 0.057106\tU-star is 0.002428\tActive ks 14\tAlpha is 8.817193\n",
      "\n",
      "[0.34912959364913226, 0.013899863710559651, 0.05169776279747329, 0.015730640714712866, 0.20092428966931364, 0.04253252376773753, 0.047251350518634105, 0.02674068803793944, 0.059364459218707845, 0.03966684509696819, 0.03152031952232617, 0.010958362820033898, 0.014656157852803236, 0.038821302531305224]\n",
      "On iteration 950\tBeta_star is 0.041143\tU-star is 0.000826\tActive ks 11\tAlpha is 7.202151\n",
      "\n",
      "[0.31451955878622145, 0.12330318656498616, 0.15660885485324572, 0.09012558076395971, 0.0686188860999723, 0.002401822300743089, 0.08164214542941411, 0.06576955439282728, 0.029699040297154138, 0.014356143832617477, 0.011811787026065768]\n",
      "On iteration 1000\tBeta_star is 0.033175\tU-star is 0.001834\tActive ks 8\tAlpha is 6.917837\n",
      "\n",
      "[0.3682115840376717, 0.10562044644841947, 0.08038350662752894, 0.2119889761935506, 0.005236050747832009, 0.11447716950916899, 0.05132612577668619, 0.0295814656103562]\n",
      "On iteration 1050\tBeta_star is 0.019832\tU-star is 0.000832\tActive ks 5\tAlpha is 4.276222\n",
      "\n",
      "[0.1918550210833455, 0.35775746371833084, 0.053932629602562114, 0.28038486491338127, 0.0962380700853725]\n",
      "On iteration 1100\tBeta_star is 0.055812\tU-star is 0.000863\tActive ks 10\tAlpha is 10.987802\n",
      "\n",
      "[0.33046136713353746, 0.050047730459761075, 0.05234457495158104, 0.15001760803283523, 0.06718929473572921, 0.10371240186548211, 0.04239573701551177, 0.0989101806156546, 0.029055307254404417, 0.02005401892236858]\n",
      "On iteration 1150\tBeta_star is 0.131708\tU-star is 0.000711\tActive ks 12\tAlpha is 8.472595\n",
      "\n",
      "[0.1690817038100171, 0.21935784290406304, 0.1936647293960574, 0.009796149055142044, 0.022448303267216557, 0.06094531918442047, 0.05707593377937542, 0.0174635608010813, 0.06669528959290952, 0.011857591155436506, 0.009463379462830043, 0.030442202925397167]\n",
      "On iteration 1200\tBeta_star is 0.061014\tU-star is 0.000203\tActive ks 7\tAlpha is 5.869961\n",
      "\n",
      "[0.4196236818317362, 0.31840444212060914, 0.055346122630317976, 0.11255418924681013, 0.019340854142645622, 0.0051577434974599875, 0.008558947181535258]\n",
      "On iteration 1250\tBeta_star is 0.107002\tU-star is 0.000440\tActive ks 14\tAlpha is 9.853493\n",
      "\n",
      "[0.3650691561271073, 0.13715379277901868, 0.009568811179728414, 0.05128945632272273, 0.08841347245452327, 0.10529450138628323, 0.011196783034752293, 0.014392681553803455, 0.011792043497224543, 0.01979656693363673, 0.018958378704564554, 0.04593415534341231, 0.00676825304363598, 0.007370003872419207]\n",
      "On iteration 1300\tBeta_star is 0.149100\tU-star is 0.001562\tActive ks 10\tAlpha is 15.680051\n",
      "\n",
      "[0.2026220569046621, 0.14034834722078726, 0.046793246464767825, 0.20171045990085384, 0.0691148008199214, 0.05430777532077651, 0.06615163745244654, 0.03463229363404158, 0.01342695322975849, 0.021792817329531734]\n",
      "On iteration 1350\tBeta_star is 0.094017\tU-star is 0.001131\tActive ks 9\tAlpha is 6.650272\n",
      "\n",
      "[0.22417190653638308, 0.19901308865273284, 0.13157128156602282, 0.07255250699464053, 0.05040989220062868, 0.1564362098130842, 0.05003990920326971, 0.005108060318343794, 0.016679945439560855]\n",
      "On iteration 1400\tBeta_star is 0.154723\tU-star is 0.000014\tActive ks 10\tAlpha is 8.385384\n",
      "\n",
      "[0.22757525056988082, 0.03188056970588711, 0.03863732295311429, 0.13186168043709767, 0.1436850666049831, 0.02560625352296379, 0.1369249089934229, 0.024107823191959907, 0.0794283355696792, 0.005569363821610367]\n",
      "On iteration 1450\tBeta_star is 0.017297\tU-star is 0.000705\tActive ks 6\tAlpha is 5.167138\n",
      "\n",
      "[0.3662395763539927, 0.4129691282701398, 0.04479804090205645, 0.0832526678053476, 0.07386302485787806, 0.0015802942709026223]\n",
      "On iteration 1500\tBeta_star is 0.099087\tU-star is 0.000578\tActive ks 15\tAlpha is 10.968095\n",
      "\n",
      "[0.3620111433939961, 0.06488779710245265, 0.06028864676134644, 0.09315224650646398, 0.035060864449106416, 0.02098349663500601, 0.016601089970653262, 0.11846621879437537, 0.0436971298890946, 0.020381606758961772, 0.009288972676736717, 0.02529334807449169, 0.02432325216040006, 0.004903465014939274, 0.0015741805103532324]\n",
      "On iteration 1550\tBeta_star is 0.108484\tU-star is 0.001561\tActive ks 10\tAlpha is 5.538648\n",
      "\n",
      "[0.3055708039580041, 0.16300500834741885, 0.2485186890873264, 0.08092400363923777, 0.054092376788968256, 0.008334354398407217, 0.0054649825354355286, 0.015816353662356435, 0.006387552844953821, 0.0034018653600395485]\n",
      "On iteration 1600\tBeta_star is 0.043892\tU-star is 0.000176\tActive ks 11\tAlpha is 9.122399\n",
      "\n",
      "[0.37255222735396437, 0.050351709127327726, 0.2231795549416557, 0.09816366003444221, 0.07214488381437446, 0.06040819906272687, 0.03156684982443019, 0.006066425729004419, 0.009887293937553812, 0.020643422862375086, 0.011143334514023853]\n",
      "On iteration 1650\tBeta_star is 0.104779\tU-star is 0.000192\tActive ks 10\tAlpha is 12.123791\n",
      "\n",
      "[0.2794556642516539, 0.16511781023376268, 0.13358411223903185, 0.1577494806952, 0.013359617006984952, 0.04122384424807002, 0.017516651913899294, 0.03517105793181096, 0.017844158544560118, 0.034198145706878895]\n",
      "On iteration 1700\tBeta_star is 0.016089\tU-star is 0.000171\tActive ks 12\tAlpha is 14.467966\n",
      "\n",
      "[0.3459953146888485, 0.2651837387153003, 0.07351070683773805, 0.01929398337467802, 0.03366060194507226, 0.038781466682961695, 0.019141944623722065, 0.03655055018985816, 0.1070973620468824, 0.0009302037374872941, 0.014762787985624101, 0.0290020857803653]\n",
      "On iteration 1750\tBeta_star is 0.223636\tU-star is 0.005819\tActive ks 8\tAlpha is 5.086558\n",
      "\n",
      "[0.1969738044565715, 0.07521580167952498, 0.05097989504773645, 0.26095027491079137, 0.08905187221577855, 0.007080969526994422, 0.06242427916245988, 0.03368695017933016]\n",
      "On iteration 1800\tBeta_star is 0.063109\tU-star is 0.001740\tActive ks 11\tAlpha is 9.732423\n",
      "\n",
      "[0.29164772840334907, 0.23146876437114386, 0.07567226714156432, 0.038547492702614115, 0.013086731122658957, 0.09666143077214032, 0.04688938964939544, 0.026736305586599653, 0.044455452594045125, 0.023428046095964137, 0.04829713098878645]\n",
      "On iteration 1850\tBeta_star is 0.074546\tU-star is 0.000246\tActive ks 11\tAlpha is 5.620974\n",
      "\n",
      "[0.3089934451151616, 0.2148990480238177, 0.1950383736404373, 0.04653782785042878, 0.08240571853615465, 0.009129044212002693, 0.00902087078144517, 0.020054544540831644, 0.01814562212739599, 0.016713955099769473, 0.004515112958078262]\n",
      "On iteration 1900\tBeta_star is 0.041955\tU-star is 0.001046\tActive ks 7\tAlpha is 4.026659\n",
      "\n",
      "[0.3576511707064658, 0.24727483909115475, 0.22074357003160883, 0.05708352491675808, 0.03055734491918413, 0.02152990418235343, 0.02320474579369306]\n",
      "On iteration 1950\tBeta_star is 0.145840\tU-star is 0.008417\tActive ks 4\tAlpha is 3.115681\n",
      "\n",
      "[0.34570450351935184, 0.3764944904758384, 0.09955166037506337, 0.03240979926761867]\n",
      "On iteration 2000\tBeta_star is 0.105382\tU-star is 0.002173\tActive ks 13\tAlpha is 12.486790\n",
      "\n",
      "[0.013356426776843146, 0.3262933828106471, 0.09609994963357088, 0.0651848915820433, 0.04006615742234946, 0.12377558810977725, 0.0172743123773627, 0.020104870951395334, 0.022223646387302905, 0.03831593871905063, 0.08062766207831823, 0.03382472831967001, 0.0174701154648641]\n",
      "On iteration 2050\tBeta_star is 0.062018\tU-star is 0.000067\tActive ks 11\tAlpha is 14.192722\n",
      "\n",
      "[0.32256825435828185, 0.14737449332134595, 0.02555668890671328, 0.05860192279887957, 0.11198053593616275, 0.05182795700157621, 0.07000121958063915, 0.08045520691336866, 0.04292786804615462, 0.00650801572643151, 0.020179947513303428]\n",
      "On iteration 2100\tBeta_star is 0.165164\tU-star is 0.000254\tActive ks 8\tAlpha is 3.418274\n",
      "\n",
      "[0.35270044025809877, 0.16794045977207236, 0.08801314263436512, 0.07564547179044959, 0.08969291287771243, 0.024592014427109055, 0.006315173610639266, 0.029936690757613123]\n",
      "On iteration 2150\tBeta_star is 0.056975\tU-star is 0.000212\tActive ks 8\tAlpha is 9.241520\n",
      "\n",
      "[0.3159359958928481, 0.36791259096791706, 0.1429239909817047, 0.08239523530971113, 0.0024700446882836274, 0.019501973612892312, 0.007191606995629122, 0.004693420022637963]\n",
      "On iteration 2200\tBeta_star is 0.025174\tU-star is 0.001834\tActive ks 10\tAlpha is 4.919164\n",
      "\n",
      "[0.3276348192043058, 0.12701779829990265, 0.12745879074513575, 0.20060590548391122, 0.05047066022095324, 0.025448538063722145, 0.06225106910997503, 0.019584781864703846, 0.003692047858212405, 0.030661418958109445]\n",
      "On iteration 2250\tBeta_star is 0.105188\tU-star is 0.000449\tActive ks 9\tAlpha is 7.445968\n",
      "\n",
      "[0.08781484941978475, 0.14576141668964873, 0.20295831822264523, 0.12279367581030902, 0.04481835405473533, 0.1200651775396387, 0.13441942986790184, 0.028237891655637594, 0.007943275931406743]\n",
      "On iteration 2300\tBeta_star is 0.095541\tU-star is 0.000739\tActive ks 16\tAlpha is 6.877556\n",
      "\n",
      "[0.23468503715924646, 0.02988811459552159, 0.06721653208556133, 0.07195734486531404, 0.0341637933347936, 0.03483569868973684, 0.09557008272872222, 0.09588390238007766, 0.018822253540147504, 0.03866855139714201, 0.028039114674649274, 0.012212678744583547, 0.04216030231911192, 0.03913654051504714, 0.029330144853815063, 0.03188859893658045]\n",
      "On iteration 2350\tBeta_star is 0.101042\tU-star is 0.000848\tActive ks 7\tAlpha is 5.835165\n",
      "\n",
      "[0.3673132921738913, 0.019386118527557956, 0.20529530340796395, 0.13966682911773298, 0.036281909524554234, 0.06893210292155777, 0.06208253715333602]\n"
     ]
    }
   ],
   "source": [
    "for cur_iter in range(2400): #already ran 100 times \n",
    "    #print \"Starting iter %i\"%(cur_iter)\n",
    "    u = np.zeros(len(Y))\n",
    "    #grab u \n",
    "    for idx, val in enumerate(Y):\n",
    "        cluster_label = int(z[idx])\n",
    "        u[idx] = np.random.uniform(0, w[cluster_label])\n",
    "    \n",
    "    #min u \n",
    "    u_star = np.min(u)\n",
    "    \n",
    "    #find k_star and initalize components until we have enough\n",
    "    beta_star = 1 - np.sum(w)\n",
    "    if cur_iter > 1 and cur_iter % 50 == 0:\n",
    "        print \"On iteration %i\\tBeta_star is %0.06f\\tU-star is %0.06f\\tActive ks %i\\tAlpha is %0.06f\\n\"%(cur_iter, beta_star, u_star, active_ks[-1], total_cs[-1])\n",
    "        print w\n",
    "    while (beta_star >= u_star):\n",
    "        _vk = np.random.beta(1, c)\n",
    "        beta_k = _vk * beta_star\n",
    "        \n",
    "        #append beta_k to the weights\n",
    "        w.append(beta_k)\n",
    "            \n",
    "        #append _vk to v\n",
    "        v.append(_vk)\n",
    "        \n",
    "        #append new mu to mus \n",
    "        mus.append(np.random.normal(0, s_sqrt))\n",
    "        \n",
    "        #append new lambda to lambda\n",
    "        new_lambd = np.random.gamma(epsilon, 1/epsilon)\n",
    "        lambdas.append(new_lambd)\n",
    "\n",
    "        \n",
    "        #finally update beta_star\n",
    "        beta_star = beta_star*(1 -_vk)\n",
    "    \n",
    "    assert len(w) == len(mus)\n",
    "    assert len(w) == len(lambdas)\n",
    "    \n",
    "    #now we get the cluster assignments z for each observation\n",
    "    for y_idx , y_val in enumerate(Y):\n",
    "        z_probs = np.zeros(len(w))\n",
    "        for cluster_idx, mu in enumerate(mus):\n",
    "            if w[cluster_idx] > u[y_idx]:\n",
    "                z_probs[cluster_idx] = norm.pdf(y_val, loc = mu, scale = lambda_to_std(lambdas[cluster_idx]))\n",
    "            else:\n",
    "                z_probs[cluster_idx] = 0\n",
    "        #sample cluster assignments\n",
    "        norm_z_probs = z_probs / np.sum(z_probs)\n",
    "        z_sampler = stats.rv_discrete(name = \"z_sampler\", values = (np.arange(len(z_probs)), norm_z_probs))\n",
    "        z_assignment = z_sampler.rvs()\n",
    "        z[y_idx] = z_assignment\n",
    "        #print \"%i\\t%0.03f\\t%0.03f\\t%0.03f\\t%i\"%(y_idx, y_val, mu_)\n",
    "    \n",
    "    z_ints = [int(x) for x in z] #make z ints for easier use in future \n",
    "    \n",
    "    #perform necessary updates for means and lambdas for each cluster \n",
    "    new_mus = []\n",
    "    new_lambdas = []\n",
    "    new_z = np.zeros(len(Y))\n",
    "    active_cluster = 0\n",
    "    count_dict = {}\n",
    "    \n",
    "    for cluster_idx in range(len(w)):\n",
    "        #update means\n",
    "        cur_lambda = lambdas[cluster_idx]    \n",
    "        eta = 0\n",
    "        m = 0\n",
    "        y_k = []\n",
    "        for y_idx, z_val in enumerate(z_ints):\n",
    "            if z_val == cluster_idx:\n",
    "                m += 1\n",
    "                eta += Y[y_idx]\n",
    "                y_k.append(Y[y_idx])\n",
    "                new_z[y_idx] = active_cluster\n",
    "        \n",
    "        if m == 0:\n",
    "            continue\n",
    "        else:\n",
    "            count_dict[active_cluster] = m\n",
    "            active_cluster += 1        \n",
    "            _mean = (eta * cur_lambda)/(m * cur_lambda + s)\n",
    "            _variance = 1 / (m * cur_lambda + s)\n",
    "            new_mu = np.random.normal(_mean, np.sqrt(_variance))\n",
    "            #mus[cluster_idx] = new_mu\n",
    "            new_mus.append(new_mu)\n",
    "            #update lambda\n",
    "            d = 0\n",
    "            for val in y_k:\n",
    "                d += (val - new_mu) ** 2\n",
    "            \n",
    "            _alpha = epsilon + m/2\n",
    "            _beta = epsilon + d/2\n",
    "            new_lambda = np.random.gamma(_alpha, 1/_beta)\n",
    "            #lambdas[cluster_idx] = new_lambda\n",
    "            #print \"added at %i\"%(cluster_idx)\n",
    "            new_lambdas.append(new_lambda)\n",
    "            stds.append(lambda_to_std(new_lambda))\n",
    "            \n",
    "    #update the stick breaking lengths v_k \n",
    "    k = active_cluster \n",
    "    vks = []\n",
    "    #print count_dict\n",
    "    for cluster_idx in range(k):\n",
    "        n_k = count_dict[cluster_idx]\n",
    "        n_j = 0\n",
    "        #print range(cluster_idx + 1, k )\n",
    "        for i in range(cluster_idx+1, k):\n",
    "            n_j += count_dict[i]\n",
    "        vks.append(np.random.beta(1 + n_k, c + n_j))\n",
    "        \n",
    "    #update weights w_k\n",
    "    new_w = []\n",
    "    old_vks = []\n",
    "    for cluster_idx in range(k):\n",
    "        if cluster_idx == 0:\n",
    "            new_w.append(vks[cluster_idx])    \n",
    "            old_vks.append(1-vks[cluster_idx])\n",
    "        else:\n",
    "            #print cluster_idx\n",
    "            vj = 1 \n",
    "            for i in range(cluster_idx):\n",
    "                #print i\n",
    "                #print old_vks\n",
    "                vj *= old_vks[i]\n",
    "            new_w.append(vks[cluster_idx] * vj)\n",
    "            old_vks.append(1-vks[cluster_idx])   \n",
    "    \n",
    "    #lastly, update c (alpha) and nu (Escobar & West 1995, section 6)\n",
    "    #update c\n",
    "    new_nu = np.random.beta(c + 1, len(Y))    \n",
    "    \n",
    "    pi_n_ratio = (a + k - 1) / (len(Y) * (b - np.log10(new_nu)))\n",
    "    pi_1 = pi_n_ratio / (1 + pi_n_ratio)\n",
    "    pi_2 = 1 - pi_1\n",
    "    #new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    #new_c = np.random.gamma(a+k, b - np.log10(new_nu))\n",
    "    #new_c = ((c**k )* gamma(c) * np.random.gamma(0.1,10)) / (gamma(c + len(Y)))      \n",
    "    \n",
    "    #store results\n",
    "    active_ks.append(k)\n",
    "    total_ks.append(len(w))\n",
    "    total_cs.append(new_c)\n",
    "    \n",
    "    #end of gibbs cycle, update all the variables for next round\n",
    "    mus = new_mus\n",
    "    lambdas = new_lambdas\n",
    "    z = new_z \n",
    "    c = new_c\n",
    "    nu = new_nu\n",
    "    v = vks \n",
    "    w = new_w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEZCAYAAABiu9n+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa03133310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.clf()\n",
    "#plt.scatter(np.arange(len(active_ks)), active_ks)\n",
    "\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(total_ks, 400), 'b-', label='Moving average total k')\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(active_ks, 400), 'r-', label='Moving average realized k')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Clusters')\n",
    "plt.xlim((0,2500))\n",
    "plt.legend(prop={'size':8})\n",
    "plt.title('Moving average of clusters vs. Gibbs Iterations')\n",
    "plt.savefig('var_6.png', dpi=500)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.92246203038\n",
      "49.4960031974\n"
     ]
    }
   ],
   "source": [
    "print np.mean(active_ks)\n",
    "print np.mean(total_ks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEZCAYAAABiu9n+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa030a7050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.clf()\n",
    "#plt.scatter(np.arange(len(active_ks)), active_ks)\n",
    "\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(total_cs, 400), 'r-', label='Moving average c')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('c')\n",
    "plt.xlim((0,2000))\n",
    "plt.legend(prop={'size':8})\n",
    "plt.title('Moving average of c vs. Gibbs Iterations')\n",
    "plt.savefig('var_6.png', dpi=500)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like our algorithm is dramatically over_estimating the number of active clusters. The c values seem to be...off. \n",
    "What if we fix $c$? (Fix $c = 1$) \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "On iteration 50\tBeta_star is 0.003304\tU-star is 0.007540\tActive ks 5\tAlpha is 13.059160\n",
      "\n",
      "[0.10856645513396039, 0.38290276419157393, 0.10077703049968506, 0.3778425973734605, 0.02660671412092553]\n",
      "On iteration 100\tBeta_star is 0.003807\tU-star is 0.000253\tActive ks 5\tAlpha is 5.811426\n",
      "\n",
      "[0.44019402524153906, 0.43446563338926614, 0.060297798575201664, 0.04428377451637674, 0.01695131200673814]\n",
      "On iteration 150\tBeta_star is 0.006383\tU-star is 0.000515\tActive ks 4\tAlpha is 1.143161\n",
      "\n",
      "[0.3424379900388352, 0.3964750378798717, 0.13310195609476583, 0.12160200695249307]\n",
      "On iteration 200\tBeta_star is 0.004055\tU-star is 0.009327\tActive ks 4\tAlpha is 2.698531\n",
      "\n",
      "[0.5412422409224596, 0.3131927825113191, 0.1143363066831397, 0.027173698204010038]\n",
      "On iteration 250\tBeta_star is 0.003343\tU-star is 0.001614\tActive ks 3\tAlpha is 1.885608\n",
      "\n",
      "[0.2587403980672141, 0.3391936120962758, 0.39872310332357574]\n",
      "On iteration 300\tBeta_star is 0.022967\tU-star is 0.013468\tActive ks 4\tAlpha is 2.420368\n",
      "\n",
      "[0.5213444780250885, 0.3464368009808677, 0.07720263580904287, 0.03204889484127986]\n",
      "On iteration 350\tBeta_star is 0.000220\tU-star is 0.012686\tActive ks 4\tAlpha is 4.885435\n",
      "\n",
      "[0.33943787564450734, 0.32258883563876645, 0.28192166912383004, 0.055831971163790274]\n",
      "On iteration 400\tBeta_star is 0.002601\tU-star is 0.000100\tActive ks 5\tAlpha is 7.089991\n",
      "\n",
      "[0.5530574597352252, 0.3286237721350379, 0.047328297010380715, 0.03236964525947264, 0.036019559250976586]\n",
      "On iteration 450\tBeta_star is 0.028309\tU-star is 0.000394\tActive ks 3\tAlpha is 2.410432\n",
      "\n",
      "[0.39542860517095496, 0.3155166555394492, 0.2607459430667056]\n",
      "On iteration 500\tBeta_star is 0.003563\tU-star is 0.000925\tActive ks 5\tAlpha is 6.132591\n",
      "\n",
      "[0.12257217167242838, 0.5017591576987488, 0.16168680882228592, 0.1759215083870432, 0.03449705939559624]\n",
      "On iteration 550\tBeta_star is 0.017273\tU-star is 0.002654\tActive ks 5\tAlpha is 9.835400\n",
      "\n",
      "[0.3475747958171956, 0.35162826486955934, 0.05392340189900217, 0.19555118748144956, 0.034049269777704116]\n",
      "On iteration 600\tBeta_star is 0.002748\tU-star is 0.000662\tActive ks 6\tAlpha is 4.290379\n",
      "\n",
      "[0.5024621990227593, 0.21602471847737478, 0.18703425657047468, 0.03440549724605831, 0.05052730767753787, 0.006798066257169266]\n",
      "On iteration 650\tBeta_star is 0.016886\tU-star is 0.007980\tActive ks 4\tAlpha is 3.513120\n",
      "\n",
      "[0.3946191188482889, 0.44940095038567857, 0.12257843119861601, 0.01651593768056932]\n",
      "On iteration 700\tBeta_star is 0.011584\tU-star is 0.001982\tActive ks 5\tAlpha is 8.898153\n",
      "\n",
      "[0.3501830401752073, 0.4610659267738192, 0.08319664286292384, 0.035106903503299966, 0.0588631008049381]\n",
      "On iteration 750\tBeta_star is 0.028065\tU-star is 0.003122\tActive ks 4\tAlpha is 11.526761\n",
      "\n",
      "[0.24388150612867562, 0.2258178577225385, 0.4875108414186887, 0.014725184112428272]\n",
      "On iteration 800\tBeta_star is 0.004214\tU-star is 0.000278\tActive ks 5\tAlpha is 2.919127\n",
      "\n",
      "[0.2658885252690766, 0.3876656432817677, 0.1861704096229101, 0.06561801380617147, 0.09044296932815032]\n",
      "On iteration 850\tBeta_star is 0.034632\tU-star is 0.002618\tActive ks 4\tAlpha is 6.983780\n",
      "\n",
      "[0.3464116661578667, 0.5689529923722951, 0.034580218922339465, 0.015422945763676749]\n",
      "On iteration 900\tBeta_star is 0.005553\tU-star is 0.002085\tActive ks 5\tAlpha is 3.631162\n",
      "\n",
      "[0.39774784333170277, 0.4179837896815976, 0.13832477954129965, 0.028820188465924924, 0.011570520381832023]\n",
      "On iteration 950\tBeta_star is 0.012104\tU-star is 0.010890\tActive ks 5\tAlpha is 9.022118\n",
      "\n",
      "[0.35837010027047, 0.5076792671366884, 0.02075515767804023, 0.08181858116796238, 0.01927314670248593]\n",
      "On iteration 1000\tBeta_star is 0.001671\tU-star is 0.002091\tActive ks 3\tAlpha is 2.099043\n",
      "\n",
      "[0.4498109238944418, 0.5366891824239246, 0.011828832232901116]\n",
      "On iteration 1050\tBeta_star is 0.006997\tU-star is 0.000174\tActive ks 3\tAlpha is 0.422371\n",
      "\n",
      "[0.26954273698823317, 0.575262800999211, 0.14819785257528081]\n",
      "On iteration 1100\tBeta_star is 0.018168\tU-star is 0.000173\tActive ks 3\tAlpha is 5.300245\n",
      "\n",
      "[0.31587895998295856, 0.4908724081331851, 0.1750804133270724]\n",
      "On iteration 1150\tBeta_star is 0.069136\tU-star is 0.003095\tActive ks 4\tAlpha is 4.632363\n",
      "\n",
      "[0.29158981655348526, 0.1554209707316997, 0.22002819928832004, 0.26382466055974657]\n",
      "On iteration 1200\tBeta_star is 0.004915\tU-star is 0.002139\tActive ks 7\tAlpha is 16.422033\n",
      "\n",
      "[0.43233646323739583, 0.3080237516669552, 0.10225527451205416, 0.024845400729449043, 0.04016384756141721, 0.08258126118016217, 0.0048790940208985984]\n",
      "On iteration 1250\tBeta_star is 0.007967\tU-star is 0.013342\tActive ks 2\tAlpha is 1.562402\n",
      "\n",
      "[0.4705819392022137, 0.5214510770232389]\n",
      "On iteration 1300\tBeta_star is 0.031664\tU-star is 0.000718\tActive ks 4\tAlpha is 13.568767\n",
      "\n",
      "[0.24050116842196448, 0.5129580627811657, 0.12748280554549404, 0.08739443647708062]\n",
      "On iteration 1350\tBeta_star is 0.016264\tU-star is 0.002292\tActive ks 3\tAlpha is 2.941276\n",
      "\n",
      "[0.3592669273823825, 0.47123221009692856, 0.15323637753828295]\n",
      "On iteration 1400\tBeta_star is 0.028932\tU-star is 0.009201\tActive ks 4\tAlpha is 2.910270\n",
      "\n",
      "[0.5181396398169263, 0.25967811066730506, 0.039792879761039485, 0.15345737057371472]\n",
      "On iteration 1450\tBeta_star is 0.014420\tU-star is 0.000756\tActive ks 5\tAlpha is 6.295506\n",
      "\n",
      "[0.4696537287124337, 0.3873529982869259, 0.048933384420351236, 0.06566225044205222, 0.01397781452082997]\n",
      "On iteration 1500\tBeta_star is 0.003839\tU-star is 0.025755\tActive ks 2\tAlpha is 3.492674\n",
      "\n",
      "[0.33325782989784664, 0.6629031575962812]\n",
      "On iteration 1550\tBeta_star is 0.043112\tU-star is 0.002643\tActive ks 2\tAlpha is 0.922700\n",
      "\n",
      "[0.3519855922777322, 0.6049026829404331]\n",
      "On iteration 1600\tBeta_star is 0.008111\tU-star is 0.004884\tActive ks 3\tAlpha is 3.003279\n",
      "\n",
      "[0.434831363729696, 0.4409648179437838, 0.11609236658326899]\n",
      "On iteration 1650\tBeta_star is 0.045740\tU-star is 0.006835\tActive ks 2\tAlpha is 1.617718\n",
      "\n",
      "[0.49240746099536853, 0.46185273022414886]\n",
      "On iteration 1700\tBeta_star is 0.008678\tU-star is 0.001334\tActive ks 4\tAlpha is 6.223494\n",
      "\n",
      "[0.4217705645474518, 0.07473684775518231, 0.37296677682600926, 0.12184790755067255]\n",
      "On iteration 1750\tBeta_star is 0.007869\tU-star is 0.001137\tActive ks 4\tAlpha is 3.912521\n",
      "\n",
      "[0.5025270198871015, 0.38527368044763954, 0.09461283405809259, 0.009717285110533833]\n",
      "On iteration 1800\tBeta_star is 0.004052\tU-star is 0.004520\tActive ks 4\tAlpha is 5.471930\n",
      "\n",
      "[0.3600647121664115, 0.4641030103454034, 0.1313833838869933, 0.04039644603190579]\n",
      "On iteration 1850\tBeta_star is 0.009592\tU-star is 0.009018\tActive ks 3\tAlpha is 13.578485\n",
      "\n",
      "[0.33371223406580214, 0.6408476687600303, 0.015848024705945627]\n",
      "On iteration 1900\tBeta_star is 0.009288\tU-star is 0.007206\tActive ks 3\tAlpha is 2.431603\n",
      "\n",
      "[0.40132587742720766, 0.5710450041137091, 0.01834132990982477]\n",
      "On iteration 1950\tBeta_star is 0.005172\tU-star is 0.003922\tActive ks 5\tAlpha is 4.318278\n",
      "\n",
      "[0.3233402780496668, 0.57389270964016, 0.020090185635554515, 0.06819475602308932, 0.009310017267685685]\n",
      "On iteration 2000\tBeta_star is 0.007719\tU-star is 0.003018\tActive ks 5\tAlpha is 5.573796\n",
      "\n",
      "[0.5517120146064677, 0.02407862582884318, 0.0666970199417801, 0.3140944295956917, 0.03569878568433487]\n",
      "On iteration 2050\tBeta_star is 0.008946\tU-star is 0.003964\tActive ks 4\tAlpha is 1.375584\n",
      "\n",
      "[0.24325199973057401, 0.20629953775234475, 0.47606938391234055, 0.0654326267563445]\n",
      "On iteration 2100\tBeta_star is 0.000566\tU-star is 0.005496\tActive ks 2\tAlpha is 1.630371\n",
      "\n",
      "[0.41668702795338713, 0.5827466909455571]\n",
      "On iteration 2150\tBeta_star is 0.009198\tU-star is 0.000832\tActive ks 4\tAlpha is 2.308890\n",
      "\n",
      "[0.3451281512274603, 0.5907241026168033, 0.04333643401229502, 0.011612913501716336]\n",
      "On iteration 2200\tBeta_star is 0.002079\tU-star is 0.005081\tActive ks 4\tAlpha is 3.540857\n",
      "\n",
      "[0.3525507639235894, 0.5623285457881313, 0.05825459550953765, 0.024787051872517386]\n",
      "On iteration 2250\tBeta_star is 0.000207\tU-star is 0.000035\tActive ks 6\tAlpha is 9.354283\n",
      "\n",
      "[0.3933370626445014, 0.2670248233029332, 0.16597257754773714, 0.15305410293066507, 0.019622471384277654, 0.0007817790786804012]\n",
      "On iteration 2300\tBeta_star is 0.024560\tU-star is 0.016717\tActive ks 4\tAlpha is 2.097741\n",
      "\n",
      "[0.41787837163692687, 0.058855998423954926, 0.3817459831721081, 0.11695978958243199]\n",
      "On iteration 2350\tBeta_star is 0.002548\tU-star is 0.004213\tActive ks 5\tAlpha is 7.333484\n",
      "\n",
      "[0.34482335694691474, 0.42173488232213224, 0.03703409984756512, 0.15433137723569085, 0.03952832595089539]\n",
      "On iteration 2400\tBeta_star is 0.002948\tU-star is 0.009696\tActive ks 2\tAlpha is 0.426718\n",
      "\n",
      "[0.40689544084561474, 0.590156432438342]\n",
      "On iteration 2450\tBeta_star is 0.010842\tU-star is 0.022854\tActive ks 2\tAlpha is 0.118997\n",
      "\n",
      "[0.3479241089216487, 0.6412341332176822]\n"
     ]
    }
   ],
   "source": [
    "epsilon = 0.5\n",
    "s = 0.1\n",
    "s_inv = 1/s\n",
    "s_sqrt = np.sqrt(s_inv)\n",
    "#s_sqrt = s_inv\n",
    "a = 0.1\n",
    "b = 0.1 \n",
    "c = 1\n",
    "nu = np.random.beta(c+1, len(Y))\n",
    "\n",
    "#cycle 1\n",
    "#initalize first weights\n",
    "w = []\n",
    "w.append(np.random.beta(1, c))\n",
    "\n",
    "v = []\n",
    "v.append(w[0])\n",
    "#initalize first mu\n",
    "mus = []\n",
    "mus.append(np.random.normal(0, s_sqrt))\n",
    "\n",
    "#initalize first lambda\n",
    "lambdas = []\n",
    "lambdas.append(np.random.gamma(epsilon,epsilon))\n",
    "stds = []\n",
    "stds.append(lambda_to_std(lambdas[0]))\n",
    "z = np.zeros(len(Y)) #cluster assignments\n",
    "u = np.zeros(len(Y))\n",
    "active_ks = []\n",
    "total_ks = []\n",
    "total_cs = []\n",
    "\n",
    "for cur_iter in range(2500):\n",
    "    #print \"Starting iter %i\"%(cur_iter)\n",
    "    u = np.zeros(len(Y))\n",
    "    #grab u \n",
    "    for idx, val in enumerate(Y):\n",
    "        cluster_label = int(z[idx])\n",
    "        u[idx] = np.random.uniform(0, w[cluster_label])\n",
    "    \n",
    "    #min u \n",
    "    u_star = np.min(u)\n",
    "    \n",
    "    #find k_star and initalize components until we have enough\n",
    "    beta_star = 1 - np.sum(w)\n",
    "    if cur_iter > 1 and cur_iter % 50 == 0:\n",
    "        print \"On iteration %i\\tBeta_star is %0.06f\\tU-star is %0.06f\\tActive ks %i\\tAlpha is %0.06f\\n\"%(cur_iter, beta_star, u_star, active_ks[-1], total_cs[-1])\n",
    "        print w\n",
    "    while (beta_star >= u_star):\n",
    "        _vk = np.random.beta(1, c)\n",
    "        beta_k = _vk * beta_star\n",
    "        \n",
    "        #append beta_k to the weights\n",
    "        w.append(beta_k)\n",
    "            \n",
    "        #append _vk to v\n",
    "        v.append(_vk)\n",
    "        \n",
    "        #append new mu to mus \n",
    "        mus.append(np.random.normal(0, s_sqrt))\n",
    "        \n",
    "        #append new lambda to lambda\n",
    "        new_lambd = np.random.gamma(epsilon, 1/epsilon)\n",
    "        lambdas.append(new_lambd)\n",
    "\n",
    "        \n",
    "        #finally update beta_star\n",
    "        beta_star = beta_star*(1 -_vk)\n",
    "    \n",
    "    assert len(w) == len(mus)\n",
    "    assert len(w) == len(lambdas)\n",
    "    \n",
    "    #now we get the cluster assignments z for each observation\n",
    "    for y_idx , y_val in enumerate(Y):\n",
    "        z_probs = np.zeros(len(w))\n",
    "        for cluster_idx, mu in enumerate(mus):\n",
    "            if w[cluster_idx] > u[y_idx]:\n",
    "                z_probs[cluster_idx] = norm.pdf(y_val, loc = mu, scale = lambda_to_std(lambdas[cluster_idx]))\n",
    "            else:\n",
    "                z_probs[cluster_idx] = 0\n",
    "        #sample cluster assignments\n",
    "        norm_z_probs = z_probs / np.sum(z_probs)\n",
    "        z_sampler = stats.rv_discrete(name = \"z_sampler\", values = (np.arange(len(z_probs)), norm_z_probs))\n",
    "        z_assignment = z_sampler.rvs()\n",
    "        z[y_idx] = z_assignment\n",
    "        #print \"%i\\t%0.03f\\t%0.03f\\t%0.03f\\t%i\"%(y_idx, y_val, mu_)\n",
    "    \n",
    "    z_ints = [int(x) for x in z] #make z ints for easier use in future \n",
    "    \n",
    "    #perform necessary updates for means and lambdas for each cluster \n",
    "    new_mus = []\n",
    "    new_lambdas = []\n",
    "    new_z = np.zeros(len(Y))\n",
    "    active_cluster = 0\n",
    "    count_dict = {}\n",
    "    \n",
    "    for cluster_idx in range(len(w)):\n",
    "        #update means\n",
    "        cur_lambda = lambdas[cluster_idx]    \n",
    "        eta = 0\n",
    "        m = 0\n",
    "        y_k = []\n",
    "        for y_idx, z_val in enumerate(z_ints):\n",
    "            if z_val == cluster_idx:\n",
    "                m += 1\n",
    "                eta += Y[y_idx]\n",
    "                y_k.append(Y[y_idx])\n",
    "                new_z[y_idx] = active_cluster\n",
    "        \n",
    "        if m == 0:\n",
    "            continue\n",
    "        else:\n",
    "            count_dict[active_cluster] = m\n",
    "            active_cluster += 1        \n",
    "            _mean = (eta * cur_lambda)/(m * cur_lambda + s)\n",
    "            _variance = 1 / (m * cur_lambda + s)\n",
    "            new_mu = np.random.normal(_mean, np.sqrt(_variance))\n",
    "            #mus[cluster_idx] = new_mu\n",
    "            new_mus.append(new_mu)\n",
    "            #update lambda\n",
    "            d = 0\n",
    "            for val in y_k:\n",
    "                d += (val - new_mu) ** 2\n",
    "            \n",
    "            _alpha = epsilon + m/2\n",
    "            _beta = epsilon + d/2\n",
    "            new_lambda = np.random.gamma(_alpha, 1/_beta)\n",
    "            #lambdas[cluster_idx] = new_lambda\n",
    "            #print \"added at %i\"%(cluster_idx)\n",
    "            new_lambdas.append(new_lambda)\n",
    "            stds.append(lambda_to_std(new_lambda))\n",
    "            \n",
    "    #update the stick breaking lengths v_k \n",
    "    k = active_cluster \n",
    "    vks = []\n",
    "    #print count_dict\n",
    "    for cluster_idx in range(k):\n",
    "        n_k = count_dict[cluster_idx]\n",
    "        n_j = 0\n",
    "        #print range(cluster_idx + 1, k )\n",
    "        for i in range(cluster_idx+1, k):\n",
    "            n_j += count_dict[i]\n",
    "        vks.append(np.random.beta(1 + n_k, c + n_j))\n",
    "        \n",
    "    #update weights w_k\n",
    "    new_w = []\n",
    "    old_vks = []\n",
    "    for cluster_idx in range(k):\n",
    "        if cluster_idx == 0:\n",
    "            new_w.append(vks[cluster_idx])    \n",
    "            old_vks.append(1-vks[cluster_idx])\n",
    "        else:\n",
    "            #print cluster_idx\n",
    "            vj = 1 \n",
    "            for i in range(cluster_idx):\n",
    "                #print i\n",
    "                #print old_vks\n",
    "                vj *= old_vks[i]\n",
    "            new_w.append(vks[cluster_idx] * vj)\n",
    "            old_vks.append(1-vks[cluster_idx])   \n",
    "    \n",
    "    #lastly, update c (alpha) and nu (Escobar & West 1995, section 6)\n",
    "    #update c\n",
    "    new_nu = np.random.beta(c + 1, len(Y))    \n",
    "    \n",
    "    pi_n_ratio = (a + k - 1) / (len(Y) * (b - np.log10(new_nu)))\n",
    "    pi_1 = pi_n_ratio / (1 + pi_n_ratio)\n",
    "    pi_2 = 1 - pi_1\n",
    "    #new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    new_c = pi_1 * np.random.gamma(a+k, b - np.log10(new_nu)) + pi_2 * np.random.gamma(a+k-1, b-np.log10(new_nu))\n",
    "    #new_c = np.random.gamma(a+k, b - np.log10(new_nu))\n",
    "    #new_c = ((c**k )* gamma(c) * np.random.gamma(0.1,10)) / (gamma(c + len(Y)))      \n",
    "    \n",
    "    #store results\n",
    "    active_ks.append(k)\n",
    "    total_ks.append(len(w))\n",
    "    total_cs.append(new_c)\n",
    "    \n",
    "    #end of gibbs cycle, update all the variables for next round\n",
    "    mus = new_mus\n",
    "    lambdas = new_lambdas\n",
    "    z = new_z \n",
    "    c = 1 #fix c\n",
    "    nu = new_nu\n",
    "    v = vks \n",
    "    w = new_w\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEZCAYAAAB1mUk3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa0304fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.clf()\n",
    "#plt.scatter(np.arange(len(active_ks)), active_ks)\n",
    "\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(total_ks, 400), 'b-', label='Moving average total k')\n",
    "plt.plot(np.arange(len(active_ks)), movingaverage(active_ks, 400), 'r-', label='Moving average realized k')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Clusters')\n",
    "plt.xlim((0,2500))\n",
    "plt.legend(prop={'size':8})\n",
    "plt.title('Moving average of clusters vs. Gibbs Iterations (fixed c)')\n",
    "plt.savefig('var_7.png', dpi=500)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEZCAYAAABrUHmEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLDMnDTMzy8xJw8zMMnPSMDOzzP4LQoZeXQzrx8QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa0304fdd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "plt.scatter(z , Y)\n",
    "plt.title('Representative Clustering')\n",
    "plt.xlabel('Cluster Index')\n",
    "plt.ylabel('Y value')\n",
    "plt.savefig('rep_clustv7.png',dpi=450)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}