pymc3-demo.ipynb

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    "This a demo that shows how dense mass matrix adaptation can help PyMC3's performance in some cases.\n",
    "See [this blog post](https://dfm.io/posts/pymc3-mass-matrix/) for a more detailed discussion.\n",
    "\n",
    "First, let's see what the PyMC3's performance is on an uncorrelated Gaussian:"
   ]
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      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [x]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 12000/12000 [00:04<00:00, 2851.12draws/s]"
     ]
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     "name": "stdout",
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     "text": [
      "time per effective sample: 0.31932 ms\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "import pymc3 as pm\n",
    "\n",
    "ndim = 5\n",
    "\n",
    "with pm.Model() as simple_model:\n",
    "    pm.Normal(\"x\", shape=(ndim,))\n",
    "\n",
    "strt = time.time()\n",
    "with simple_model:\n",
    "    simple_trace = pm.sample(draws=3000, tune=3000, random_seed=42)\n",
    "    \n",
    "    # About half the time is spent in tuning so correct for that\n",
    "    simple_time = 0.5*(time.time() - strt)\n",
    "    \n",
    "stats = pm.summary(simple_trace)\n",
    "simple_time_per_eff = simple_time / stats.n_eff.min()\n",
    "print(\"time per effective sample: {0:.5f} ms\".format(simple_time_per_eff * 1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As discussed in the blog post, PyMC3 doesn't do so well if there are correlations.\n",
    "But we can use the `QuadPotentialFullAdapt` potential to get nearly the same performance as above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [x]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 30000/30000 [00:21<00:00, 1391.33draws/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time per effective sample: 0.30707 ms\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Generate a random positive definite matrix\n",
    "np.random.seed(42)\n",
    "L = np.random.randn(ndim, ndim)\n",
    "L[np.diag_indices_from(L)] = 0.1*np.exp(L[np.diag_indices_from(L)])\n",
    "L[np.triu_indices_from(L, 1)] = 0.0\n",
    "cov = np.dot(L, L.T)\n",
    "\n",
    "with pm.Model() as model:\n",
    "    pm.MvNormal(\"x\", mu=np.zeros(ndim), chol=L, shape=(ndim,))\n",
    "    \n",
    "    # *** This is the new part ***\n",
    "    potential = pm.step_methods.hmc.quadpotential.QuadPotentialFullAdapt(\n",
    "        model.ndim, np.zeros(model.ndim))\n",
    "    step = pm.NUTS(model=model, potential=potential)\n",
    "    # *** end new part ***\n",
    "    \n",
    "    strt = time.time()\n",
    "    full_adapt_trace = pm.sample(draws=10000, tune=5000, random_seed=42, step=step)\n",
    "    full_adapt_time = 0.5 * (time.time() - strt)\n",
    "\n",
    "stats = pm.summary(full_adapt_trace)\n",
    "full_adapt_time_per_eff = full_adapt_time / stats.n_eff.min()\n",
    "print(\"time per effective sample: {0:.5f} ms\".format(full_adapt_time_per_eff * 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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