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   "source": [
    "# Example 3: Custom value functions\n",
    "#### These examples are from section 5.1 of the Faith-Shap paper: https://arxiv.org/abs/2203.00870"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c10cfd76",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set_context(\"notebook\", rc={'axes.linewidth': 2, 'grid.linewidth': 1},  font_scale=1.5)\n",
    "\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "import nshap"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f0b5f063",
   "metadata": {},
   "source": [
    "### Example 1\n",
    "##### A value function takes two arguments: A single data point x (a numpy.ndarray) and a python list S with the indices the the coordinates that belong to the coaltion.\n",
    "##### In this example, the value does not actually depend on the point x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "44978e93",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "p = 0.1\n",
    "def v_func(x, S):\n",
    "    \"\"\" The value function from Example 1 in the Faith-Shap paper.\n",
    "    \"\"\"\n",
    "    if len(S) <= 1:\n",
    "        return 0\n",
    "    return len(S) - p * math.comb(len(S), 2)\n",
    "\n",
    "\n",
    "v_func(np.zeros((1,11)), [1,2,3,4])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "86a0f974",
   "metadata": {},
   "source": [
    "##### Equipped with the value function, we can compute different kinds of interaction indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fbbbbcf5",
   "metadata": {},
   "outputs": [],
   "source": [
    "faith_shap = nshap.faith_shap(np.zeros((1,11)), v_func, 1)\n",
    "faith_shap[(0,1)], faith_shap[(1,2)]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "08657d28",
   "metadata": {},
   "source": [
    "##### We can replicate Table 1 in the Faith-Shap paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d4bcee91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 1 in the Faith-Shap paper:\n",
      "\n",
      "p=0.1 l=1\n",
      "\n",
      "Faith-Shap:  0.5000000000001867\n",
      "Shapley Taylor:  0.500000000000185\n",
      "Interaction Shapley:  0.4999999999999939\n",
      "Banzhaf Interaction:  0.5087890624999979\n",
      "Faith-Banzhaf:  0.5087890624999989\n",
      "\n",
      "p=0.1 l=2\n",
      "\n",
      "Faith-Shap:  0.9545454545463214 -0.09090909090923938\n",
      "Shapley Taylor:  0 0.10000000000002415\n",
      "Interaction Shapley:  0.4999999999999939 -5.759281940243e-16\n",
      "Banzhaf Interaction:  0.5087890624999979 -0.11367187500000073\n",
      "Faith-Banzhaf:  1.0771484374999503 -0.11367187499999737\n",
      "\n",
      "p=0.2 l=1\n",
      "\n",
      "Faith-Shap:  1.6486811915683575e-13\n",
      "Shapley Taylor:  1.7552626019323725e-13\n",
      "Interaction Shapley:  2.7755575615628914e-17\n",
      "Banzhaf Interaction:  0.0087890625\n",
      "Faith-Banzhaf:  0.008789062500008604\n",
      "\n",
      "p=0.2 l=2\n",
      "\n",
      "Faith-Shap:  0.9545454545460967 -0.19090909090925617\n",
      "Shapley Taylor:  0 -3.7941871866564725e-14\n",
      "Interaction Shapley:  2.7755575615628914e-17 -0.10000000000000021\n",
      "Banzhaf Interaction:  0.0087890625 -0.21367187500000198\n",
      "Faith-Banzhaf:  1.0771484374999574 -0.21367187499998952\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('Table 1 in the Faith-Shap paper:\\n')\n",
    "for p in [0.1, 0.2]:\n",
    "    for l in [1, 2]:\n",
    "        print(f'p={p} l={l}\\n')\n",
    "\n",
    "        # define the value function\n",
    "        def v_func(x, S):\n",
    "            if len(S) <= 1:\n",
    "                return 0\n",
    "            return len(S) - p * math.comb(len(S), 2)\n",
    "\n",
    "        # compute interaction indices\n",
    "        faith_shap = nshap.faith_shap(np.zeros((1,11)), v_func, l)\n",
    "        shapley_taylor = nshap.shapley_taylor(np.zeros((1,11)), v_func, l)\n",
    "        shapley_interaction = nshap.shapley_interaction_index(np.zeros((1,11)), v_func, l)\n",
    "        banzhaf_interaction = nshap.banzhaf_interaction_index(np.zeros((1,11)), v_func, l)\n",
    "        faith_banzhaf = nshap.faith_banzhaf(np.zeros((1,11)), v_func, l)\n",
    "\n",
    "        # print result\n",
    "        if l == 1:\n",
    "            print('Faith-Shap: ', faith_shap[(0,)])\n",
    "            print('Shapley Taylor: ', shapley_taylor[(0,)])\n",
    "            print('Interaction Shapley: ', shapley_interaction[(0,)])\n",
    "            print('Banzhaf Interaction: ', banzhaf_interaction[(0,)])\n",
    "            print('Faith-Banzhaf: ', faith_banzhaf[(0,)])\n",
    "        else:\n",
    "            print('Faith-Shap: ', faith_shap[(0,)], faith_shap[(0,1)])\n",
    "            print('Shapley Taylor: ', shapley_taylor[(0,)], shapley_taylor[(0,1)])\n",
    "            print('Interaction Shapley: ', shapley_interaction[(0,)], shapley_interaction[(0,1)])\n",
    "            print('Banzhaf Interaction: ', banzhaf_interaction[(0,)], banzhaf_interaction[(0,1)])\n",
    "            print('Faith-Banzhaf: ', faith_banzhaf[(0,)], faith_banzhaf[(0,1)])\n",
    "        print('')"
   ]
  }
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