{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Causal Structures - Intervention-Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "# execute the creation & training notebook first\n",
    "%run \"02-02-prediction.ipynb\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the [prediction section](./02-02-prediction.ipynb) made prediction based on our trained causal structure.\n",
    "The ``prediction`` method propagates information to all directions. This is correct from an information theoretical point of view. An observation of a certain parameter can contain information about all other parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ``InterventionPredictor``, that can be applied by calling the ``predict_interventions`` method of the ``CausalStructure``, distinguishes between interventions and observations by applying the Do calculus for causal models. Information from parameters that are subject to an intervention can only propagate forwards in the causal model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can observe this difference when making intervention predictions given the parameter \"(b|a)\". This parameter depends on \"(a)\" and influences \"(c|a,b)\". In that sense it is both input and output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CausalStructure([({'(a)'}, '(b|a)'),\n",
       "                 (set(), '(a)'),\n",
       "                 ({'(a)', '(b|a)'}, '(c|a,b)')])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "causal_structure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With neither observations nor interventions we just get the learned mean values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>(a)</th>\n",
       "      <th>(b|a)</th>\n",
       "      <th>(c|a,b)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.989583</td>\n",
       "      <td>-24.723056</td>\n",
       "      <td>40.030782</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "        (a)      (b|a)    (c|a,b)\n",
       "0  4.989583 -24.723056  40.030782"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "causal_structure.predict_interventions(data={}, interventions={})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the observation b=0 we see that both the predicted values for \"(a)\" and \"(c|a,b)\" change, since observational information travels forwards and backwards."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>(a)</th>\n",
       "      <th>(b|a)</th>\n",
       "      <th>(c|a,b)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.526823</td>\n",
       "      <td>0.0</td>\n",
       "      <td>47.290798</td>\n",
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       "  </tbody>\n",
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      "text/plain": [
       "        (a)  (b|a)    (c|a,b)\n",
       "0  4.526823    0.0  47.290798"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "causal_structure.predict_interventions(data={\"(b|a)\": [0]}, interventions={})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the intervention b=0 we see that only \"(c|a,b)\" changes, since interventional information only travels forwards.\n",
    "The predicted values for \"(c|a,b)\" also changed because \"(c|a,b)\" also depends on \"(a)\" (and therefore its estimate)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>(a)</th>\n",
       "      <th>(b|a)</th>\n",
       "      <th>(c|a,b)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.989583</td>\n",
       "      <td>0.0</td>\n",
       "      <td>51.021084</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        (a)  (b|a)    (c|a,b)\n",
       "0  4.989583    0.0  51.021084"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "causal_structure.predict_interventions(data={}, interventions={\"(b|a)\": [0]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the [next section](./02-04-evaluation.ipynb) we will evaluate the causal structures predictive performance."
   ]
  }
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