{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(['seaborn-darkgrid'])\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import  pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model averaging\n",
    "\n",
    "When confronted with more than one model we have several options. One of them is to perform model selection, using for example a given Information Criterion as exemplified [in this notebook](model_comparison.ipynb) and this other [example](GLM-model-selection.ipynb). Model selection is appealing for its simplicity, but we are discarding information about the uncertainty in our models. This is somehow similar to computing the full posterior and then just keep a point-estimate like the posterior mean; we may become overconfident of what we really know.\n",
    "\n",
    "One alternative is to perform model selection but discuss all the different models together with the computed values of a given Information Criterion. It is important to put all these numbers and tests in the context of our problem so that we and our audience can have a better feeling of the possible limitations and shortcomings of our methods. If you are in the academic world you can use this approach to add elements to the discussion section of a paper, presentation, thesis, and so on.\n",
    "\n",
    "Yet another approach is to perform model averaging. The idea now is to generate a meta-model (and meta-predictions) using a weighted average of the models. There are several ways to do this and PyMC3 includes 3 of them that we are going to briefly discuss, you will find a more thorough explanation in the work by [Yuling Yao et. al.](https://arxiv.org/abs/1704.02030)\n",
    "\n",
    "## Pseudo Bayesian model averaging\n",
    "\n",
    "Bayesian models can be weighted by their marginal likelihood, this is known as Bayesian Model Averaging. While this is theoretically appealing, is problematic in practice: on the one hand the marginal likelihood is highly sensible to the specification of the prior, in a way that parameter estimation is not, and on the other computing the marginal likelihood is usually a challenging task. An alternative route is to use the values of WAIC (Widely Applicable Information Criterion) or LOO (pareto-smoothed importance sampling Leave-One-Out cross-validation), which we will call generically IC, to estimate weights. We can do this by using the following formula:\n",
    "\n",
    "$$w_i = \\frac {e^{ - \\frac{1}{2} dIC_i }} {\\sum_j^M e^{ - \\frac{1}{2} dIC_j }}$$\n",
    "\n",
    "Where $dIC_i$ is the difference between the i-esim information criterion value and the lowest one. Remember that the lowest the value of the IC, the better. We can use any information criterion we want to compute a set of weights, but, of course, we cannot mix them. \n",
    "\n",
    "This approach is called pseudo Bayesian model averaging, or Akaike-like weighting and is an heuristic way to compute the relative probability of each model (given a fixed set of models) from the information criteria values. Look how the denominator is just a normalization term to ensure that the weights sum up to one.\n",
    "\n",
    "## Pseudo Bayesian model averaging with Bayesian Bootstrapping\n",
    "\n",
    "The above formula for computing weights is a very nice and simple approach, but with one major caveat it does not take into account the uncertainty in the computation of the IC. We could compute the standard error of the IC (assuming a Gaussian approximation) and modify the above formula accordingly. Or we can do something more robust, like using a [Bayesian Bootstrapping](http://www.sumsar.net/blog/2015/04/the-non-parametric-bootstrap-as-a-bayesian-model/) to estimate, and incorporate this uncertainty.\n",
    "\n",
    "## Stacking\n",
    "\n",
    "The third approach implemented in PyMC3 is know as _stacking of predictive distributions_ and it has been recently [proposed](https://arxiv.org/abs/1704.02030). We want to combine several models in a metamodel in order to minimize the diverge between the meta-model and the _true_ generating model, when using a logarithmic scoring rule this is equivalently to:\n",
    "\n",
    "$$\\max_{n} \\frac{1}{n} \\sum_{i=1}^{n}log\\sum_{k=1}^{K} w_k p(y_i|y_{-i}, M_k)$$\n",
    "\n",
    "Where $n$ is the number of data points and $K$ the number of models. To enforce a solution we constrain $w$ to be $w_k \\ge 0$ and  $\\sum_{k=1}^{K} w_k = 1$. \n",
    "\n",
    "The quantity $p(y_i|y_{-i}, M_k)$ is the leave-one-out predictive distribution for the $M_k$ model. Computing it requires fitting each model $n$ times, each time leaving out one data point. Fortunately we can approximate the exact leave-one-out predictive distribution using LOO (or even WAIC), and that is what we do in practice.\n",
    "\n",
    "## Weighted posterior predictive samples\n",
    "\n",
    "Once we have computed the weights, using any of the above 3 methods,  we can use them to get a weighted posterior predictive samples. PyMC3 offers functions to perform these steps in a simple way, so let see them in action using an example.\n",
    "\n",
    "The following example is taken from the superb book [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking/) by Richard McElreath. You will find more PyMC3 examples from this book in this [repository](https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3). We are going to explore a simplified version of it. Check the book for the whole example and a more thorough discussion of both, the biological motivation for this problem and a theoretical/practical discussion of using Information Criteria to compare, select and average models.\n",
    "\n",
    "Briefly, our problem is as follows: We want to explore the composition of milk across several primate species, it is hypothesized that females from species of primates with larger brains produce more _nutritious_ milk (loosely speaking this is done _in order to_ support the development of such big brains). This is an important question for evolutionary biologists and try to give and answer we will use 3 variables, two predictor variables: the proportion of neocortex compare to the total mass of the brain and the logarithm of the body mass of the mothers. And for predicted variable, the kilocalories per gram of milk. With these variables we are going to build 3 different linear models:\n",
    " \n",
    "1. A model using only the neocortex variable\n",
    "2. A model using only the logarithm of the mass variable\n",
    "3. A model using both variables\n",
    "\n",
    "Let start by uploading the data and centering the `neocortex` and `log mass` variables, for better sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>kcal.per.g</th>\n",
       "      <th>neocortex</th>\n",
       "      <th>log_mass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.49</td>\n",
       "      <td>-0.123706</td>\n",
       "      <td>-0.831353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.47</td>\n",
       "      <td>-0.030706</td>\n",
       "      <td>0.158647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.56</td>\n",
       "      <td>-0.030706</td>\n",
       "      <td>0.181647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.89</td>\n",
       "      <td>0.000294</td>\n",
       "      <td>-0.579353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.92</td>\n",
       "      <td>0.012294</td>\n",
       "      <td>-1.885353</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   kcal.per.g  neocortex  log_mass\n",
       "0        0.49  -0.123706 -0.831353\n",
       "1        0.47  -0.030706  0.158647\n",
       "2        0.56  -0.030706  0.181647\n",
       "3        0.89   0.000294 -0.579353\n",
       "4        0.92   0.012294 -1.885353"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = pd.read_csv('../data/milk.csv')\n",
    "d.iloc[:,1:] = d.iloc[:,1:] - d.iloc[:,1:].mean()\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the data we are going to build our first model using only the `neocortex`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta, alpha]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:04<00:00, 1028.80draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_0:\n",
    "    alpha = pm.Normal('alpha', mu=0, sigma=10)\n",
    "    beta = pm.Normal('beta', mu=0, sigma=10)\n",
    "    sigma = pm.HalfNormal('sigma', 10)\n",
    "    \n",
    "    mu = alpha + beta * d['neocortex']\n",
    "    \n",
    "    kcal = pm.Normal('kcal', mu=mu, sigma=sigma, observed=d['kcal.per.g'])\n",
    "    trace_0 = pm.sample(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second model is exactly the same as the first one, except we now use the logarithm of the mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta, alpha]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:04<00:00, 1163.58draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_1:\n",
    "    alpha = pm.Normal('alpha', mu=0, sigma=10)\n",
    "    beta = pm.Normal('beta', mu=0, sigma=1)\n",
    "    sigma = pm.HalfNormal('sigma', 10)\n",
    "    \n",
    "    mu = alpha + beta * d['log_mass']\n",
    "    \n",
    "    kcal = pm.Normal('kcal', mu=mu, sigma=sigma, observed=d['kcal.per.g'])\n",
    "    \n",
    "    trace_1 = pm.sample(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally the third model using the `neocortex` and `log_mass` variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta, alpha]\n",
      "Sampling 2 chains: 100%|██████████| 5000/5000 [00:05<00:00, 962.26draws/s] \n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model_2:\n",
    "    alpha = pm.Normal('alpha', mu=0, sigma=10)\n",
    "    beta = pm.Normal('beta', mu=0, sigma=1, shape=2)\n",
    "    sigma = pm.HalfNormal('sigma', 10)\n",
    "\n",
    "    mu = alpha + pm.math.dot(beta, d[['neocortex','log_mass']].T)\n",
    "\n",
    "    kcal = pm.Normal('kcal', mu=mu, sigma=sigma, observed=d['kcal.per.g'])\n",
    "\n",
    "    trace_2 = pm.sample(2000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have sampled the posterior for the 3 models, we are going to compare them visually. One option is to use the `forestplot` function that supports plotting more than one trace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "traces = [trace_0, trace_1, trace_2]\n",
    "pm.forestplot(traces, figsize=(10, 5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another option is to plot several traces in a same plot is to use `densityplot`. This plot is somehow similar to a forestplot, but we get truncated KDE plots (by default 95% credible intervals) grouped by variable names together with a point estimate (by default the mean)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.densityplot(traces, var_names=['alpha', 'sigma']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have sampled the posterior for the 3 models, we are going to use WAIC (Widely applicable information criterion) to compare the 3 models. We can do this using the `compare` function included with PyMC3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/junpenglao/Documents/pymc3/pymc3/stats.py:219: UserWarning: For one or more samples the posterior variance of the\n",
      "        log predictive densities exceeds 0.4. This could be indication of\n",
      "        WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
      "        \n",
      "  \"\"\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "      <th>dSE</th>\n",
       "      <th>var_warn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-15.44</td>\n",
       "      <td>2.58</td>\n",
       "      <td>0</td>\n",
       "      <td>0.89</td>\n",
       "      <td>4.76</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-8.88</td>\n",
       "      <td>2.05</td>\n",
       "      <td>6.56</td>\n",
       "      <td>0.04</td>\n",
       "      <td>3.96</td>\n",
       "      <td>2.1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-7.13</td>\n",
       "      <td>1.94</td>\n",
       "      <td>8.31</td>\n",
       "      <td>0.07</td>\n",
       "      <td>2.95</td>\n",
       "      <td>4.13</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    WAIC pWAIC dWAIC weight    SE   dSE var_warn\n",
       "2 -15.44  2.58     0   0.89  4.76     0        1\n",
       "1  -8.88  2.05  6.56   0.04  3.96   2.1        1\n",
       "0  -7.13  1.94  8.31   0.07  2.95  4.13        0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dict = dict(zip([model_0, model_1, model_2], traces))\n",
    "comp = pm.compare(model_dict, method='BB-pseudo-BMA')\n",
    "comp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the best model is `model_2`, the one with both predictor variables. Notice the DataFrame is ordered from lowest to highest WAIC (_i.e_ from _better_ to _worst_ model). Check [this notebook](model_comparison.ipynb) for a more detailed discussing on model comparison.\n",
    "\n",
    "We can also see that we get a column with the relative `weight` for each model (according to the first equation at the beginning of this notebook). This weights can be _vaguely_ interpreted as the probability that each model will make the correct predictions on future data. Of course this interpretation is conditional on the models used to compute the weights, if we add or remove models the weights will change. And also is dependent on the assumptions behind WAIC (or any other Information Criterion used). So try to do not overinterpret these `weights`. \n",
    "\n",
    "Now we are going to use copmuted `weights` to generate predictions based not on a single model but on the weighted set of models. This is one way to perform model averaging. Using PyMC3 we can call the `sample_posterior_predictive_w` function as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ppc_w = pm.sample_posterior_predictive_w(traces, 1000, [model_0, model_1, model_2],\n",
    "                        weights=comp.weight.sort_index(ascending=True),\n",
    "                        progressbar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we are passing the weights ordered by their index. We are doing this because we pass `traces` and `models` ordered from model 0 to 2, but the computed weights are ordered from lowest to highest WAIC (or equivalently from larger to lowest weight). In summary, we must be sure that we are correctly pairing the weights and models.\n",
    "\n",
    "We are also going to compute PPCs for the lowest-WAIC model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "ppc_2 = pm.sample_posterior_predictive(trace_2, 1000, model_2,\n",
    "                     progressbar=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple way to compare both kind of predictions is to plot their mean and hpd interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_w = ppc_w['kcal'].mean()\n",
    "hpd_w = pm.hpd(ppc_w['kcal']).mean(0)\n",
    "\n",
    "mean = ppc_2['kcal'].mean()\n",
    "hpd = pm.hpd(ppc_2['kcal']).mean(0)\n",
    "\n",
    "plt.errorbar(mean, 1, xerr=[[mean - hpd]], fmt='o', label='model 2')\n",
    "plt.errorbar(mean_w, 0, xerr=[[mean_w - hpd_w]], fmt='o', label='weighted models')\n",
    "\n",
    "plt.yticks([])\n",
    "plt.ylim(-1, 2)\n",
    "plt.xlabel('kcal per g')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see the mean value is almost the same for both predictions but the uncertainty in the weighted model is larger. We have effectively propagated the uncertainty about which model we should select to the posterior predictive samples. You can now try with the other two methods for computing weights `stacking` (the default and recommended method) and `pseudo-BMA`.\n",
    "\n",
    "**Final notes:** \n",
    "\n",
    "There are other ways to average models such as, for example, explicitly building a meta-model that includes all the models we have. We then perform parameter inference while jumping between the models. One problem with this approach is that jumping between models could hamper the proper sampling of the posterior.\n",
    "\n",
    "Besides averaging discrete models we can sometimes think of continuous versions of them. A toy example is to imagine that we have a coin and we want to estimated it's degree of bias, a number between 0 and 1 being 0.5 equal chance of head and tails. We could think of two separated models one with a prior biased towards heads and one towards tails. We could fit both separate models and then average them using, for example, IC-derived weights. An alternative, is to build a hierarchical model to estimate the prior distribution, instead of contemplating two discrete models we will be computing a continuous model that includes these the discrete ones as particular cases. Which approach is better? That depends on our concrete problem. Do we have good reasons to think about two discrete models, or is our problem better represented with a continuous bigger model?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pymc3 3.8\n",
      "arviz 0.8.3\n",
      "numpy 1.17.5\n",
      "last updated: Thu Jun 11 2020 \n",
      "\n",
      "CPython 3.8.2\n",
      "IPython 7.11.0\n",
      "watermark 2.0.2\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}