Session 10.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cc9a2070-5b32-4599-b631-2dbfe08da171",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy\n",
    "\n",
    "tfd = tfp.distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7a8d796f-54b4-4add-b10c-2eed3391f4a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "14f96651-a643-418a-bc10-9c60148aa44d",
   "metadata": {},
   "outputs": [],
   "source": [
    "frogs = pandas.read_csv('frogs.csv', sep='\\t', dtype={'density': numpy.float32, 'surv': numpy.float32})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "98a127ab-591a-4fe1-9425-2e61482e7694",
   "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>density</th>\n",
       "      <th>pred</th>\n",
       "      <th>size</th>\n",
       "      <th>surv</th>\n",
       "      <th>propsurv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.0</td>\n",
       "      <td>no</td>\n",
       "      <td>big</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>no</td>\n",
       "      <td>big</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.0</td>\n",
       "      <td>no</td>\n",
       "      <td>big</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10.0</td>\n",
       "      <td>no</td>\n",
       "      <td>big</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10.0</td>\n",
       "      <td>no</td>\n",
       "      <td>small</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   density pred   size  surv  propsurv\n",
       "0     10.0   no    big   9.0       0.9\n",
       "1     10.0   no    big  10.0       1.0\n",
       "2     10.0   no    big   7.0       0.7\n",
       "3     10.0   no    big  10.0       1.0\n",
       "4     10.0   no  small   9.0       0.9"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frogs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "df031c3d-ca65-41a1-afe1-7f50a8849169",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x197940880>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(data=frogs, x='propsurv', col='pred')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "599864d6-cf87-4555-9dbe-0880dd7e3ce6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x197940040>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(data=frogs, x='propsurv', col='size')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "af2715c7-ffea-4b4e-ba82-30e3e63e8371",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2021-11-03 12:33:31.786156: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA\n",
      "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n"
     ]
    }
   ],
   "source": [
    "surv = tf.constant(frogs['surv'])\n",
    "big_tank = tf.constant(frogs['size'] == 'big', tf.float32)\n",
    "pred = tf.constant(frogs['pred'] == 'yes', tf.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b72c9068-0bf7-4aec-9e18-d47d7ece1f61",
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.get_logger().setLevel('ERROR')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d75fcd4e-cf23-47cd-a2bd-45036f0e57af",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Simple Model\n",
    "\n",
    "$$\\begin{align}\n",
    "\\theta_i &\\sim \\operatorname{LogitNormal}(0.5, 2)\\\\\n",
    "s_i &\\sim \\operatorname{Binomial}(N_i, \\theta_i)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9ff94b11-3915-4d7f-9e34-0a94406cadbe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x197af9d00>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(tfd.LogitNormal(0.5, 2).sample(1000).numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "74782b73-2290-43c3-bb0a-19a9b1b4e02b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x197944310>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 405.725x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(tfd.LogitNormal(0.5, [2, 4, 6]).sample(1000).numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2a6a602b-4966-46a0-8f30-02cbca426991",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = tfd.JointDistributionNamedAutoBatched({\n",
    "    'theta': tfd.Independent(tfd.LogitNormal(0.5*tf.ones(frogs.shape[0]), 2)),\n",
    "    's': lambda theta: tfd.Independent(tfd.Binomial(frogs['density'], probs=theta))\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3674ed1b-ffa8-4e48-b688-02e94a69bb9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(('theta', ()), ('s', ('theta',)))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.resolve_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7a55a30a-901d-4ccd-9de9-042cadfc30a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'theta': <tf.Tensor: shape=(3, 48), dtype=float32, numpy=\n",
       " array([[0.25070485, 0.8849838 , 0.9726698 , 0.3345939 , 0.04289815,\n",
       "         0.743765  , 0.9321073 , 0.76890767, 0.48404548, 0.9831492 ,\n",
       "         0.8679998 , 0.9969816 , 0.8867942 , 0.67212665, 0.95158637,\n",
       "         0.964478  , 0.9716575 , 0.9601581 , 0.91522205, 0.3018184 ,\n",
       "         0.98624384, 0.9784788 , 0.99610245, 0.9509904 , 0.97095037,\n",
       "         0.4144117 , 0.07510614, 0.6644594 , 0.96148133, 0.23806265,\n",
       "         0.49170086, 0.9741353 , 0.65268767, 0.9586655 , 0.56373304,\n",
       "         0.71313167, 0.90488577, 0.77886677, 0.6455966 , 0.9515068 ,\n",
       "         0.27115405, 0.68141055, 0.79667675, 0.93013084, 0.296449  ,\n",
       "         0.8096272 , 0.96637666, 0.61298835],\n",
       "        [0.86203957, 0.8692752 , 0.12089875, 0.13728139, 0.53664297,\n",
       "         0.6887969 , 0.59824014, 0.78698444, 0.9208908 , 0.98496115,\n",
       "         0.92557716, 0.79088324, 0.9392315 , 0.24093997, 0.66190535,\n",
       "         0.62346727, 0.9039001 , 0.83075297, 0.06368989, 0.83029306,\n",
       "         0.314081  , 0.05415592, 0.34643656, 0.36611015, 0.87590873,\n",
       "         0.46522373, 0.90194833, 0.48710442, 0.57854253, 0.28732806,\n",
       "         0.9977458 , 0.40644133, 0.39159536, 0.14623645, 0.47070676,\n",
       "         0.65426564, 0.9091    , 0.58644766, 0.5300592 , 0.7292205 ,\n",
       "         0.31527007, 0.6661667 , 0.80859625, 0.77122146, 0.22440276,\n",
       "         0.20822161, 0.9811411 , 0.8049052 ],\n",
       "        [0.13521838, 0.24134818, 0.34301275, 0.19684926, 0.77104807,\n",
       "         0.17500228, 0.5312457 , 0.14650527, 0.7709389 , 0.912248  ,\n",
       "         0.8865353 , 0.73607993, 0.81086624, 0.11618641, 0.0667477 ,\n",
       "         0.9693385 , 0.4508969 , 0.26943147, 0.33880216, 0.9158866 ,\n",
       "         0.01964119, 0.49609572, 0.39482772, 0.98465455, 0.80160487,\n",
       "         0.5990845 , 0.72035563, 0.18852666, 0.11190054, 0.06226563,\n",
       "         0.9299475 , 0.41918036, 0.60238373, 0.13593435, 0.5952253 ,\n",
       "         0.49640584, 0.03780797, 0.02105197, 0.0111452 , 0.832835  ,\n",
       "         0.9433865 , 0.8611435 , 0.6694578 , 0.92379135, 0.8557215 ,\n",
       "         0.11822805, 0.10042766, 0.06371343]], dtype=float32)>,\n",
       " 's': <tf.Tensor: shape=(3, 48), dtype=float32, numpy=\n",
       " array([[ 4.,  9., 10.,  1.,  0.,  5.,  8., 10.,  5., 10.,  9., 10., 10.,\n",
       "          6.,  9.,  9., 25., 24., 23.,  9., 25., 24., 24., 25., 25., 13.,\n",
       "          0., 15., 25.,  3., 12., 24., 25., 35., 20., 25., 31., 25., 24.,\n",
       "         34.,  7., 22., 26., 32.,  9., 24., 34., 20.],\n",
       "        [10.,  9.,  3.,  1.,  6.,  7.,  7., 10., 10., 10., 10.,  4., 10.,\n",
       "          1.,  8.,  5., 21., 18.,  2., 22.,  9.,  2., 10.,  7., 24., 11.,\n",
       "         23., 13., 17.,  8., 25.,  6., 15.,  3., 19., 21., 33., 20., 18.,\n",
       "         27., 10., 21., 26., 25.,  6., 10., 35., 26.],\n",
       "        [ 0.,  1.,  3.,  2.,  9.,  2.,  3.,  0.,  8.,  8.,  8.,  6.,  9.,\n",
       "          0.,  1., 10., 10., 12.,  7., 25.,  0., 13.,  7., 25., 23., 17.,\n",
       "         22.,  5.,  3.,  5., 23., 11., 26.,  6., 22., 16.,  0.,  1.,  1.,\n",
       "         33., 35., 27., 24., 34., 27.,  2.,  5.,  2.]], dtype=float32)>}"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.sample(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f00afd47-a142-4ad5-9bed-74175a77681e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([-89.754234, -79.66706 , -89.30952 ], dtype=float32)>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.log_prob(model.sample(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b22a2c06-6821-40af-83cf-688afce1bf30",
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def log_prob(theta):\n",
    "    return model.log_prob({'theta': theta, 's': surv})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bab1e431-96eb-4a77-8381-d326aeae5936",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([-646.082 , -762.0449, -571.031 ], dtype=float32)>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_prob(model.sample(3)['theta'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "0d78c16e-df3a-4fe9-b697-804aaf8f0cf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def sample_chain(nobs, nburn, nchains):\n",
    "    sample = model.sample(nchains) # throw away sample for s\n",
    "    kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "        inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n",
    "            target_log_prob_fn=log_prob,\n",
    "            num_leapfrog_steps=3,\n",
    "            step_size=0.01\n",
    "        ),\n",
    "        num_adaptation_steps=int(0.8*nburn))\n",
    "    states = tfp.mcmc.sample_chain(\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=nburn,\n",
    "        num_results=nobs,\n",
    "        current_state=[sample['theta']])\n",
    "    return states\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "304111fc-e6a6-431e-bc04-e172038d6db7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dirkhesse/.pyenv/versions/3.9.6/lib/python3.9/site-packages/tensorflow_probability/python/mcmc/sample.py:342: UserWarning: Tracing all kernel results by default is deprecated. Set the `trace_fn` argument to None (the future default value) or an explicit callback that traces the values you are interested in.\n",
      "  warnings.warn('Tracing all kernel results by default is deprecated. Set '\n"
     ]
    }
   ],
   "source": [
    "tr, kr = sample_chain(5000, 1000, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "ad873a6c-69cf-4a29-bace-4cdee27950d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.71485"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kr.inner_results.is_accepted.numpy().mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "fbd115bf-d8b4-452e-9436-103b9de11d66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.catplot(data=pandas.DataFrame(tf.reshape(tr[0], (-1, 48)).numpy()), kind='box')\n",
    "plt.plot(frogs.index, frogs.propsurv, 'd')\n",
    "plt.gcf().set_size_inches(18, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dde58fc-831f-41bd-b002-7c241547b23d",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Pooling Model\n",
    "\n",
    "$$\\begin{align}\n",
    "\\alpha &\\sim \\operatorname{Normal}(0, 2)\\\\\n",
    "\\sigma &\\sim \\operatorname{HalfCauchy}(0, 1)\\\\\n",
    "a_i &\\sim \\operatorname{Normal}(\\alpha, \\sigma)\\\\\n",
    "\\theta_i &= \\operatorname{logistic}(a_i)\\\\\n",
    "s_i &\\sim \\operatorname{Binomial}(N_i, \\theta_i)\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "44d74366-d490-4398-a5b0-40fe36672f0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic(p):\n",
    "    return tf.math.exp(p) / (1 + tf.math.exp(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "ac3ec1a0-f70c-4473-973d-f5c084c7a92f",
   "metadata": {},
   "outputs": [],
   "source": [
    "pooling_model = tfd.JointDistributionNamedAutoBatched({\n",
    "    'alpha': tfd.Normal(0, 2),\n",
    "    'sigma': tfd.HalfCauchy(0, 1),\n",
    "    'theta': lambda alpha, sigma :tfd.Independent(tfd.Normal(alpha*tf.ones(frogs.shape[0]), sigma)),\n",
    "    's': lambda theta: tfd.Independent(tfd.Binomial(frogs['density'], probs=logistic(theta)))\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "e9f0d620-1ad4-4f59-b0a9-468a6d33144c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(('sigma', ()),\n",
       " ('alpha', ()),\n",
       " ('theta', ('alpha', 'sigma')),\n",
       " ('s', ('theta',)))"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pooling_model.resolve_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "88666969-d8d7-4776-9519-3a3431ce0fcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def pooling_log_prob(alpha, sigma, theta):\n",
    "    return pooling_model.log_prob(\n",
    "        {'alpha': alpha,\n",
    "         'sigma': sigma,\n",
    "         'theta': theta,\n",
    "         's': surv})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "d2a2a928-71b9-4320-a00e-93276bb79be9",
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def pooling_sample_chain(nobs, nburn, nchains):\n",
    "    sample = pooling_model.sample(nchains) # throw away sample for s\n",
    "    kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
    "        inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n",
    "            target_log_prob_fn=pooling_log_prob,\n",
    "            num_leapfrog_steps=3,\n",
    "            step_size=0.01\n",
    "        ),\n",
    "        num_adaptation_steps=int(0.8*nburn))\n",
    "    states = tfp.mcmc.sample_chain(\n",
    "        kernel=kernel,\n",
    "        num_burnin_steps=nburn,\n",
    "        num_results=nobs,\n",
    "        current_state=[\n",
    "            sample['alpha'],\n",
    "            sample['sigma'],\n",
    "            sample['theta']])\n",
    "    return states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f4661cce-2a3f-4562-be28-6bb5a5e8c425",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/dirkhesse/.pyenv/versions/3.9.6/lib/python3.9/site-packages/tensorflow_probability/python/mcmc/sample.py:342: UserWarning: Tracing all kernel results by default is deprecated. Set the `trace_fn` argument to None (the future default value) or an explicit callback that traces the values you are interested in.\n",
      "  warnings.warn('Tracing all kernel results by default is deprecated. Set '\n"
     ]
    }
   ],
   "source": [
    "tr_pooling, kr_pooling = pooling_sample_chain(5000, 1000, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "85f00155-72f0-4cea-bdf8-0d6f76e587b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7565"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kr_pooling.inner_results.is_accepted.numpy().mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "88bee440-16f2-4e0b-9699-5d2484c3242a",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<tf.Tensor: shape=(5000, 4), dtype=float32, numpy=\n",
       " array([[1.6598322, 1.5888729, 1.5016837, 1.1703875],\n",
       "        [1.0552022, 1.1906809, 1.4567803, 1.6789708],\n",
       "        [1.4724422, 1.6811236, 1.4567803, 1.2193668],\n",
       "        ...,\n",
       "        [1.3557577, 1.1832073, 1.7645457, 1.2386963],\n",
       "        [1.950095 , 1.5475075, 0.9861453, 1.2007405],\n",
       "        [1.2006868, 1.2876163, 1.7863233, 1.2007405]], dtype=float32)>,\n",
       " <tf.Tensor: shape=(5000, 4), dtype=float32, numpy=\n",
       " array([[1.4845858, 1.4127817, 1.4227797, 1.6769102],\n",
       "        [1.9423263, 1.7752112, 1.4836378, 1.5873448],\n",
       "        [1.9263442, 1.5594995, 1.4836378, 1.6055398],\n",
       "        ...,\n",
       "        [1.8236454, 1.4816883, 1.4915607, 1.8596101],\n",
       "        [2.3211906, 1.9231224, 1.5890989, 1.3184707],\n",
       "        [1.9346502, 1.2834662, 1.6822395, 1.3184707]], dtype=float32)>,\n",
       " <tf.Tensor: shape=(5000, 4, 48), dtype=float32, numpy=\n",
       " array([[[ 4.4580245e+00,  4.0492668e+00,  3.4853816e-03, ...,\n",
       "          -5.2673244e-01,  2.3217375e+00,  4.1392782e-01],\n",
       "         [ 5.8317894e-01,  3.4134789e+00,  9.9020994e-01, ...,\n",
       "          -4.5728025e-01,  2.7398505e+00,  3.9272568e-01],\n",
       "         [ 2.2339520e+00,  1.1325588e+00,  5.6639045e-01, ...,\n",
       "          -6.5700053e-03,  2.0725636e+00,  1.4151439e-01],\n",
       "         [ 1.5343670e+00,  4.0332742e+00,  8.6072403e-01, ...,\n",
       "          -3.5797030e-01,  1.9640806e+00,  9.1637969e-03]],\n",
       " \n",
       "        [[ 3.8364050e+00,  3.8800747e+00,  9.5616114e-01, ...,\n",
       "          -6.5207249e-01,  2.1852186e+00,  9.5973581e-02],\n",
       "         [ 9.3014002e-01,  3.1768413e+00,  1.4159924e+00, ...,\n",
       "          -6.0069793e-01,  3.1388645e+00,  2.2890723e-01],\n",
       "         [ 1.8967812e+00,  2.4394765e+00,  1.1231619e+00, ...,\n",
       "          -7.7032483e-01,  2.5944116e+00,  4.6545401e-01],\n",
       "         [ 1.7511960e+00,  4.7480483e+00,  6.0032016e-01, ...,\n",
       "          -7.6437318e-01,  1.4488373e+00, -8.0663025e-02]],\n",
       " \n",
       "        [[ 3.4313126e+00,  3.8718135e+00,  1.1430198e+00, ...,\n",
       "          -6.6914387e-02,  1.9413599e+00,  1.6384242e-01],\n",
       "         [ 2.0237429e+00,  2.9934416e+00,  1.6298615e+00, ...,\n",
       "          -3.3548257e-01,  2.7212698e+00,  1.9003722e-01],\n",
       "         [ 1.8967812e+00,  2.4394765e+00,  1.1231619e+00, ...,\n",
       "          -7.7032483e-01,  2.5944116e+00,  4.6545401e-01],\n",
       "         [ 1.5365658e+00,  4.5610042e+00,  3.1556687e-01, ...,\n",
       "           1.1368008e-01,  1.5168123e+00, -6.2627548e-01]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[ 2.5360034e+00,  3.0028851e+00,  1.5877712e+00, ...,\n",
       "          -7.3473996e-01,  1.9019642e+00, -3.0503768e-01],\n",
       "         [ 1.2520444e+00,  3.2798853e+00,  1.4216015e+00, ...,\n",
       "           7.8914613e-02,  1.4432019e+00,  7.1556646e-01],\n",
       "         [ 1.4002086e+00,  3.1231518e+00,  1.0215237e+00, ...,\n",
       "          -1.9819146e-01,  2.5890393e+00, -1.4379075e-01],\n",
       "         [ 2.2963071e+00,  1.2607386e+00,  5.0384003e-01, ...,\n",
       "          -5.4905033e-01,  1.9986118e+00,  3.6123914e-01]],\n",
       " \n",
       "        [[ 2.6663365e+00,  3.4576352e+00,  4.2220664e-01, ...,\n",
       "          -1.0269423e+00,  2.3393650e+00,  1.9993813e-01],\n",
       "         [ 1.3843229e+00,  2.9946680e+00,  1.0339339e+00, ...,\n",
       "          -8.4145856e-01,  1.9398062e+00,  1.1513340e+00],\n",
       "         [ 2.0075943e+00,  3.2591484e+00,  1.5816002e+00, ...,\n",
       "          -7.8313798e-01,  1.7853827e+00,  2.9041901e-01],\n",
       "         [ 1.4678340e+00,  1.1582695e+00,  3.4913328e-01, ...,\n",
       "          -4.0365446e-01,  1.7591127e+00, -6.9543272e-02]],\n",
       " \n",
       "        [[ 2.5278280e+00,  3.9523382e+00,  6.4159626e-01, ...,\n",
       "          -2.6023063e-01,  2.7654850e+00,  6.2366143e-02],\n",
       "         [ 8.9938152e-01,  4.3867307e+00,  6.8069303e-01, ...,\n",
       "          -2.0140232e-01,  1.9385597e+00,  3.3903944e-01],\n",
       "         [ 2.8590541e+00,  3.1864767e+00,  2.0404856e+00, ...,\n",
       "          -5.6322753e-01,  2.4415796e+00, -1.2405467e-01],\n",
       "         [ 1.4678340e+00,  1.1582695e+00,  3.4913328e-01, ...,\n",
       "          -4.0365446e-01,  1.7591127e+00, -6.9543272e-02]]], dtype=float32)>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tr_pooling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "a92455f2-e2ad-4474-a391-630989e89089",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x19d9651f0>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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wcImIJGHgEhFJwsAlIpKEgUtEJAkDl4hIEr8Cd+XKlV3ali5dOuDFEBGFsx4nPqxatQo2mw1VVVVwOBzedlVVcfLkSc2LIyIKJz0G7ty5c/HVV1/hiy++QFpamrddr9d717olIiL/9Bi4EyZMwIQJE3D77bdj9OjRsmoiIgpLfq2lcObMGSxfvhyNjY2d7s5QWlqqWWFEROHGr8Bds2YNcnJyMH78+IBvfUNERFf4FbgGgwEPPvig1rUQEYU1v4aF3Xzzzfjiiy+0roWIKKz5dYZ79uxZ5OTk4IYbbkBkZKS3nX24RET+8ytw8/LytK6DiCjs+RW4P/zhD7Wug4go7PkVuNOmTYNOp4MQwjtKwWg0Yu/evZoWR0QUTvwK3BMnTni3XS4X3n///U5tRKHMc4devV7HO/RSUAW8WpjBYEBWVhY+/fRTLeohGlCeO/S+/H//D9v21nS6PTqRbH6d4TY0NHi3hRA4evQompqatKqJaEA5GlvR0OKC6lKDXQoNcQH34QJAXFwc8vPzNS2MiCjcBNyHS0REfeNX4HZ0dGDLli3Yu3cvVFXFHXfcgSVLlkBR/Ho7ERHBz4tmL730Ej777DPcf//9ePDBB/HPf/4T69ev17o2IqKw4lfgfvLJJ3jttdcwY8YMpKamYvPmzX6PwX3hhRewYsUKAEB1dTVycnKQlpaG/Px8qOqVixgXLlzAwoULkZ6ejsceewwtLS19/N8hou7odEBEhA56vY6jNYLEr8AVQsBgMHgfDxs2rNPj7uzfvx/bt2/3Pl6+fDkKCwuxa9cuCCFQVFQEAFi9ejUWLFgAq9WKW265BZs2bQr0/4OIenFdzHAUV5zEm6XHOUQuSPwK3KSkJDz//PM4c+YMzpw5g+eff77X6b4NDQ3YuHEjlixZAgA4f/482traMGnSJABAdnY2rFYrXC4XDh486L2Fj6edaKB5zvAiIoZu0DgaW2FvaIWjsTXYpQxJfl31WrVqFZ599lnMmzcPHR0duOuuu1BYWNjje373u98hLy8PX3/9NQCgtrYWRqPR+7zRaITNZsPFixcRHR3tvQDnaQ9UXFx0wO/pD6MxRur+esN6uqcYFAAuXH/dNSjZdwojrxkGxaDAYFCgV/RQFPnbAKAowdu/YlAQG9v5dyaUPjOPUKupv/X0GLiXL19GYWEhZs6ciXXr1gEAFi1aBL1ej+jo7gPu3XffxZgxY5CcnIxt27YBQKdb83j4ju39bnug6uud6OiQM23TaIyB3d4sZV/+YD3d0+t13gkPbtUNR3MbVJcbqqrC5VLhVoOzDVy5+7VbVYKyf9WlwuFweqc6h9Jn5hFqNfVUj79B3GPgvvLKK3A6nZ3u0PvMM89g9erV+OMf/9jtso3l5eWw2+2YPXs2GhsbcenSJeh0OtTV1XlfY7fbYTKZEBsbC6fTCbfbDb1e720nIgo3Pfbh7tmzBy+99BLi4uK8bfHx8Vi/fj0+/PDDbt/31ltvoaysDDt27MCyZcvws5/9DGvXrkVkZCSqqqoAACUlJTCbzTAYDJgyZQrKy8s7tRMRhZseA9dgMGD48OFd2qOjozFs2LCAd7ZhwwasXbsWGRkZaG1tRW5uLoArfcRFRUXIzMzEoUOH8OSTTwb8s4mIQl2PXQoRERFwOp1d+mudTqd3DG1vsrOzkZ2dDeDKaIfi4uIur0lISMDWrVv9rZmIaFDq8Qx31qxZKCgowKVLl7xtly5dQkFBAVJTUzUvjogonPQYuPfffz9iYmJwxx134J577sHcuXNxxx13YOTIkXj88cdl1UhEFBZ67VJ45plnsHjxYhw/fhwRERGYMGEC4uPjZdVHRBQ2/Jr4cOONN+LGG2/UuhYiorAW8C12iIiobxi4RESSMHCJiCRh4BIRScLAJSKShIFLNAT53v2B5OFdIImGIM/dHyCAbPO4YJczZDBwiYYoR2MrIGcJafoWA5fCkuefykP5djoUehi4FHb0eh227a2Bo7EV4xJGAcxcChG8aEZhyXOzxMbm9mCXQuTFwCUikoSBS0QkCQOXiEgSBi4RkSQMXCIiSRi4RESSMHCJiCRh4BINYZ5FbABwIRsJONOMaAjzLGLT1OLCyCgDss3j4HZzgQWtMHCJhjhHYysanC6oLjXYpYQ9dikQEUnCwCUikoSBS0QkiaaB+4c//AGZmZnIysrCW2+9BQCorKyExWJBamoqNm7c6H1tdXU1cnJykJaWhvz8fKgq+5OIKLxoFrgHDhzAZ599hp07d+K9997D1q1bceLECaxcuRKbNm1CeXk5jh49ioqKCgDA8uXLUVhYiF27dkEIgaKiIq1KIyIKCs0Cd+rUqfjrX/8KRVFQX18Pt9uNpqYmjB07FomJiVAUBRaLBVarFefPn0dbWxsmTZoEAMjOzobVatWqNCKioNC0S8FgMOCVV15BVlYWkpOTUVtbC6PR6H3eZDLBZrN1aTcajbDZbFqWRmFIr79yF1reVodClebjcJctW4ZHH30US5YswalTp7o8r9PpIETXgdY6XWC/NHFx0X0tsU+Mxhip++sN6wHeLjsGR1M7bhoTA8WgwGBQoFf0UBQFgMu77fmv7/OytwGERC2+x0cxKIiNlft71Jtw+15rFrj/+c9/cPnyZfzoRz/CiBEjkJqaCqvVCr1e731NbW0tTCYT4uPjUVdX52232+0wmUwB7a++3omODjkzZIzGGNjtzVL25Q/Wc+Xstra+BfaGVowcoUBVVbhcKtyq23sB1rPtVrs+L3sbQEjU4tk/AKguFQ6HM2Rmmg2m77W/QaxZl8K5c+dQUFCAy5cv4/Lly/joo48wb9481NTU4PTp03C73SgrK4PZbEZCQgIiIyNRVVUFACgpKYHZbNaqNCKioNDsDDclJQWHDx/GnDlzoNfrkZqaiqysLMTGxmLp0qVob29HSkoK0tPTAQAbNmxAQUEBWlpaMH78eOTm5mpVGhFRUGjah7ts2TIsW7asU1tycjJ27tzZ5bVJSUkoLi7WshwioqDiTDMiIkkYuEREkjBwiYgk4Xq4RASg890fAITM8LBwwsAlIgD/vfuDo6EVsaNG8O4PGmDgEpGXo7EV9obWYJcRttiHS0QkCQOXiEgSBi4RkSTsw6VBTa+/clWdSzLSYMDApUFLr9dh294aOBpbMS5hFMDMpRDHLgUa1DxX1Rub24NdClGvGLhERJIwcImIJGHgEhFJwsAlIpKEgUtEJAkDl4hIEgYuEZEknPhARF1wbVxtMHCJqAuujasNBi4NOlw/QQ6ujTvwGLg0KPiGbPGek1w/gQYlBi6FvO8uUuNounLmFTtyeLBLIwoIRynQoMBFaigcMHCJiCRh4BIRScLAJSKSRNPAffXVV5GVlYWsrCysX78eAFBZWQmLxYLU1FRs3LjR+9rq6mrk5OQgLS0N+fn5UFVVy9KIiKTTLHArKyuxb98+bN++HSUlJTh27BjKysqwcuVKbNq0CeXl5Th69CgqKioAAMuXL0dhYSF27doFIQSKioq0Ko2IKCg0C1yj0YgVK1Zg2LBhMBgM+P73v49Tp05h7NixSExMhKIosFgssFqtOH/+PNra2jBp0iQAQHZ2NqxWq1alEREFhWaBe/PNN3sD9NSpUygvL4dOp4PRaPS+xmQywWazoba2tlO70WiEzWbTqjQioqDQfOLDV199hcWLF+Ppp5+Goiioqanp9LxOp4MQXedo63SBTSGKi4vuV52BMhpjpO6vN+Fej2JQYDAo0Ct6KErg24DLu93XnzGQ2wBCoparHZ/vvlYxKIiNlfv75RFu32tNA7eqqgrLli3DypUrkZWVhQMHDqCurs77fG1tLUwmE+Lj4zu12+12mEymgPZVX+9ER4ecxTWMxhjY7c1S9uWPcK9Hr9dBdalwuVS4VTdUNfBtAN5tt6r06WcM5DaAkKjFs3/f4/Pd16ouFQ6HU/riNYPpe+1vEGvWpfD111/j8ccfx4YNG5CVlQUAmDhxImpqanD69Gm43W6UlZXBbDYjISEBkZGRqKqqAgCUlJTAbDZrVRoNEnq9Dnq9jovUUNjQ7Ax3y5YtaG9vx7p167xt8+bNw7p167B06VK0t7cjJSUF6enpAIANGzagoKAALS0tGD9+PHJzc7UqjQaB766fwEVqKBxoFrgFBQUoKCi46nM7d+7s0paUlITi4mKtyqFByLN+AhepoXDBmWZERJIwcImIJGHgEhFJwgXIiahH372hpC/e5ywwDFwi6pHvDSXHJYxCY8tl3lyyjxi4RNQr3xEjjuY23lyyjxi4FFJ4R14KZwxcChmc7EDhjqMUKKTwZpEUzhi4RESSMHCJiCRh4BIRScLAJSKShIFLRCQJA5eISBIGLhGRJAxcIiJJGLhERJIwcImIJGHgEhFJwsVrKCg8q4IBXMSahg4GLknnuyoYF7GmoYSBS0HhWRWMaChh4FJQ+d4vi4uOU7hj4FJQffd+WVx0nMIZRylQ0HHRcRoqGLhERJIwcImIJGEfLhENCI6t7p3mZ7hOpxOzZs3CuXPnAACVlZWwWCxITU3Fxo0bva+rrq5GTk4O0tLSkJ+fD1VVtS6NiPrBM8JEr9fBYIjAtr01eLP0OLbtrekUvvRfmgbu4cOHMX/+fJw6dQoA0NbWhpUrV2LTpk0oLy/H0aNHUVFRAQBYvnw5CgsLsWvXLgghUFRUpGVpRNRPnhEmb5YexweHzsHRdOXip6OR46u7o2ngFhUVYdWqVTCZTACAI0eOYOzYsUhMTISiKLBYLLBarTh//jza2towadIkAEB2djasVquWpRHRAOAIk8Bo2of73HPPdXpcW1sLo9HofWwymWCz2bq0G41G2Gy2gPYVFxfdv2IDZDTGSN1fbwZbPYpBgcGgQK/ooSjabwMu77asffa0DSAkarna8envz1YMCmJjB+b3cbB9r3sj9aKZEF070nU6Xbftgaivd6KjQ05HvdEYA7u9Wcq+/BGK9TgcTu/j715A0et1UF0qXC4VbtUNVdV+G4B3260qUvbZ0zaAkKjFs3/f49Pfn626VDgczn5fOAvF73V39fgbxFIDNz4+HnV1dd7HtbW1MJlMXdrtdru3G4IGJ8/iNHGjRiDnf7/n/WPIq9c0lEkdhztx4kTU1NTg9OnTcLvdKCsrg9lsRkJCAiIjI1FVVQUAKCkpgdlsllkaDTBP354QwnthZfveGhgMEVwzgYYsqWe4kZGRWLduHZYuXYr29nakpKQgPT0dALBhwwYUFBSgpaUF48ePR25urszSSEOe8I0deeWq9qhrhnHNBBqSpATu7t27vdvJycnYuXNnl9ckJSWhuLhYRjkURI7GVkBSXztRqOHUXiIiSRi4RESScC0FGjCczknUMwYuDQjf+5T94H+u40UxoqtglwINGO80T+flYJdCFJJ4hktEA8r3PnUAJ7v4YuBSv3j6bTmZgTx871PHmYadMXCpz3z7bXkDSPL13ckujoZWxI4agWzzuCEdugxc6hffXyyiq/F8R4gXzYiIpOEZLhFJwYtpDFwiksT3YtpQ7c9l4FLAODKB+mqo9+cycCkgHJlA1He8aEYB440DifqGgUtEJAm7FKhbvqt/DbWLG0RaYODSVfn21fpOz+SFMqK+Y+BSJ74jEK42PZMXymgg+I7JHUr/emLgkldPIxA4hZcGkmdMLgSG1HhcBi51wmAlWRyNrcDQyFkvBi4RBc1Qm+7LwCWioOlp7dxwxMAloqDqbu3cR+ZMCHZpA46BOwR4Rh509881ro1AoSLc11pg4IY5z8gDHXDVf65FROhQvOck10agkBYuk3AYuGHE90vp4RlP+92xtI0tl73bjiaOTKDQ5TtccbAv68jAHeQ8IWswRHQ6U/UNVM9Zq29fmaO5jSFLIUv37XdWr9d1moQz2IVU4JaWlmLz5s1wuVx44IEHsHDhwmCXJN3VzlK74+kOaLrkQqLpmk5nqgxUGsyuixmOt8uOoba+pdNJQ0/DyAZDt0PIBK7NZsPGjRuxbds2DBs2DPPmzcNtt92GH/zgB8EubcB094XwvWjV3Vlqd9uOplY0OF0YOSJkPkqiAeFoau9y0tDdXSMGS7dDyPyWVlZWYtq0abj22msBAGlpabBarfj1r3/t1/sDvcIeyJnk1RgMga1sGRGhQ+UxG5qdlxETPQy3/zjeuxiMpz3++msQHWWAqroRNVyBu0NAdfW8/T+jRyK2VcWYuBGIvmYYRkYNwxjjNV22Y6IMPT4/oNvXR2FEpD40avl22/cYBWP/3R2jYNfi2b8/3yEt93+1569tdyNqWESX9uZLLqguN6KjDFCUCEREXPk98vzu+LYHqreQ7u9InpAJ3NraWhiNRu9jk8mEI0eO+P3+6667RouyunXttYHvLz15XEDtROS/ealJmu8jLi66X+8PmQXIhej6l0Wn4xglIgofIRO48fHxqKur8z6ura2FyWQKYkVERAMrZAL39ttvx/79++FwONDa2or3338fZrM52GUREQ2YkOnDjY+PR15eHnJzc+FyuTB37lzceuutwS6LiGjA6MTVOk+JiGjAhUyXAhFRuGPgEhFJwsAlIpKEgUtEJAkD10dpaSkyMzMxc+ZM/O1vf+vy/MmTJ/HLX/4Sd999Nx5++GE0NjYCAC5cuICFCxciPT0djz32GFpaWoJeU0lJCe68807Mnj0bs2fPxsaNGzWvp7q62ru/2bNn46677sKsWbMAaHeM+lqPVsent5oA4NixY8jJycHdd9+NxYsXo6mpCQDQ1NSERYsWISMjAwsXLoTdbg9qPQcPHsRtt93mPUa//e1vpdRTUVEBi8UCi8WC3/zmN97vilbHpz81BXyMBAkhhPjmm2/E9OnTxcWLF0VLS4uwWCziq6++8j7f0dEhUlNTRUVFhRBCiBdffFGsX79eCCHEokWLRFlZmRBCiFdffdXbHsya1qxZI0pLSwekDn/r8XXp0iWRlZUlDh48KITQ5hj1px4tjo+/Nc2fP1/s2bNHCCHE2rVrxcsvvyyEEGL16tXi9ddfF0IIsX37dvHEE08EtZ4tW7aI1157rd81BFJPY2OjmDZtmrftjTfeEM8884wQQpvj09+aAj1GPMP9lu/iOVFRUd7FczyOHTuGqKgo72SMJUuWYOHChXC5XDh48CDS0tIAANnZ2Z3eF4yaAODzzz9HSUkJ7r77bjz11FPeM18t6/H1+uuv46c//SmmTJmi2THqaz2ANsfH35o6Ojq8Z0itra0YPvzKalh79uyBxWIBAMyaNQt79+6Fy+UKWj2ff/45Pv30U8yZMwdLlizB119/3a9a/Knn1KlTuOGGG7yrBE6fPh0ffvghAG2OT39rCvQYMXC/dbXFc2w2m/fxmTNncP311+Ppp5+GxWLBqlWrEBUVhYsXLyI6OhqKcmUOidFo7PS+YNTkqWPp0qXYsWMHxowZgzVr1mhej0dTUxOKioq8K71pdYz6Wo+nhoE+Pv7WtGLFCuTn5+POO+9EZWUl5s2b1+W9iqIgOjoaDocjaPXExMQgNzcXJSUlSElJQV5eXr9q8aeem266Cd988w1OnDgBAPjHP/7hnfKvxfHpb02BHiMG7rdEL4vnqKqKAwcO4L777kNpaSkSExOxbt06TRfd6WtNAPCnP/0JEydOhE6nwyOPPIK9e/dqXo9HaWkpZsyYgbi4uIDeJ6seQJvj409NbW1tyM/Px1/+8hfs27cPCxYswNNPP93tz4uI6N+vaH/qWbNmDWbMmAEAmD9/Pv7973+jublZ03pGjhyJF154AYWFhcjJyYHJZILBYOj25/X3+PS3pkCPEQP3W70tnmM0GjF27FhMmHDl1s2zZs3CkSNHEBsbC6fTCbfbDQCw2+0DtuhOX2tqbm7G22+/7X2dEMJ7dqllPR4ffvghMjMzvY+1OkZ9rUer4+NPTV9++SUiIyO909bvvfdeHDhwAMCVMyvPe1VVhdPp9K4PLbuejo4ObN682fuZefT3OPVWj9vtxujRo/Huu+/ivffewy233ILExEQA2hyf/tTUl2PEwP1Wb4vnTJ48GQ6Hw/vPit27d+PHP/4xDAYDpkyZgvLycgBXrn4P1KI7fa0pKioKb775Jg4fPgwAeOeddzBz5kzN6wGuhNexY8cwefJkb5tWx6iv9Wh1fPypaezYsfjmm29w8uRJAMBHH33k/YOZkpKCkpISAEB5eTmmTJnS49mdlvVERETggw8+wK5duwBc+cwmTpyIESNGaFqPTqfDQw89BJvNBiEE/vznP3v/WGpxfPpTU5+OUf+u74WXnTt3iqysLJGamireeOMNIYQQjzzyiDhy5IgQQoh//etfIicnR2RmZoqHHnpI1NXVCSGEOHfunLjvvvtERkaGeOihh0RDQ0PQazp48KCYM2eOSE9PF0uWLBFNTU1S6qmrqxO33357l/dpdYz6Wo9Wx8efmvbs2SMsFouYNWuWuP/++8WZM2eEEEJcvHhRLF68WGRmZop7771XnD17Nqj1fPnll+Lee+8VmZmZ4r777hMXLlyQUs/HH38sZs2aJVJTU8WqVavE5cuXhRDaHZ/+1BToMeLiNUREkrBLgYhIEgYuEZEkDFwiIkkYuEREkjBwiYgkYeASEUnCwCUikoSBS0Qkyf8HMyvtSbDIvKUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(tf.reshape(logistic(tr_pooling[0]), (-1)).numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "5a84f294-6f58-468b-bd61-6e78ea58abad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.catplot(data=pandas.DataFrame(tf.reshape(logistic(tr_pooling[-1]), (-1, 48)).numpy()), kind='box')\n",
    "plt.plot(frogs.index, frogs.propsurv, 'd')\n",
    "plt.gcf().set_size_inches(18, 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b91ac9d2-dbb1-4fa0-95de-8754a787acf6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<tf.Tensor: shape=(), dtype=float32, numpy=1.0010403>,\n",
       " <tf.Tensor: shape=(), dtype=float32, numpy=1.0029483>,\n",
       " <tf.Tensor: shape=(48,), dtype=float32, numpy=\n",
       " array([1.0032957 , 1.0162851 , 1.0032014 , 1.0034423 , 1.000331  ,\n",
       "        1.005807  , 1.0043355 , 1.0034584 , 1.000688  , 1.0002229 ,\n",
       "        1.0006173 , 1.0003661 , 1.0018457 , 1.001163  , 1.0008967 ,\n",
       "        1.0011443 , 1.0055776 , 1.0004107 , 1.003336  , 1.0048571 ,\n",
       "        1.0027169 , 1.0005136 , 1.0030075 , 1.0005587 , 0.99981385,\n",
       "        1.0000011 , 1.0017562 , 1.0003108 , 1.0007849 , 1.0007653 ,\n",
       "        1.000334  , 1.000117  , 1.0014032 , 1.0016639 , 1.000521  ,\n",
       "        1.0008492 , 1.0006292 , 1.005789  , 1.000446  , 1.0000975 ,\n",
       "        1.0001079 , 1.0006268 , 1.0001785 , 1.0011575 , 0.9998694 ,\n",
       "        1.0000169 , 1.0003971 , 1.0000731 ], dtype=float32)>]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfp.mcmc.potential_scale_reduction(tr_pooling)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "43ec8ee8-47f1-4c20-8f47-027cb0c28faa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[0;31mSignature:\u001b[0m\n",
       "\u001b[0mtfp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmcmc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpotential_scale_reduction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mchains_states\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mindependent_chain_ndims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0msplit_chains\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mvalidate_args\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m    \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
       "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mDocstring:\u001b[0m\n",
       "Gelman and Rubin (1992)'s potential scale reduction for chain convergence.\n",
       "\n",
       "Given `N > 1` states from each of `C > 1` independent chains, the potential\n",
       "scale reduction factor, commonly referred to as R-hat, measures convergence of\n",
       "the chains (to the same target) by testing for equality of means.\n",
       "Specifically, R-hat measures the degree to which variance (of the means)\n",
       "between chains exceeds what one would expect if the chains were identically\n",
       "distributed. See [Gelman and Rubin (1992)][1]; [Brooks and Gelman (1998)][2].\n",
       "\n",
       "Some guidelines:\n",
       "\n",
       "* The initial state of the chains should be drawn from a distribution\n",
       "  overdispersed with respect to the target.\n",
       "* If all chains converge to the target, then as `N --> infinity`, R-hat --> 1.\n",
       "  Before that, R-hat > 1 (except in pathological cases, e.g. if the chain\n",
       "  paths were identical).\n",
       "* The above holds for any number of chains `C > 1`.  Increasing `C` does\n",
       "  improve effectiveness of the diagnostic.\n",
       "* Sometimes, R-hat < 1.2 is used to indicate approximate convergence, but of\n",
       "  course this is problem-dependent. See [Brooks and Gelman (1998)][2].\n",
       "* R-hat only measures non-convergence of the mean. If higher moments, or\n",
       "  other statistics are desired, a different diagnostic should be used. See\n",
       "  [Brooks and Gelman (1998)][2].\n",
       "\n",
       "Args:\n",
       "  chains_states:  `Tensor` or Python structure of `Tensor`s representing the\n",
       "    states of a Markov Chain at each result step.  The `ith` state is\n",
       "    assumed to have shape `[Ni, Ci1, Ci2,...,CiD] + A`.\n",
       "    Dimension `0` indexes the `Ni > 1` result steps of the Markov Chain.\n",
       "    Dimensions `1` through `D` index the `Ci1 x ... x CiD` independent\n",
       "    chains to be tested for convergence to the same target.\n",
       "    The remaining dimensions, `A`, can have any shape (even empty).\n",
       "  independent_chain_ndims: Integer type `Tensor` with value `>= 1` giving the\n",
       "    number of dimensions, from `dim = 1` to `dim = D`, holding independent\n",
       "    chain results to be tested for convergence.\n",
       "  split_chains: Python `bool`. If `True`, divide samples from each chain into\n",
       "    first and second halves, treating these as separate chains.  This makes\n",
       "    R-hat more robust to non-stationary chains, and is recommended in [3].\n",
       "  validate_args: Whether to add runtime checks of argument validity. If False,\n",
       "    and arguments are incorrect, correct behavior is not guaranteed.\n",
       "  name: `String` name to prepend to created tf.  Default:\n",
       "    `potential_scale_reduction`.\n",
       "\n",
       "Returns:\n",
       "  `Tensor` structure parallel to `chains_states` representing the\n",
       "  R-hat statistic for the state(s).  Same `dtype` as `state`, and\n",
       "  shape equal to `state.shape[1 + independent_chain_ndims:]`.\n",
       "\n",
       "Raises:\n",
       "  ValueError:  If `independent_chain_ndims < 1`.\n",
       "\n",
       "#### Examples\n",
       "\n",
       "Diagnosing convergence by monitoring 10 chains that each attempt to\n",
       "sample from a 2-variate normal.\n",
       "\n",
       "```python\n",
       "import tensorflow as tf\n",
       "import tensorflow_probability as tfp\n",
       "tfd = tfp.distributions\n",
       "\n",
       "target = tfd.MultivariateNormalDiag(scale_diag=[1., 2.])\n",
       "\n",
       "# Get 10 (2x) overdispersed initial states.\n",
       "initial_state = target.sample(10) * 2.\n",
       "==> (10, 2)\n",
       "\n",
       "# Get 1000 samples from the 10 independent chains.\n",
       "chains_states = tfp.mcmc.sample_chain(\n",
       "    num_burnin_steps=200,\n",
       "    num_results=1000,\n",
       "    current_state=initial_state,\n",
       "    trace_fn=None,\n",
       "    kernel=tfp.mcmc.HamiltonianMonteCarlo(\n",
       "        target_log_prob_fn=target.log_prob,\n",
       "        step_size=0.05,\n",
       "        num_leapfrog_steps=20))\n",
       "chains_states.shape\n",
       "==> (1000, 10, 2)\n",
       "\n",
       "rhat = tfp.mcmc.diagnostic.potential_scale_reduction(\n",
       "    chains_states, independent_chain_ndims=1)\n",
       "\n",
       "# The second dimension needed a longer burn-in.\n",
       "rhat.eval()\n",
       "==> [1.05, 1.3]\n",
       "```\n",
       "\n",
       "To see why R-hat is reasonable, let `X` be a random variable drawn uniformly\n",
       "from the combined states (combined over all chains).  Then, in the limit\n",
       "`N, C --> infinity`, with `E`, `Var` denoting expectation and variance,\n",
       "\n",
       "```R-hat = ( E[Var[X | chain]] + Var[E[X | chain]] ) / E[Var[X | chain]].```\n",
       "\n",
       "Using the law of total variance, the numerator is the variance of the combined\n",
       "states, and the denominator is the total variance minus the variance of the\n",
       "the individual chain means.  If the chains are all drawing from the same\n",
       "distribution, they will have the same mean, and thus the ratio should be one.\n",
       "\n",
       "#### References\n",
       "\n",
       "[1]: Stephen P. Brooks and Andrew Gelman. General Methods for Monitoring\n",
       "     Convergence of Iterative Simulations. _Journal of Computational and\n",
       "     Graphical Statistics_, 7(4), 1998.\n",
       "\n",
       "[2]: Andrew Gelman and Donald B. Rubin. Inference from Iterative Simulation\n",
       "     Using Multiple Sequences. _Statistical Science_, 7(4):457-472, 1992.\n",
       "\n",
       "[3]: Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, Paul-Christian\n",
       "     Burkner. Rank-normalization, folding, and localization: An improved R-hat\n",
       "     for assessing convergence of MCMC, 2019. Retrieved from\n",
       "     http://arxiv.org/abs/1903.08008\n",
       "\u001b[0;31mFile:\u001b[0m      ~/.pyenv/versions/3.9.6/lib/python3.9/site-packages/tensorflow_probability/python/mcmc/diagnostic.py\n",
       "\u001b[0;31mType:\u001b[0m      function\n"
      ]
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