Dirichlet process mixtures

dp.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dirichlet Process Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The stick-breaking process\n",
    "\n",
    "The stick-breaking process generates an infinite sequence that sums to 1. Because we can't really draw an infinite sequence on the computer, we take an on-demand sequential procedure, draw them one by one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyro\n",
    "from pyro.distributions import Beta, Normal, Gamma, Uniform\n",
    "from pyro.infer import config_enumerate\n",
    "\n",
    "import torch\n",
    "import torch.tensor as T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the Beta distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "with pyro.plate(\"n\", size=500):\n",
    "    x = pyro.sample(\"x\", Beta(1, 100))\n",
    "\n",
    "sns.histplot(x, bins=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fix the first parameter and varying the second:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 648x432 with 6 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 3, figsize=(9, 6), sharex=True)\n",
    "axs = axs.flat\n",
    "\n",
    "αs = [0.5, 1, 3, 5, 10, 20]\n",
    "for i, α in enumerate(αs):\n",
    "    with pyro.plate(\"n\", size=500):\n",
    "        x = pyro.sample(\"x\", Beta(1, α))\n",
    "    axs[i].set_title('α = {}'.format(α))\n",
    "    sns.histplot(x, bins=50, ax=axs[i]);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as we can see, as α grows bigger, the draws gets smaller and smaller.\n",
    "\n",
    "We use the Beta distribution to build the GEM distribution, the stick-breaking procedure to draw (on-demand) an infinite sequence that sums to 1. The only parameter for GEM is the varying parameter in Beta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GEM:\n",
    "    rest = 1\n",
    "    i = 0\n",
    "\n",
    "    def __call__(self, α):\n",
    "        draw = pyro.sample(\"lambda_{}\".format(self.i), Beta(1, α))\n",
    "        out = draw * self.rest\n",
    "        # print(self.i, out)\n",
    "        self.rest -= out\n",
    "        self.i += 1\n",
    "        return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "[tensor(0.0425),\n tensor(0.1228),\n tensor(0.2029),\n tensor(0.0263),\n tensor(0.0615),\n tensor(0.1636),\n tensor(0.0597),\n tensor(0.0158),\n tensor(0.0699),\n tensor(0.0330)]"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "G = GEM()\n",
    "[G(3) for i in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The parameter α in the GEM distribution decides the spread of the probability. Here we plot the first 50 values of the GEM distribution with different values for α"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2, 3, figsize=(9, 6))\n",
    "axs = axs.flat\n",
    "\n",
    "αs = [0.5, 1, 3, 5, 10, 20]\n",
    "for i, α in enumerate(αs):\n",
    "    for j in range(50):\n",
    "        G = GEM()\n",
    "        axs[i].set_title('α = {}'.format(α))\n",
    "        axs[i].plot(torch.stack([G(α) for n in range(50)]), 'b', alpha=0.2);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that as α grows bigger, we are more likely to see bigger values in later draws. However, the values always decrease exponentially. We can roughly see the exponential decrease from the graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dirichlet Process Gaussian Mixture Model\n",
    "\n",
    "Because in Dirichlet Process Mixture Model, the number of observed clusters grow with the amount of data, we start by drawing cluster indices for each datum. \n",
    "\n",
    "Because the simplex is of infinite length, we can't draw a cluster index like with the Categorical distribution; instead, we'll draw the cluster index in an on-demand fashion: first we draw a value from the `Uniform(0, 1)` distribution, then we keep drawing $\\lambda$s till the desired cluster is covered.\n",
    "\n",
    "that is, first we draw \n",
    "\n",
    "$$\\eta_n \\sim \\text{Uniform} (0, 1), \\; n \\in 1, ..., N$$\n",
    "\n",
    "$\\eta$ is the same size as the observation, and the maximum value of $\\eta$ will determine the number of realised clusters. We keep drawing $\\lambda_k \\sim \\text{GEM} (\\alpha)$ till all the realised clusters are covered. that is\n",
    "\n",
    "\n",
    "$$\\sum_{k=1}^{K-1} \\lambda_k \\leq \\text{max} (\\eta) \\leq  \\sum_{k=1}^K \\lambda_k $$\n",
    "\n",
    "\n",
    "and K is the final realised number of clusters.\n",
    "\n",
    "The cluster index $z_n$ for each datum is then determind by looking up the location of each $\\eta_n$ in the cumulative distribution of $\\lambda$ (the code is vectorised)\n",
    "\n",
    "```python\n",
    "z = torch.searchsorted(cumsum(λ), η)\n",
    "```\n",
    "\n",
    "Now we have the number of clusters , we can draw the emission parameters.\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    "\\mu_k &\\sim \\text{Νormal} (\\mu_0, \\sigma_0) , \\; k \\in 1, ..., K \\\\\n",
    "\\sigma_k &\\sim \\text{Gamma} (\\alpha_0, \\beta_0), \\; k \\in 1, ..., K \\\\\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "Finally the observations\n",
    "\n",
    "$$y_n \\sim \\text{Νormal}(\\mu_{z_n}, \\sigma_{z_n}), \\; n \\in 1, ..., N$$\n",
    "\n",
    "The whole process is as follows. The number of observations is needed to start the whole process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(tensor(0.9974),\n tensor([0.8894, 0.0637, 0.0448]),\n tensor([0.8894, 0.9531, 0.9980]),\n tensor([0, 0, 0, 0, 0, 0, 0, 2, 0, 0]),\n 3,\n 3,\n tensor([11.7500, -6.4484,  2.5021]),\n tensor([8.2060, 2.7880, 8.9468]),\n tensor([ 8.8438, -2.2442, 21.8244,  8.0924, 15.9224, -3.1924, 21.3603,  3.9302,\n          8.3737, 21.9766]))"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "N = 10 \n",
    "with pyro.plate('n_obs', size=N):\n",
    "    η = pyro.sample('η', Uniform(0, 1))\n",
    "\n",
    "total = T(0.)\n",
    "G = GEM()\n",
    "\n",
    "λs = []\n",
    "while total < η.max():\n",
    "    λ = G(1)\n",
    "    total += λ\n",
    "    λs.append(λ)\n",
    "\n",
    "λs = torch.stack(λs)\n",
    "λs_cumsum = torch.cumsum(λs, dim=0)\n",
    "\n",
    "z = torch.searchsorted(λs_cumsum, η)\n",
    "\n",
    "with pyro.plate('components', len(λs)):\n",
    "    μ = pyro.sample('μ', Normal(0, 5))\n",
    "    σ = pyro.sample('σ', Gamma(3, 1))\n",
    "\n",
    "with pyro.plate('n_obs', size=N):\n",
    "    y = pyro.sample('y', Normal(μ[z], σ[z]))\n",
    "\n",
    "η.max(), λs, λs_cumsum, z, G.i, len(λs), μ, σ, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "collected into a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "tensor([-3.1397,  1.7518, -5.3565, 12.1867, -3.5892, -0.0277, -0.4660, -3.2969,\n         0.5638, -4.1732])"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "@config_enumerate\n",
    "def DPGMM(N):\n",
    "    \"\"\"\n",
    "    Dirichlet Process Gaussian Mixture Model.\n",
    "    N : the number of observations\n",
    "    \"\"\"\n",
    "    obs_plate = pyro.plate('n_obs', size=N)\n",
    "    with obs_plate:\n",
    "        η = pyro.sample('η', Uniform(0, 1))\n",
    "\n",
    "    total = T(0.)\n",
    "    G = GEM()\n",
    "\n",
    "    λs = []\n",
    "    while total < η.max():\n",
    "        λ = G(1)\n",
    "        total += λ\n",
    "        λs.append(λ)\n",
    "\n",
    "    λs = torch.stack(λs)\n",
    "    λs_cumsum = torch.cumsum(λs, dim=0)\n",
    "\n",
    "    z = torch.searchsorted(λs_cumsum, η)\n",
    "\n",
    "    with pyro.plate('components', len(λs)):\n",
    "        μ = pyro.sample('μ', Normal(0, 5))\n",
    "        σ = pyro.sample('σ', Gamma(3, 1))\n",
    "\n",
    "    with obs_plate:\n",
    "        return pyro.sample('y', Normal(μ[z], σ[z]))\n",
    "\n",
    "DPGMM(N=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "generate some data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "torch.Size([400])"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "N = 100\n",
    "\n",
    "data = torch.cat((Normal(-5, 1).sample([N*2]),\n",
    "                  Normal(0, 0.5).sample([N]),\n",
    "                  Normal(5, 1.5).sample([N])))\n",
    "data.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "do inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": "Warmup:   0%|          | 0/200 [00:00, ?it/s]"
    },
    {
     "output_type": "error",
     "ename": "RuntimeError",
     "evalue": "isDifferentiableType(variable.scalar_type()) INTERNAL ASSERT FAILED at \"/Users/distiller/project/conda/conda-bld/pytorch_1595629430416/work/torch/csrc/autograd/functions/utils.h\":59, please report a bug to PyTorch. \nTrace Shapes:      \n Param Sites:      \nSample Sites:      \n   n_obs dist     |\n        value 400 |\n       η dist 400 |\n        value 400 |\nlambda_0 dist     |\n        value     |\nlambda_1 dist     |\n        value     |\nlambda_2 dist     |\n        value     |\nlambda_3 dist     |\n        value     |\nlambda_4 dist     |\n        value     |",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-11-c3e549972edc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mkernel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNUTS\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpyro\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcondition\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDPGMM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'y'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mmcmc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mMCMC\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkernel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_samples\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mN_sample\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwarmup_steps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mN_sample\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mmcmc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0mmcmc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msummary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/messenger.py\u001b[0m in \u001b[0;36m_context_wrap\u001b[0;34m(context, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_context_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcontext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/api.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    378\u001b[0m         with optional(pyro.validation_enabled(not self.disable_validation),\n\u001b[1;32m    379\u001b[0m                       self.disable_validation is not None):\n\u001b[0;32m--> 380\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchain_id\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msampler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    381\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mnum_samples\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mchain_id\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    382\u001b[0m                     \u001b[0mnum_samples\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mchain_id\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/api.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    167\u001b[0m             for sample in _gen_samples(self.kernel, self.warmup_steps, self.num_samples, hook_w_logging,\n\u001b[1;32m    168\u001b[0m                                        \u001b[0mi\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum_chains\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m                                        *args, **kwargs):\n\u001b[0m\u001b[1;32m    170\u001b[0m                 \u001b[0;32myield\u001b[0m \u001b[0msample\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m  \u001b[0;31m# sample, chain_id\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkernel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcleanup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/api.py\u001b[0m in \u001b[0;36m_gen_samples\u001b[0;34m(kernel, warmup_steps, num_samples, hook, chain_id, *args, **kwargs)\u001b[0m\n\u001b[1;32m    109\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    110\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_gen_samples\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkernel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwarmup_steps\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_samples\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhook\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchain_id\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 111\u001b[0;31m     \u001b[0mkernel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwarmup_steps\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    112\u001b[0m     \u001b[0mparams\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkernel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial_params\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    113\u001b[0m     \u001b[0;31m# yield structure (key, value.shape) of params\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/hmc.py\u001b[0m in \u001b[0;36msetup\u001b[0;34m(self, warmup_steps, *args, **kwargs)\u001b[0m\n\u001b[1;32m    301\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_warmup_steps\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwarmup_steps\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    302\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 303\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_initialize_model_properties\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    304\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial_params\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    305\u001b[0m             \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdetach\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitial_params\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/hmc.py\u001b[0m in \u001b[0;36m_initialize_model_properties\u001b[0;34m(self, model_args, model_kwargs)\u001b[0m\n\u001b[1;32m    253\u001b[0m             \u001b[0mskip_jit_warnings\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_ignore_jit_warnings\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    254\u001b[0m             \u001b[0minit_strategy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_init_strategy\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 255\u001b[0;31m             \u001b[0minitial_params\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_initial_params\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    256\u001b[0m         )\n\u001b[1;32m    257\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpotential_fn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpotential_fn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/util.py\u001b[0m in \u001b[0;36minitialize_model\u001b[0;34m(model, model_args, model_kwargs, transforms, max_plate_nesting, jit_compile, jit_options, skip_jit_warnings, num_chains, init_strategy, initial_params)\u001b[0m\n\u001b[1;32m    419\u001b[0m                                                     \u001b[0mpe_maker\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_potential_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprototype_params\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    420\u001b[0m                                                     \u001b[0mnum_chains\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnum_chains\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minit_strategy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minit_strategy\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 421\u001b[0;31m                                                     trace=model_trace)\n\u001b[0m\u001b[1;32m    422\u001b[0m     \u001b[0mpotential_fn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpe_maker\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_potential_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjit_compile\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mskip_jit_warnings\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjit_options\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    423\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0minitial_params\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpotential_fn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtransforms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel_trace\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/util.py\u001b[0m in \u001b[0;36m_find_valid_initial_params\u001b[0;34m(model, model_args, model_kwargs, transforms, potential_fn, prototype_params, max_tries_initial_params, num_chains, init_strategy, trace)\u001b[0m\n\u001b[1;32m    318\u001b[0m         \u001b[0msamples\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"value\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdetach\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mname\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    319\u001b[0m         \u001b[0mparams\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtransforms\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msamples\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 320\u001b[0;31m         \u001b[0mpe_grad\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpe\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpotential_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpotential_fn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    321\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    322\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpe\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mall\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpe_grad\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/ops/integrator.py\u001b[0m in \u001b[0;36mpotential_grad\u001b[0;34m(potential_fn, z)\u001b[0m\n\u001b[1;32m     80\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mgrads\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz_nodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_tensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'nan'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     81\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 82\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     83\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     84\u001b[0m     \u001b[0mgrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpotential_energy\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mz_nodes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/ops/integrator.py\u001b[0m in \u001b[0;36mpotential_grad\u001b[0;34m(potential_fn, z)\u001b[0m\n\u001b[1;32m     73\u001b[0m         \u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrequires_grad_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     74\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 75\u001b[0;31m         \u001b[0mpotential_energy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpotential_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mz\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     76\u001b[0m     \u001b[0;31m# deal with singular matrices\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     77\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mRuntimeError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/infer/mcmc/util.py\u001b[0m in \u001b[0;36m_potential_fn\u001b[0;34m(self, params)\u001b[0m\n\u001b[1;32m    259\u001b[0m         \u001b[0mcond_model\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpoutine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcondition\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparams_constrained\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    260\u001b[0m         model_trace = poutine.trace(cond_model).get_trace(*self.model_args,\n\u001b[0;32m--> 261\u001b[0;31m                                                           **self.model_kwargs)\n\u001b[0m\u001b[1;32m    262\u001b[0m         \u001b[0mlog_joint\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrace_prob_evaluator\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog_prob\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel_trace\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    263\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtransforms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/trace_messenger.py\u001b[0m in \u001b[0;36mget_trace\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    185\u001b[0m         \u001b[0mCalls\u001b[0m \u001b[0mthis\u001b[0m \u001b[0mpoutine\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mreturns\u001b[0m \u001b[0mits\u001b[0m \u001b[0mtrace\u001b[0m \u001b[0minstead\u001b[0m \u001b[0mof\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;31m'\u001b[0m\u001b[0ms\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    186\u001b[0m         \"\"\"\n\u001b[0;32m--> 187\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    188\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmsngr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/trace_messenger.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    169\u001b[0m                 \u001b[0mexc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mexc_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mu\"{}\\n{}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexc_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshapes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    170\u001b[0m                 \u001b[0mexc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mexc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtraceback\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 171\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mexc\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    172\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmsngr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_node\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"_RETURN\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"_RETURN\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"return\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mret\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    173\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/trace_messenger.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    163\u001b[0m                                       args=args, kwargs=kwargs)\n\u001b[1;32m    164\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 165\u001b[0;31m                 \u001b[0mret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    166\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mValueError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    167\u001b[0m                 \u001b[0mexc_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexc_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtraceback\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexc_info\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/messenger.py\u001b[0m in \u001b[0;36m_context_wrap\u001b[0;34m(context, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_context_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcontext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/messenger.py\u001b[0m in \u001b[0;36m_context_wrap\u001b[0;34m(context, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_context_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcontext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/messenger.py\u001b[0m in \u001b[0;36m_context_wrap\u001b[0;34m(context, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_context_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcontext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/messenger.py\u001b[0m in \u001b[0;36m_context_wrap\u001b[0;34m(context, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_context_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcontext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/miniconda3/envs/rolemodels/lib/python3.7/site-packages/pyro/poutine/messenger.py\u001b[0m in \u001b[0;36m_context_wrap\u001b[0;34m(context, fn, *args, **kwargs)\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_context_wrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcontext\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-9-d1bb46373d98>\u001b[0m in \u001b[0;36mDPGMM\u001b[0;34m(N)\u001b[0m\n\u001b[1;32m     21\u001b[0m     \u001b[0mλs_cumsum\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcumsum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mλs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdim\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m     \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msearchsorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mλs_cumsum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mη\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mpyro\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'components'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mλs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mRuntimeError\u001b[0m: isDifferentiableType(variable.scalar_type()) INTERNAL ASSERT FAILED at \"/Users/distiller/project/conda/conda-bld/pytorch_1595629430416/work/torch/csrc/autograd/functions/utils.h\":59, please report a bug to PyTorch. \nTrace Shapes:      \n Param Sites:      \nSample Sites:      \n   n_obs dist     |\n        value 400 |\n       η dist 400 |\n        value 400 |\nlambda_0 dist     |\n        value     |\nlambda_1 dist     |\n        value     |\nlambda_2 dist     |\n        value     |\nlambda_3 dist     |\n        value     |\nlambda_4 dist     |\n        value     |"
     ]
    }
   ],
   "source": [
    "from pyro.infer.mcmc import MCMC, NUTS\n",
    "\n",
    "N_sample = 100\n",
    "kernel = NUTS(pyro.condition(DPGMM, data={'y':data}))\n",
    "mcmc = MCMC(kernel, num_samples=N_sample, warmup_steps=N_sample)\n",
    "mcmc.run(len(data))\n",
    "mcmc.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "seems like the `z = torch.searchsorted(λs_cumsum, η)` is causing problems because it's a discrete variable and thus non-differentiable."
   ]
  }
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