gistfile1.txt

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Compare integrators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v3.0-283-g209d35f4\r\n"
     ]
    }
   ],
   "source": [
    "!git describe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb\n",
    "import pymc3 as pm\n",
    "import theano.tensor as tt\n",
    "import theano\n",
    "import pystan\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We use a simple hierarchical model to compare the integrators\n",
    "`\"leapfrog\"` and `\"three-stage\"`:\n",
    "\\begin{align*}\n",
    "y_i &\\sim \\text{StudentT}(5, \\mu + \\beta_{k[i]}, \\sigma)\\\\\n",
    "\\beta_k &\\sim N(0, \\sigma_\\beta)\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Generate data\n",
    "n_per_group = 2\n",
    "n_groups = 10000\n",
    "N = n_per_group * n_groups\n",
    "mu = 1\n",
    "sigma = 1\n",
    "sigma_group = 0.5\n",
    "\n",
    "i_group = np.repeat(np.arange(n_groups), n_per_group)\n",
    "beta = mu + sigma_group * np.random.randn(n_groups)[i_group]\n",
    "observed = stats.t(5, loc=beta, scale=sigma).rvs(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "model = pm.Model()\n",
    "with model:\n",
    "    intercept = pm.Flat('intercept')\n",
    "    sigma = pm.HalfCauchy('sigma', 2.5)\n",
    "    sigma_group = pm.HalfCauchy('sigma_group', 2.5)\n",
    "    group = pm.Normal('group', 0, 1, shape=n_groups)\n",
    "    # Using a 2d array would be faster than indexing, but less\n",
    "    # realistic. All groups would need to have the same the size.\n",
    "    mu = intercept + sigma_group * group[i_group]\n",
    "    pm.StudentT('obs', nu=5, mu=mu, sd=sigma, observed=observed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We use advi to initialize the chains and guess a mass matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average ELBO = -34,287: 100%|██████████| 20000/20000 [00:59<00:00, 335.39it/s]\n",
      "Finished [100%]: Average ELBO = -34,281\n",
      "INFO:pymc3:Finished [100%]: Average ELBO = -34,281\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 1s, sys: 227 ms, total: 1min 1s\n",
      "Wall time: 1min 1s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "with model:\n",
    "    advi = pm.variational.advi(n=20000)\n",
    "    stds = model.dict_to_array(advi.stds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd3c9d51390>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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CNquARWY2Btjh7uvdvRW4D1iYZo4iIpKGnvQYzjOzi4AW4Fp3/3MY/6GZNQDP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\nR4VBRETiqDCIiEic/w927X+dZTS2iQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3d1656710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(advi.elbo_vals[5000:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Time to make one step\n",
    "\n",
    "Each step is implemented as a theano function. `leapfrog3` does three\n",
    "leapfrog steps in a row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 loops, best of 3: 2.03 ms per loop\n",
      "100 loops, best of 3: 2.69 ms per loop\n",
      "100 loops, best of 3: 3.4 ms per loop\n",
      "100 loops, best of 3: 3.64 ms per loop\n"
     ]
    }
   ],
   "source": [
    "for integrator in ['leapfrog', 'two-stage', 'three-stage', 'leapfrog3']:\n",
    "    step = pm.step_methods.hmc.base_hmc.BaseHMC(\n",
    "        vars=model.vars, model=model, integrator=integrator,\n",
    "        use_single_leapfrog=True, profile=False)\n",
    "\n",
    "    q = model.dict_to_array(advi.means)\n",
    "    p = np.ones(model.ndim) * .05\n",
    "    dlogp = step.dlogp(q)\n",
    "    \n",
    "    %%timeit step.leapfrog(q, p, dlogp, np.array(0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Run four chains per integration method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "nuts_args = {\n",
    "    'scaling': stds ** 2,\n",
    "    'is_cov': True,\n",
    "    'max_treedepth': 10,\n",
    "    'target_accept': 0.95,\n",
    "}\n",
    "sample_args = {\n",
    "    'draws': 2000,\n",
    "    'tune': 1000,\n",
    "    'start': advi.means\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def sample(integrator):\n",
    "    with model:\n",
    "        step = pm.NUTS(integrator=integrator, **nuts_args)\n",
    "        chains = []\n",
    "        # Run 4 chains in total, two at a time\n",
    "        for i in range(2):\n",
    "            trace = pm.sample(step=step, njobs=2, chain=2 * i, **sample_args)\n",
    "            chains.append(trace)\n",
    "        trace = pm.backends.base.merge_traces(chains)\n",
    "    return trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [06:56<00:00,  6.68it/s]\n",
      "100%|██████████| 2000/2000 [06:21<00:00,  7.27it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7.16 s, sys: 1.3 s, total: 8.46 s\n",
      "Wall time: 13min 24s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "trace1 = sample('leapfrog')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [03:25<00:00,  9.73it/s] \n",
      "100%|██████████| 2000/2000 [02:59<00:00, 11.14it/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.42 s, sys: 1.11 s, total: 10.5 s\n",
      "Wall time: 6min 35s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "trace2 = sample('three-stage')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [06:40<00:00,  4.99it/s] \n",
      "100%|██████████| 2000/2000 [07:00<00:00, 16.58it/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.44 s, sys: 1.08 s, total: 10.5 s\n",
      "Wall time: 13min 50s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "trace3 = sample('leapfrog3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'group': array([ 4000.,  4000.,  4000., ...,  4000.,  4000.,  4000.]),\n",
       " 'intercept': 4000.0,\n",
       " 'sigma': 1430.0,\n",
       " 'sigma_group': 897.0,\n",
       " 'sigma_group_log_': 898.0,\n",
       " 'sigma_log_': 1430.0}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.effective_n(trace1[1000:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'group': array([ 4000.,  4000.,  4000., ...,  4000.,  4000.,  4000.]),\n",
       " 'intercept': 4000.0,\n",
       " 'sigma': 1600.0,\n",
       " 'sigma_group': 958.0,\n",
       " 'sigma_group_log_': 958.0,\n",
       " 'sigma_log_': 1600.0}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.effective_n(trace2[1000:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'group': array([ 4000.,  4000.,  4000., ...,  4000.,  4000.,  4000.]),\n",
       " 'intercept': 4000.0,\n",
       " 'sigma': 1250.0,\n",
       " 'sigma_group': 665.0,\n",
       " 'sigma_group_log_': 666.0,\n",
       " 'sigma_log_': 1251.0}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.effective_n(trace3[1000:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd3b8d5ea58>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LLmcTIzl3QiqLMhqpr7VWWB169m94mlqoTbfjagsx1leGMX4y3j0d3Vq+0lJC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\nxGStG25VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3b9563080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(trace1['step_size_bar'])\n",
    "plt.plot(trace2['step_size_bar'] / 3)\n",
    "plt.plot(trace3['step_size_bar'] / 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# TODO use pd.concat instead of stupid loops...\n",
    "def collect_stats(traces):\n",
    "    names = set()\n",
    "    for trace in traces.values():\n",
    "        names.update(trace.stat_names)\n",
    "    statnames = list(names)\n",
    "    \n",
    "    data = []\n",
    "    for name, trace in traces.items():\n",
    "        for sample in range(len(trace)):\n",
    "            for chain in range(trace.nchains):\n",
    "                row = {\n",
    "                    'integrator': name,\n",
    "                    'sample': sample,\n",
    "                    'chain': chain,\n",
    "                }\n",
    "                for stat_name in trace.stat_names:\n",
    "                    stats = trace.get_sampler_stats(\n",
    "                        stat_name, combine=False, chains=chain)\n",
    "                    row[stat_name] = stats[sample]\n",
    "                data.append(row)\n",
    "\n",
    "    return pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "trace_stats = collect_stats({\n",
    "    'leapfrog': trace1[1000:],\n",
    "    'three_stage': trace2[1000:],\n",
    "    'leapfrog3': trace3[1000:],\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "trace_stats['trajectory_length'] = trace_stats.eval('step_size * tree_size')\n",
    "trace_stats['log_trajectory_length'] = np.log(trace_stats['trajectory_length'])\n",
    "trace_stats['grads_per_step'] = ((trace_stats['integrator'] != 'leapfrog') * 2) + 1\n",
    "trace_stats['step_size_eff'] = trace_stats['step_size'] / trace_stats['grads_per_step']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd3bacc6710>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8d1+VrwCjUAIQEclerncC13chcg3Qv575IiJSIHIaC6gpqQYgIpK9nGoAZtaX4K7dQUA1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\n7NcUp1E2iwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3ba24bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.violinplot(y='trajectory_length', x='integrator', hue='chain', data=trace_stats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Effective step size (step size per grad eval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x7fd3ba22e4e0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2W2kkSUeR5hd4PvCMpLcCb46IzbWOKZIAHwcey20v7k+QZmZlyHqeHNebY4qMBf6YpEOB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\nvTMsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3ba72c9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.factorplot('integrator', 'step_size_eff', data=trace_stats, hue='chain', kind='bar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_grad_evals1 = trace1['tree_size']\n",
    "n_grad_evals2 = 3 * trace2['tree_size']\n",
    "n_grad_evals3 = 3 * trace3['tree_size']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(65.804571428571435, 51.034285714285716, 117.03428571428572)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_grad_evals1[1000:].mean(), n_grad_evals2[1000:].mean(), n_grad_evals3[1000:].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, False, False)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace1['diverging'].any(), trace2['diverging'].any(), trace3['diverging'].any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.94856764173948027, 0.95123333225621964, 0.94937178350932838)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace1['mean_tree_accept'].mean(), trace2['mean_tree_accept'].mean(), trace3['mean_tree_accept'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Integration error (difference of hamiltonians)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd3bf4ade80>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TwjTJhpsJ51IEyjmGR8u0B1oBZK9cOEYKuWgIlm3TNVoZjy2+u83RLNlIMwB9+WmGRsq0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\nHAS3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3bf70c518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.distplot(trace1['energy_error', 1000:])\n",
    "sb.distplot(trace2['energy_error', 1000:])\n",
    "sb.distplot(trace3['energy_error', 1000:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The maximum error along the whole tree is larger for leapfrog integration. But this might just be because of the different tree sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd3bf7e1b00>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fZiJirLG8nfrQzDPAWU37LKyXJA3JSov63cCVjeWrgbuAvcD5EXFm4wTpDuD+1UeUJPVq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\nUZekgljUJakgFnVJKsj/B1haLo8LukzyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3bba21518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.distplot(trace1['max_energy_error', 1000:], kde=False)\n",
    "sb.distplot(trace2['max_energy_error', 1000:], kde=False)\n",
    "sb.distplot(trace3['max_energy_error', 1000:], kde=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def energy_plot(trace):\n",
    "    energy = trace.get_sampler_stats('energy', combine=False)\n",
    "    nchains = len(energy)\n",
    "    fig, axes = plt.subplots(2, nchains // 2)\n",
    "    for energy, ax in zip(energy, axes.flat):\n",
    "        sb.distplot(energy - energy.mean(), label='energy', ax=ax)\n",
    "        sb.distplot(np.diff(energy), label='energy diffs', ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1R1dDlWM3ds1Je/gqppVIYPUb79lJjtvOU2+0MrjG2siK7KaxI8ATzzficdr4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\nG5slhm34bWxsbJYY/x+MsBVn0taJ/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3b8e768d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "energy_plot(trace1[1000:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The correlation does not look geat, but this seems to be unrelated to\n",
    "the integration method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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85m7n5dcmb4t4zN2946ld7k46b4tl1iZ3zduO8dQub4u4Zjp3p7boliRJkqbF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3b83c6f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3b82c3e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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L/FW1zHXAnwCvBh4FPCwizgfuArwuM79e76VI0639JmC/bkmSZk+tojsiHg58lNZPv89F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\nzKJbkiRJatj/BzM/dBm1LI7JAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3b815e748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = pm.autocorrplot(trace1[1000:], ['sigma_group_log_'], max_lag=100)\n",
    "_ = pm.autocorrplot(trace2[1000:], ['sigma_group_log_'], max_lag=100)\n",
    "_ = pm.autocorrplot(trace3[1000:], ['sigma_group_log_'], max_lag=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Stan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting binomial.stan\n"
     ]
    }
   ],
   "source": [
    "%%file binomial.stan\n",
    "data {\n",
    "    int N;\n",
    "    int n_groups;\n",
    "    int i_group[N];\n",
    "    vector[N] y;\n",
    "}\n",
    "parameters {\n",
    "    real intercept;\n",
    "    real<lower=0> sigma;\n",
    "    real<lower=0> sigma_group;\n",
    "    vector[n_groups] group;\n",
    "}\n",
    "transformed parameters {\n",
    "    vector[N] mu;\n",
    "    \n",
    "    mu = intercept + sigma_group * group[i_group];\n",
    "}\n",
    "model {\n",
    "    sigma ~ cauchy(0, 2.5);\n",
    "    sigma_group ~ cauchy(0, 2.5);\n",
    "    group ~ normal(0, 1);\n",
    "    y ~ student_t(5, mu, sigma);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_008f2dd06ee2127d7943ff0898e0e5de NOW.\n"
     ]
    }
   ],
   "source": [
    "stan_model = pystan.StanModel('binomial.stan')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "data = {\n",
    "    'N': N,\n",
    "    'i_group': i_group + 1,\n",
    "    'n_groups': n_groups,\n",
    "    'y': observed,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.01 s, sys: 2.47 s, total: 6.48 s\n",
      "Wall time: 45min 31s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "stan_trace = stan_model.sampling(data, control={'adapt_delta': 0.95}, chains=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def get_trajectory_len(trace, chain):\n",
    "    n_leapfrog = trace.get_sampler_params()[chain]['n_leapfrog__']\n",
    "    step_size = trace.get_sampler_params()[chain]['stepsize__']\n",
    "    return n_leapfrog * step_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 10)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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oLlMIgmAcoZwf5PZl2R5fAWyOamph9FPoljX7UEXKwzIT7zL2SxXnuu0Xy4TihDytLhHv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\nAxHxFgRBMBARb0EQBAMR8RYEQTCQ/w+pD0Gt3/OEwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd3bf228f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for chain in range(4):\n",
    "    plt.plot(get_trajectory_len(stan_trace, chain)[1000:])\n",
    "plt.ylim(0, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.928298339344\n",
      "0.944478724007\n",
      "0.956853308722\n",
      "0.919931618767\n"
     ]
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    print(stan_trace.get_sampler_params()[i]['accept_stat__'][1000:].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0952579241263\n",
      "0.0862117192884\n",
      "0.0781050493422\n",
      "0.100605904905\n"
     ]
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    print(stan_trace.get_sampler_params()[i]['stepsize__'][-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One chain is going crazy (treedepth reaches 10). The others finished after ~20min. They seem to favor a slightly larger trajectory length, but on the other hand the acceptance rates are a bit lower...\n",
    "\n",
    "The mass matrix is different, for comparison we try a mass matrix based on the variance of a previous trace in pymc:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [06:12<00:00,  5.85it/s]\n",
      "100%|██████████| 2000/2000 [06:28<00:00,  6.99it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7.08 s, sys: 1.58 s, total: 8.66 s\n",
      "Wall time: 12min 55s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "samples = [model.dict_to_array(p) for p in trace1[1000:]]\n",
    "nuts_args['scaling'] = np.array(samples).var(0)\n",
    "trace4 = sample('leapfrog')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd3a92a97b8>]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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B88zs0nh5H9EtnRuB77v7q/H86RSd9bv7YeA+4Edm9gxwIvDNcTkKkQbIaZxNaUJJund2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd39b168c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(trace4[1000:]['step_size'] * trace4[1000:]['tree_size'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.07949173,  0.08037735,  0.08220298,  0.08069547])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace4[-1:]['step_size']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I guess that is close enough?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}