threshold_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2e99d708",
   "metadata": {},
   "source": [
    "*Data Challenge for MODE 2022 Workshop on Differentiable Programming, Crete\n",
    "Copyright (C) 2022 Giles C Strong*\n",
    "\n",
    "*This program is free software: you can redistribute it and/or modify\n",
    "it under the terms of the GNU Affero General Public License as published\n",
    "by the Free Software Foundation, version 3 only of the License.*\n",
    "\n",
    "*This program is distributed in the hope that it will be useful,\n",
    "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
    "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
    "GNU Affero General Public License for more details.*\n",
    "\n",
    "*You should have received a copy of the GNU Affero General Public License\n",
    "along with this program.  If not, see <https://www.gnu.org/licenses/>.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06bb7f65",
   "metadata": {},
   "source": [
    "# Starter notebook\n",
    "\n",
    "Welcome! This starter notebook for the challenge will cover:\n",
    "\n",
    "1. Loading the data\n",
    "1. Viewing the data\n",
    "1. Applying a simple threshold-based approach\n",
    "1. Evaluating performance using the intersection-over-union metric\n",
    "1. Creating a submission with predictions for the test data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fba77db",
   "metadata": {},
   "source": [
    "First, well load some basic modules. These may not be installed in your environment, so please install them if they are missing, e.g. with `pip` by uncommenting and running the cell below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "75104ffc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install h5py matplotlib seaborn numpy tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "405caca5",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%reload_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d0d16b8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import h5py\n",
    "from pathlib import Path\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from tqdm import tqdm\n",
    "import math\n",
    "from matplotlib.colors import LogNorm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8107755",
   "metadata": {},
   "source": [
    "## Data loading\n",
    "If you haven't already downloaded the dataset, do so using, e.g. the uncommented command below. You only need to run this once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cfcbe72c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !mkdir data\n",
    "# !wget -O data/train.h5 https://zenodo.org/record/6866891/files/train.h5\n",
    "# !wget -O data/test.h5 https://zenodo.org/record/6866891/files/test.h5    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987dab53",
   "metadata": {},
   "source": [
    "Point this to the directory where you have the data stored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ec1e9e9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "DATA = Path('data')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8015e84e",
   "metadata": {},
   "source": [
    "Data files are in HDf5 format. The training file contains two datasets:\n",
    "- `'x0'`: a set of voxelwise X0 predictions (float32)\n",
    "- `'targs'`: a set of voxelwise classes (int):\n",
    "    - 0 = soil\n",
    "    - 1 = wall\n",
    "    \n",
    "The format of the datasets is a rank-4 array, with dimensions corresponding to (samples, z position, x position, y position).\n",
    "All passive volumes are of the same size: 10x10x10 m, with cubic voxels of size 1x1x1 m, i.e. every passive volume contains 1000 voxels.\n",
    "The arrays are ordered such that zeroth z layer is the bottom layer of the passive volume, and the ninth layer is the top layer.\n",
    "\n",
    "Our job is to convert the X0 values into the target class values, for every voxel.\n",
    "\n",
    "Since we want to evaluate the performance of our methods, we split off a portion of the training data to be used for validating performance, see e.g. https://www.fast.ai/2017/11/13/validation-sets/."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "54f5ed7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "h5 = h5py.File(DATA/'train.h5', 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d40390aa",
   "metadata": {},
   "source": [
    "Let's check the number of samples available:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "df0c03aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(106129, 10, 10, 10)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h5['targs'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "129034c6",
   "metadata": {},
   "source": [
    "So in total we have over 100,000 samples. This is quite large for the simple method we will apply, so for this tutorial we will limit ourselves to just a subsample of the data. This would also be recommended when developing more advanced methods, too, to allow us to quickly implement the method and make sure it gives reasonable results. Then the data count can be scaled up to further improve performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "06e4af7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10000\n",
    "n_train = int(0.8*n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e3631c00",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x = h5['x0'][:n_train]\n",
    "train_y = h5['targs'][:n_train]\n",
    "valid_x = h5['x0'][n_train:n]\n",
    "valid_y = h5['targs'][n_train:n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "345a8f73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((8000, 10, 10, 10), (2000, 10, 10, 10))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_x.shape, valid_y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "670c09d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "h5.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6677a3bf",
   "metadata": {},
   "source": [
    "We can look at the data and see that the X0 values are a dense set of float values, and the targets are a dense set of integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ad72c934",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        [0.04836598, 0.01032941, 0.00962548, 0.01606161, 0.0146331 ,\n",
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       "         0.01204619, 0.01565159, 0.00536949, 0.03826122, 0.0276596 ],\n",
       "        [0.02242324, 0.02221848, 0.01893466, 0.03084317, 0.02404932,\n",
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       "         0.01359756, 0.03552259, 0.02264982, 0.01033839, 0.03313649]],\n",
       "\n",
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       "         0.02659281, 0.01656766, 0.01112393, 0.01551366, 0.00863312],\n",
       "        [0.02065468, 0.01628422, 0.02715931, 0.01654512, 0.01325587,\n",
       "         0.02137633, 0.00854327, 0.01623905, 0.01360858, 0.01122903],\n",
       "        [0.04997383, 0.00765627, 0.00949208, 0.01573577, 0.01777289,\n",
       "         0.01747249, 0.01070041, 0.02217116, 0.02346101, 0.00525454],\n",
       "        [0.01148351, 0.01362854, 0.01714316, 0.05276163, 0.01945322,\n",
       "         0.01617654, 0.03634318, 0.01165309, 0.02569894, 0.02270224],\n",
       "        [0.05760854, 0.02582305, 0.01407046, 0.02015643, 0.03491168,\n",
       "         0.01445151, 0.02486442, 0.01907524, 0.02601464, 0.09757681],\n",
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       "         0.0085961 , 0.0238745 , 0.02445967, 0.02146766, 0.01676015],\n",
       "        [0.01672867, 0.03128871, 0.03677249, 0.01946019, 0.00846147,\n",
       "         0.01981026, 0.00975918, 0.01842598, 0.02613117, 0.02384503],\n",
       "        [0.04549435, 0.01400287, 0.01270819, 0.01090681, 0.0217675 ,\n",
       "         0.00780732, 0.02175012, 0.02337266, 0.01679006, 0.01363721],\n",
       "        [0.02915875, 0.01108897, 0.03450097, 0.0179869 , 0.0498978 ,\n",
       "         0.00488202, 0.03449443, 0.03859461, 0.02757462, 0.03495628]],\n",
       "\n",
       "       [[0.07014965, 0.03852357, 0.02997698, 0.07073732, 0.04047349,\n",
       "         0.01996168, 0.01513943, 0.00895797, 0.01062554, 0.0223197 ],\n",
       "        [0.03909805, 0.01666361, 0.04809711, 0.02839677, 0.04922859,\n",
       "         0.01567754, 0.01176475, 0.02842233, 0.02860018, 0.01534691],\n",
       "        [0.03838351, 0.01632464, 0.01985816, 0.01301283, 0.00849943,\n",
       "         0.0222359 , 0.04354533, 0.00759545, 0.03673624, 0.00992402],\n",
       "        [0.172341  , 0.0320149 , 0.01708671, 0.0244522 , 0.01126415,\n",
       "         0.00712102, 0.01456945, 0.01183947, 0.02872075, 0.01339215],\n",
       "        [0.02763284, 0.01942738, 0.0176607 , 0.02325932, 0.01665332,\n",
       "         0.02040054, 0.02195702, 0.02681368, 0.02280066, 0.02435793],\n",
       "        [0.09084312, 0.05306529, 0.0146268 , 0.01729502, 0.0109829 ,\n",
       "         0.05406513, 0.02736747, 0.02852118, 0.03117992, 0.01211647],\n",
       "        [0.04401651, 0.05808744, 0.01708821, 0.04262411, 0.0043595 ,\n",
       "         0.0119557 , 0.0272309 , 0.08596043, 0.03126844, 0.03428475],\n",
       "        [0.03397225, 0.04781191, 0.02095303, 0.01316227, 0.01744379,\n",
       "         0.01903181, 0.04072122, 0.01774159, 0.03969534, 0.03312233],\n",
       "        [0.04856082, 0.01982909, 0.05492821, 0.03386741, 0.01380518,\n",
       "         0.00897145, 0.01012996, 0.02183265, 0.02657337, 0.01357781],\n",
       "        [0.07571995, 0.02578318, 0.02918896, 0.02686322, 0.03927996,\n",
       "         0.02087925, 0.01661446, 0.03295247, 0.00763911, 0.08875364]],\n",
       "\n",
       "       [[0.04742706, 0.0566911 , 0.0361872 , 0.03270449, 0.0654803 ,\n",
       "         0.03411669, 0.06304108, 0.0523834 , 0.02072198, 0.0381369 ],\n",
       "        [0.04775725, 0.05692315, 0.09421954, 0.0428982 , 0.04104369,\n",
       "         0.08137649, 0.03078986, 0.02614742, 0.03373987, 0.04311407],\n",
       "        [0.04553129, 0.04441627, 0.0449705 , 0.0160167 , 0.02483793,\n",
       "         0.04136937, 0.06499658, 0.03852939, 0.03368752, 0.0232068 ],\n",
       "        [0.05858817, 0.02711604, 0.31772563, 0.04250965, 0.03234477,\n",
       "         0.04194384, 0.01177655, 0.02764176, 0.03328613, 0.05298675],\n",
       "        [0.03896191, 0.0317511 , 0.05266161, 0.04683249, 0.0791949 ,\n",
       "         0.12453242, 0.03347108, 0.03584898, 0.08209599, 0.06878505],\n",
       "        [0.08073382, 0.01316036, 0.03616333, 0.04811254, 0.03506215,\n",
       "         0.0653068 , 0.04575544, 0.05120711, 0.03073375, 0.0181579 ],\n",
       "        [0.05439541, 0.05130078, 0.0553367 , 0.05153395, 0.01432928,\n",
       "         0.03005199, 0.03687037, 0.04811093, 0.04049636, 0.05977318],\n",
       "        [0.02195775, 0.03914621, 0.05566295, 0.01834413, 0.01167942,\n",
       "         0.01594236, 0.0316839 , 0.00898946, 0.03562313, 0.05260224],\n",
       "        [0.07053474, 0.06245457, 0.09430872, 0.0655605 , 0.00675937,\n",
       "         0.03612784, 0.03012972, 0.0315193 , 0.04200373, 0.06240804],\n",
       "        [0.05745292, 0.05437577, 0.07759779, 0.02977942, 0.05703569,\n",
       "         0.02486483, 0.0418782 , 0.06130472, 0.05502896, 0.02401716]],\n",
       "\n",
       "       [[0.07338078, 0.20688741, 0.08051582, 0.02633768, 0.06038466,\n",
       "         0.07800426, 0.06383465, 0.05373909, 0.03846067, 0.05242689],\n",
       "        [0.03108134, 0.10811808, 0.05595137, 0.17095077, 0.17025796,\n",
       "         0.38825974, 0.11453428, 0.02124004, 0.0727196 , 0.13522671],\n",
       "        [0.11156762, 0.07700823, 0.08584958, 0.09869287, 1.024841  ,\n",
       "         0.15087174, 0.05244856, 0.17949608, 0.06705384, 0.0679569 ],\n",
       "        [0.08270118, 0.0905768 , 0.05336018, 0.14272314, 0.04820027,\n",
       "         0.12594898, 0.22644342, 0.1548675 , 0.11488957, 0.09454685],\n",
       "        [0.08679496, 0.04383291, 0.05387353, 0.02957525, 0.16565648,\n",
       "         0.1372901 , 0.03363756, 0.05400229, 0.20097551, 0.07232137],\n",
       "        [0.10543329, 0.18275844, 0.13770518, 0.03886762, 0.04344242,\n",
       "         0.03332785, 0.083772  , 0.1162312 , 0.03637709, 0.07432567],\n",
       "        [0.19158983, 0.11463566, 0.13853237, 0.09827641, 0.02978961,\n",
       "         0.13124806, 0.09486115, 0.02977088, 0.07395852, 0.10296552],\n",
       "        [0.05732806, 0.03747008, 0.05641041, 0.3168577 , 0.12160943,\n",
       "         0.02192828, 0.16632266, 0.02333885, 0.13627678, 0.06538853],\n",
       "        [0.07131544, 0.18459955, 0.18173847, 0.04124959, 0.09526408,\n",
       "         0.03475902, 0.01310545, 0.26131493, 0.0843983 , 0.07202978],\n",
       "        [0.06727056, 0.03764205, 0.10442224, 0.05425235, 0.12735257,\n",
       "         0.07094689, 0.07536215, 0.15214536, 0.07550602, 0.06818954]]],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "51b99bb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_y[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e6fe46d",
   "metadata": {},
   "source": [
    "## Data viewing\n",
    "\n",
    "Looking at raw 3D arrays of data is a bit uninformative, so in this section we'll plot it out.\n",
    "\n",
    "Fist, we'll look at the targets from a top-down perspective, and plot them in x & y.\n",
    "\n",
    "Below, we plot out 5 examples and flatten them along the z axis (`.any(0)`). The black sections are soil (class=0) and the white sections are the walls (class=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "720bd9fb",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for targ in train_y[:5]:\n",
    "    sns.heatmap(targ.any(0), square=True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a26bf53",
   "metadata": {},
   "source": [
    "To better show the 3D nature of the walls, we can plot the z-layers separately. The function below will plot one sample. Remember, that in the data the zeroth z-layer is the bottom (deepest) layer. To improve the visualisation, we will plot the most shallow layer first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e1e8bf35",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def plot_x0_targ(x0:np.ndarray, targ:np.ndarray) -> None:\n",
    "    n_layers = x0.shape[0]\n",
    "    fig, axs = plt.subplots(n_layers,2, figsize=(8, 8*16/9))\n",
    "    pred_cbar_ax = fig.add_axes([0.45, 0.25, 0.03, 0.5])\n",
    "    true_cbar_ax = fig.add_axes([0.90, 0.25, 0.03, 0.5])\n",
    "\n",
    "    for layer in range(n_layers-1,-1,-1):\n",
    "        sns.heatmap(x0[layer], ax=axs[n_layers-layer-1,0], vmin=np.nanmin(x0), vmax=np.nanmax(x0), cbar=(layer==0), cbar_ax=pred_cbar_ax if layer == 0 else None, square=True, cmap='viridis')\n",
    "        sns.heatmap(targ[layer], ax=axs[n_layers-layer-1,1], vmin=np.nanmin(targ), vmax=np.nanmax(targ), cbar=(layer==0), cbar_ax=true_cbar_ax if layer == 0 else None, square=True, cmap='viridis')\n",
    "        axs[n_layers-layer-1][0].set_ylabel(f\"Layer {layer}\")\n",
    "    axs[-1][0].set_xlabel(\"X0\")\n",
    "    axs[-1][1].set_xlabel(\"Target\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cc101415",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1024 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 1\n",
    "plot_x0_targ(train_x[idx], train_y[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8745da96",
   "metadata": {},
   "source": [
    "Due to the large range of X0s the colour scale gets compressed. Instead we can plot on a log-scale to better see differences in the low X0 region"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "87229060",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def plot_x0_targ_log(x0:np.ndarray, targ:np.ndarray) -> None:\n",
    "    n_layers = x0.shape[0]\n",
    "    fig, axs = plt.subplots(n_layers,2, figsize=(8, 8*16/9))\n",
    "    pred_cbar_ax = fig.add_axes([0.45, 0.25, 0.03, 0.5])\n",
    "    true_cbar_ax = fig.add_axes([0.90, 0.25, 0.03, 0.5])\n",
    "    cbar_ticks = [math.pow(10, i) for i in range(math.floor(math.log10(np.nanmin(x0))), 1+math.ceil(math.log10(np.nanmax(x0))))]\n",
    "    log_norm = LogNorm(vmin=np.nanmin(x0), vmax=np.nanmax(x0))\n",
    "    \n",
    "    for layer in range(n_layers-1,-1,-1):\n",
    "        sns.heatmap(x0[layer], ax=axs[n_layers-layer-1,0], vmin=np.nanmin(x0), vmax=np.nanmax(x0), cbar=(layer==0), cbar_ax=pred_cbar_ax if layer == 0 else None, square=True, cmap='viridis', norm=log_norm, cbar_kws={\"ticks\": cbar_ticks})\n",
    "        sns.heatmap(targ[layer], ax=axs[n_layers-layer-1,1], vmin=np.nanmin(targ), vmax=np.nanmax(targ), cbar=(layer==0), cbar_ax=true_cbar_ax if layer == 0 else None, square=True, cmap='viridis')\n",
    "        axs[n_layers-layer-1][0].set_ylabel(f\"Layer {layer}\")\n",
    "    axs[-1][0].set_xlabel(\"X0\")\n",
    "    axs[-1][1].set_xlabel(\"Target\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4bc24a07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1024 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 1\n",
    "plot_x0_targ_log(train_x[idx], train_y[idx])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd94702c",
   "metadata": {},
   "source": [
    "It's still a bit difficult to see differences in the low-value X0s. Plotting out the X0 distributions, we see a very long tail, with the majority of interesting information at below 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4e3c5e37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd09c3e6940>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tloskaRYGXZIaYdAlqREGXZIaYdAlqREGXZIaYdAlqRH/D8nru7uAtAo5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(train_x.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "58f2f4a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd09c3b8130>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(train_x[train_x<0.5].flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5e6ec05",
   "metadata": {},
   "source": [
    "We can clip the plot values to 0.1 and try plotting again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c484731a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x1024 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 1\n",
    "x0, targ = train_x[idx], train_y[idx]\n",
    "plot_x0_targ_log(np.clip(x0, 0,0.1), targ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a54cbe3",
   "metadata": {},
   "source": [
    "We expect that the voxels with walls should have a lower X0 than the voxels with soil, and we can almost see this, however we the image is suffers a prediction bias that naturally causes the central layers to have lower X0 values than the top and bottom layers. We may wish to try to account for this somehow.\n",
    "\n",
    "A quick and easy way to convert the X0 into classes is to apply a threshold on their values. Below the threshold are wall predictions, and above are soil predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b467a9f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1024 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 1\n",
    "x0, targ = train_x[idx], train_y[idx]\n",
    "plot_x0_targ(x0<0.015, targ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53696089",
   "metadata": {},
   "source": [
    "## Threshold optimisation - single cut\n",
    "\n",
    "We can build on the approach above by tuning the threshold. If we lower it, then in theory we should arrive at predictions that have a lower false positive rate for walls, however we may end up classifying many of the wall voxels as soil (high false negative rate). To govern the trade-off between these rates, we can look to the maximising the competition metric: the intersection over union. The intersection is the area of overlap between predicted walls and true wall, and the union is the summed area of predicted walls and true walls. By taking the ratio, we quantify the precision of our predictions: if we predicted a large area for one walls, then we would identify all the voxels with walls, however if there are only a few voxels that actually are walls, then the large union would reduce the IOU. This is computed separately for each sample, and then we compute the mean IOU across the samples.\n",
    "\n",
    "The IOU is a float between 0 and 1, with 1 being a perfect prediction, in which only every voxel is correctly identified as either soil or wall."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "58c49d80",
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_iou(preds:np.ndarray, targs:np.ndarray, as_mean:bool=True, smooth:float=1e-17) -> float:\n",
    "    r'''\n",
    "    Assumes that preds and targs have a batch dimension, and no class dimension, i.e. (batch, z, x, y)\n",
    "    If the batch dimesion is missing, e.g. your are computing the IOU for a single sample,\n",
    "    add it with e.g. preds[None], targs[None]\n",
    "    '''\n",
    "    \n",
    "    preds = preds.reshape(len(preds), 1, -1).astype(bool)\n",
    "    targs = targs.reshape(len(targs), 1, -1).astype(bool)\n",
    "    \n",
    "    inter = (preds*targs).sum(-1)\n",
    "    union = (preds+targs).sum(-1)\n",
    "    iou = ((inter+smooth)/(union+smooth))  # Small epsilon in case of zero union\n",
    "\n",
    "    if as_mean: iou = iou.mean() \n",
    "    return iou"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c09f2dbb",
   "metadata": {},
   "source": [
    "This is the IOU for our initial threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fa96b9ea",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20358334920982027"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_iou(train_x<0.015, train_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ed2ea95",
   "metadata": {},
   "source": [
    "Let's see if we can optimise it by scanning across a range of thresholds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "75316837",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [00:06<00:00,  8.16it/s]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd06743b370>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xScaYFGPMdCvrw40xa4wxZ40x0y5Zt8cYs80Ys9kYk2jLOFX5fk3OobBItHlJ1Vh4i0bMuimG1Y8OZtLAMFYl53DdWwnc8HYCP2w7qENkHYzNziCMMe7Am8AwIBPYYIxZKCI7S212BLgfuLaM3cSJiM45bGfLk7Lw9/GgZ5sm9g5FuYgWjX2YPjKcewd35MsNGcz5NZ2/frqJ0KYN+EvfdtzUuzX+PjqVvL3Z8gziCiBFRNJE5BzwBTCu9AYikiUiGwCd/ctBFQ9vzWZg5yA8dHirqmV+3h5M7N+elQ/H8c6fexLS2Id/f/87fWYu46lFO0jPybN3iPWaLfsgWgEZpV5nAldWobwAPxljBHhXRGZb28gYMwmYBNCmTZtqhqrKsvPgCbJOnuVqnXtJ2ZC7ZeTTiG4hbM08xpzV6Xy8Zi9zf93DgE6B3NanHYPDg3F3M/YOtV6x5b+E1o5kVRoY+4lIT2AkMMUYM9DaRiIyW0RiRSQ2KEi/xGrbheGtg7roe6vqRnRoE14d34OExwbz0LDOJB8+xd0fJTLwheW8tSKFnFNn7R1ivWHLBJEJtC71OhQ4UNnCInLA8jMLmE9xk5WqY8t3ZRHVqjHB/jq8VdWtYH8f7h/SiVWPxvH2LT1p06whLyxJos/MX7jv899Yk5qLiHZq25Itm5g2AJ2MMe2B/cB44ObKFDTG+AJuInLS8nw48C+bRaqsOp5fwKZ9R5kS19Heoah6zNPdjZFRIYyMCiEl6ySfrcvg640ZLNpygA5Bvtx8RRuu7xlKM18ve4fqcmyWIETkvDHmXuBHwB2YIyI7jDGTLevfMca0ABKBRkCRMWYqEAEEAvONMRdi/ExEltgqVmVdfHI2RaJXTyvH0THYn3+OieCREV34butBPlu3l39//zvPL9nF0K7N+VNsKAM76YCK2mJc6RQtNjZWEhP1kona8tCXm1m2K4uNTwzTzkHlsHYdOsFXiZks+G0/uXnnCPb35vqeodzQK5SOwX72Ds/hGWM2ikis1XWaIJQ1RUXCFc/+TN+wQF6f0MPe4ShVoXPni1i2K4uvEjNYsTubwiKhe2hjru8ZypjuLbUJqgzlJQidakNZtf3AcXJOndPZW5XT8PJwY0S3Fozo1oKsk2dYuPkA8zbtZ8bCHTz93U7iwoO5vkcr4sKD8fF0t3e4TkEThLJq+a5sjIGBnTRBKOcT7O/DXQM6cNeADuw8cIL5v2WyYPMBlu48jL+3B8MjWzA2piX9wgK0v6IcmiCUVSt2ZxEd2oQAP297h6JUjUS0bEREywgeHRHOmrRcFm4+wJIdh5i3KZNAPy9GRYUwpntLerVpipv2tV1EE4S6zJG8c2zOOMYDQzrZOxSlao2HuxsDOgUxoFMQT1/bjRVJ2SzacoD/bsjgozV7ad7Im1FRIYyOCqGnJgtAE4SyIn53NqLDW5UL8/F0L+mvOHX2PL/8fpjvtx7k03X7mPvrHlo08mFkVAtGdguhV9um9XYUnyYIdZkVSVkE+HoR3aqxvUNRyub8vD0YF9OKcTGtOHmmgGW7sli05X/JItDPm+GRzRkR2YI+YQH16p7smiDURQqLhJW7s4nrEqyn2Kre8ffxLEkWp86eZ/muLJZsP8SC3/bz2bp9NPLxYEjX5gyLaM7AzkH4ebv2V6hr105V2ZbMYxzNL9DJ+VS95+ftwZjuLRnTvSVnCgqJ353Nku2HWJaUxfzf9uPl7kbfjgGW26o2d8nb8WqCUBdZkZSNmw5vVeoiPp7uDI9swfDIFpwvLCJx71GW7jzM0p2H+fv87fx9/naiWjUmLjyYuC5BdA9t4hJn4HoltbrI2DdW4+nuxry/9rV3KEo5PBEhOesUS3ceZtmuLH7bd5QigQBfLwZ1CSKuSzADOwXRuKHj3h1Pr6RWlZJ98ixbM4/zt2Gd7R2KUk7BGEPn5v50bu7PlLiOHM07R3xyNst2ZbFsVxbfbNqPm4EebZoyqHMQgzoHEdWqsdOcXWiCUCXidxffHCguXIe3KlUdTX29Sjq5C4uEzRlHWZmUzcrd2bzy825mLd1NM18vBnQKtFyTEejQfReaIFSJ5UlZBPl7ExHSyN6hKOX03N0Mvdo2o1fbZjw0vAu5p86yOiWHlUnZxCdn8+3m4vundQr2o3+nQPp3DOTKDgEONTLKcSJRdlVUJKxOyWFIeHOnOf1VypkE+HmXnF0UFQm/HzrBryk5rErO4TPLNRceboYebZrQJyyQvmEB9GjTBG8P+00sqAlCAbDz4AmO5RfQv1OAvUNRyuW5uRkiWzYmsmVjJg0M40xBIZv2HmVVSg4JKTm8sSyZ139JxtvDjdh2TenTIYA+YYFEhzau0wv1NEEoANak5gLQp0OgnSNRqv7x8XSnb8dA+nYs/vydOFPA+rQjJKTmkpCaw0s/7QZ208DTnV5tm3Jl+2Zc2SGA7q0b2/QMQxOEAiAhNYcOQb60aOy4HWZK1ReNfDwZGtGcoRHNAcg9dZZ16UdYl5bLuvQjvLx0NwDeHm70aNOEK9sHcP+QTrU+Z5QmCEVBYRHr049wXc9W9g5FKWVFgF/xTLOjokIAOJp3jvV7jrA+/Qjr0nP5busBHrTB8HRNEIqtmcfJO1dI3zBtXlLKGTT19eIPkS34Q2QLoPh2q7ZQf6YlVGVak5oDwFUdtINaKWfk5WGbr3JNEIqE1Fy6hjTSm7orpS6iCaKeO1NQSOLeo/QN07MHpdTFyu2DMMY0u2SRAMfElWb4q+c27T3KufNF9OuoCUIpdbGKOqk3UpwUSo+d8jPGbAHuEpE9tgpM1Y2E1Fzc3Qy92136v4BSqr4rN0GISHtry40x1wPvACNsEZSqOwmpOUSHNsbfx3GnI1ZK2Ue1+iBE5BtAp/x0cqfOnmdL5nHtf1BKWVWtBGGM8atuWeU4NqQfobBI9PoHpZRVFXVSP2RlcVNgLPCGTSJSdSYhNQcvdzd6tW1q71CUUg6ook5q/0teC3AI+LOIbLNNSKquJKTm0rNtE3w87TedsFLKcVXUSf3UheeWZiURkTybR6Vs7mjeOXYePMGDQ/X2okop6yrsRzDG/NUYsw/YC+wzxuw1xvw/24embGldei4iaAe1UqpM5SYIY8wTwBjgahEJEJEAIA4YaVmnnFRCai4NvdyJDm1i71CUUg6qojOIW4HrRSTtwgLL8xuB22wZmLKthNRcerdrZrNJvpRSzq/CbwcROWNl2WnANvPLKpvLOnGGlKxT2ryklCpXRQki0xgz5NKFxpjBwEHbhKRsbU1a8e1F9foHpVR5KkoQ9wPvGmM+MMbcZ4y51xjzITAbuLeinRtjRhhjkowxKcaY6VbWhxtj1hhjzhpjplWlrKq+X1NyaNzAk4iWjewdilLKgZWbIERkB9ANiAfaAR0sz7tZ1pXJGOMOvAmMBCKACcaYiEs2O0JxEnqpGmVVNSWk5nJVh2a1fv9apZRrqfCWo5Y+iDnV2PcVQMqFDm5jzBfAOGBnqX1nAVnGmNFVLauqJ+NIPplHT3P3gA72DkUp5eAqmmrjJMVXT1+2iuKL5spro2gFZJR6nQlcWcm4Kl3WGDMJmATQpk2bSu6+/kqw3F5UO6iVUhWp6ErqS6faqApr7ReVvdFQpcuKyGyK+0SIjY3VGxlVICE1l0A/bzoG+9k7FKWUg7PlIPhMoHWp16HAgTooq8ogIiSk5tI3LABjtP9BKVU+WyaIDUAnY0x7Y4wXMB5YWAdlVRlSs0+RffKsNi8ppSqlwk7q6hKR88aYe4EfAXdgjojsMMZMtqx/xxjTAkgEGgFFxpipQISInLBW1lax1hcJqXr9g1Kq8myWIABEZDGw+JJl75R6foji5qNKlVU1k5CSS6smDWjdrIG9Q1FKOQGdiKeeKCoS1qRp/4NSqvI0QdQTOw+e4PjpAvp21P4HpVTlaIKoJ9ZY+h/6dND+B6VU5WiCqCcSUnPoEORLi8Y+9g5FKeUkNEHUAwWFRaxPP0I/Hb2klKoCTRD1wNbMY+SdK9TrH5RSVaIJoh5ISCnuf7iqgyYIpVTlaYKoBxJSc4kIaURTXy97h6KUciKaIFzcmYJCNu47qs1LSqkq0wTh4jbtPcq580V6/YNSqso0Qbi4hNRc3N0Mvds1s3coSiknownCxSWk5hAd2hh/H097h6KUcjKaIFzYqbPn2ZJ5XPsflFLVognCha1Ly6WwSHR6b6VUtWiCcFEFhUW88vNuAny96NW2qb3DUUo5IZveD0LZz7srU9m+/wRv39ITH093e4ejlHJCegbhgnYdOsFrvyRzTXQII6NC7B2OUspJaYJwMQWFRUz7aguNfDx5amykvcNRSjkxbWJyMbPj09i+/wRv3dKTAD9ve4ejlHJiegbhQpIOneTVn3czOjqEUdq0pJSqIU0QLuK8pWnJ38eTf2nTklKqFmgTk4t4Nz6NbfuP8+bN2rSklKodegbhApIOneS1n5MZHRXC6GhtWlJK1Q5NEE7ufGERD3+9BT8fD54ap01LSqnao01MTm72qjS2Zh7njZt7EKhNS0qpWqRnEE5s9+GTvLo0mVFRLbgmuqW9w1FKuRhNEE7qfGERD3+1BV9vd/41rpu9w1FKuSBtYnJS761KZ0vmcf5vgjYtKaVsQ88gnFDy4ZO8snQ3IyJbcI2OWlJK2YgmCCdzvrCIaV9vxdfbnaev7YYxxt4hKaVclDYxOZn/rE5nS8YxXp/QgyB/bVpSStmOnkE4kZSsk8xaups/RDZnjDYtKaVsTBOEkzhfWMTfvtpKQy93/n1tlDYtKaVsTpuYnMT7lqal18bHaNOSUqpO6BmEE0jJOsnLS3czPKI5Y7vrBXFKqbph0wRhjBlhjEkyxqQYY6ZbWW+MMa9b1m81xvQstW6PMWabMWazMSbRlnE6ssIiYdqFpqXrdNSSUqru2KyJyRjjDrwJDAMygQ3GmIUisrPUZiOBTpbHlcDblp8XxIlIjq1idAbvr05js6VpKdjfx97hKKXqEVueQVwBpIhImoicA74Axl2yzTjgIym2FmhijNHhORYpWad46afdDNOmJaWUHdgyQbQCMkq9zrQsq+w2AvxkjNlojJlU1i8xxkwyxiQaYxKzs7NrIWzHUFgkPPL1Fhp4uvOMNi0ppezAlgnC2jeaVGGbfiLSk+JmqCnGmIHWfomIzBaRWBGJDQoKqn60DmbO6nQ27TvGU2MjtWlJKWUXtkwQmUDrUq9DgQOV3UZELvzMAuZT3GRVL6Rmn+Kln5IY2rU542K0aUkpZR+2TBAbgE7GmPbGGC9gPLDwkm0WArdZRjNdBRwXkYPGGF9jjD+AMcYXGA5st2GsDqOwSHj4qy34eLrzrDYtKaXsyGajmETkvDHmXuBHwB2YIyI7jDGTLevfARYDo4AUIB+4w1K8OTDf8uXoAXwmIktsFasjmftrcdPSKzd1J7iRNi0ppezHpldSi8hiipNA6WXvlHouwBQr5dKA7raMzRGlZZ/ixR+TGNo1mGtjLu3PV0qpuqVXUjuIwiLh4a+34u3hxrPX6VxLSin707mYHMTcX9PZuPcos27UpiWllGPQMwgHkJ6Tx4s/JjEkPJjremjTklLKMWiCsLMLo5a8Pdx49nptWlJKOQ5NEHb2QcIeEvceZcaYSJpr05JSyoFogrCj4qalXQwOD+b6ntq0pJRyLJog7KTIMteSp7uOWlJKOSZNEHbyQcIeNuwpblpq0ViblpRSjkcThB3sycnjhR93EdcliD9q05JSykFpgqhjxU1LW/F0d2Pm9dHatKSUcliaIOrYh2v2sH7PEf55TYQ2LSmlHJomiDq0JyeP55fs4uouQdzQK9Te4SilVLk0QdSRoiLhkXkXmpZ01JJSyvFpgqgjH63Zw/r0I/zjmghCGjewdzhKKVUhTRB1YG9uHs8vSWJQ5yD+pE1LSiknoQnCxoos03h7uBme+6M2LSmlnIcmCBv7eO1ebVpSSjklTRA2tC83n+d+2MXAzkH8KVablpRSzkUThI0Uj1raUty0pKOWlFJOSBOEjXyybi9r047wxDVdadlEm5aUUs5HE4QNXGhaGtApkBtjW9s7HKWUqhZNELXsQtOSmzE890eda0kp5bw0QdSyTy80LY3uSittWr92UwwAABFoSURBVFJKOTFNELUo40g+My1NSzf11qYlpZRz0wRRSy5M461NS0opV6EJopZ8un4fa9Jy+bs2LSmlXISHvQNwBRlH8pm5+Hf6dwxkvDYt1YqCggIyMzM5c+aMvUNRyiX4+PgQGhqKp6dnpctogqghEeHReVsxoHMt1aLMzEz8/f1p166dvqdK1ZCIkJubS2ZmJu3bt690OW1iqqFP1+0jITWXx0d3JbRpQ3uH4zLOnDlDQECAJgelaoExhoCAgCqfkWuCqIHSTUs3X9HG3uG4HE0OStWe6nyeNEFUk4gw/ZutAHqHOKWUS9IEUU2frd/Hrym5PDaqK62badOSKzLGcOutt5a8Pn/+PEFBQVxzzTU13veKFSsu2s+CBQuIjo4mPDycqKgoFixYULLu6quvJjExseT1nj176NatW6V/18aNG4mKiqJjx47cf//9iMhl2yxdupRevXoRFRVFr169WLZsGQD5+fmMHj2a8PBwIiMjmT59ekmZWbNmERERQXR0NEOGDGHv3r1Veg+effbZKm1flmPHjvHWW29Vudzrr79O165dueWWWy5anpubS1xcHH5+ftx7771llv/qq6+IjIzEzc3tsuPToEEDYmJiiImJYfLkyUD57+WTTz5Jq1atSsrExMRw7Nixy37nkSNHGDZsGJ06dWLYsGEcPXoUKPv41ZiIuMyjV69eUhcyjuRJxD9+kAmz10hRUVGd/M76ZufOnfYOQXx9fSUmJkby8/NFRGTx4sXSvXt3GT16dI33vXz58pL9bN68WcLCwiQtLU1ERNLS0iQsLEy2bNkiIiKDBg2SDRs2lJRNT0+XyMjISv+u3r17S0JCghQVFcmIESNk8eLFl22zadMm2b9/v4iIbNu2TVq2bCkiInl5ebJs2TIRETl79qz079+/pPyyZcskLy9PRETeeustufHGG6v0Hvj6+lZp+7JU9f24oEuXLiXveWmnTp2SVatWydtvvy1Tpkwps/zOnTtl165dlT4+5b2XM2bMkBdffLHCmB9++GGZOXOmiIjMnDlTHnnkEREp+/hZi/lSQKKU8Z2qo5iqSESYPm8bAjyvF8TViacW7WDngRO1us+Ilo2YMSaywu1GjhzJ999/zw033MDnn3/OhAkTWLVqFQDr169n6tSpnD59mgYNGjB37ly6dOnCrFmz2L59O3PmzGHbtm1MmDCB9evX07Ch9TPNl156iccff7xkdEn79u157LHHePHFF/n4449rVM+DBw9y4sQJ+vTpA8Btt93GggULGDly5EXb9ejRo+R5ZGQkZ86c4ezZszRs2JC4uDgAvLy86NmzJ5mZmQAlywGuuuoqPvnkE6sxXHvttWRkZHDmzBkeeOABJk2axPTp0zl9+jQxMTFERkby6aefXlRmyZIlPP744xQWFhIYGMgvv/zCk08+iZ+fH9OmTQOgW7dufPfdd0yfPp3U1FRiYmIYNmwYL7744kX7mjVrFnPmzAHgrrvuYurUqUyePJm0tDTGjh3LxIkTefDBB0u29/X1pX///qSkpJT73nbt2rXc9Zcq772srG+//ZYVK1YAcPvtt3P11Vfz/PPPl3n8vL29q7T/S2mCqKLP12ewOiWHp6/tpk1L9cD48eP517/+xTXXXMPWrVuZOHFiSYIIDw8nPj4eDw8Pfv75Zx5//HHmzZvH1KlTufrqq5k/fz7PPPMM7777bpnJAWDHjh0lX3oXxMbG8uabb1YYX1JSEjfddJPVdStWrGD//v2Ehv7vZlWhoaHs37+/3H3OmzePHj16XPblcuzYMRYtWsQDDzxwWZn333//sqRzwZw5c2jWrBmnT5+md+/e/PGPf+S5557jjTfeYPPmzZdtn52dzd133018fDzt27fnyJEj5cb73HPPsX37dqv72rhxI3PnzmXdunWICFdeeSWDBg3inXfeYcmSJSxfvpzAwMBy918d6enp9OjRg0aNGvHvf/+bAQMGXLTe2nv5yiuvlCTZpk2bsnz58sv2e/jwYUJCQgAICQkhKyvrsm3KOn7VoQmiCjKP5vPM9zvpGxbALTpqqc5U5j99W4mOjmbPnj18/vnnjBo16qJ1x48f5/bbbyc5ORljDAUFBQC4ubnxwQcfEB0dzT333EO/fv3K/R0ictmZaOll1s5SLyzr0qWL1S/G0vspq6w1O3bs4NFHH+Wnn366aPn58+eZMGEC999/Px06dLho3SeffEJiYiIrV660us/XX3+d+fPnA5CRkUFycjIBAQFlxrB27VoGDhxYckbVrFmzMretyOrVq7nuuuvw9fUF4Prrr2fVqlUX/cdd20JCQti3bx8BAQFs3LiRa6+9lh07dtCoUSOg7PfywQcfvOwfhaoq6/hVl007qY0xI4wxScaYFGPMdCvrjTHmdcv6rcaYnpUtW9dEhMe++V/TkpubNi3VF2PHjmXatGlMmDDhouX/+Mc/iIuLY/v27SxatOiiMebJycn4+flx4MCBCvcfGRl5UScnwKZNm4iIiAAgICCgpDMSijsqL/zXm5SUdFHH5qWdnKGhoRc1Y2RmZtKyZUurcWRmZnLdddfx0UcfERYWdtG6SZMm0alTJ6ZOnXrR8p9//plnnnmGhQsXWv2PdcWKFfz888+sWbOGLVu20KNHjwrH4ltLmAAeHh4UFRWVvK7MmH5rCdLWvL29SxJgr169CAsLY/fu3SXry3ovrbnjjjuIiYkp+eekefPmHDx4EChuPgwODi7ZtrzjV102SxDGGHfgTWAkEAFMMMZEXLLZSKCT5TEJeLsKZevUFxsyWJWcw2Mjw7VpqZ6ZOHEi//znP4mKirpo+fHjx2nVqhUAH3zwwUXLH3jgAeLj48nNzeXrr78ud//Tpk1j5syZ7NmzBygeBfPss8/yt7/9DSgexfTJJ5+UfNl9+OGHJW3ZF84grD2aNGlCSEgI/v7+rF27FhHho48+Yty4cZfFcOzYMUaPHs3MmTMvO+N54oknOH78OK+++upFy3/77TfuueceFi5ceNEX1aXvUdOmTWnYsCG7du1i7dq1Jes8PT1LzrpK69OnDytXriQ9PR2gpImpXbt2bNq0CShOoBfW+/v7c/LkSau/f+DAgSxYsID8/Hzy8vKYP3/+Zc09tS07O5vCwkIA0tLSSE5OLjlTKOu9LMvcuXPZvHkzixcvBor/Wfnwww+B4r+DC8eyvONXI2X1Xtf0AfQBfiz1+jHgsUu2eReYUOp1EhBSmbLWHtUdxTT69XgZ8vKKch+d/75Yxr+7RgoLddRSXXCUUUyXKj36KCEhQTp16iR9+/aVJ554Qtq2bSsiInfccYe89tprIiKyb98+CQsLk8OHD5e5HxGRefPmSbdu3aRLly7SrVs3mTdvXsm6s2fPypQpUyQqKkqio6Nl4sSJJaOHKmPDhg0SGRkpHTp0kClTppSMvPv222/lH//4h4iIPP3009KwYUPp3r17yePw4cOSkZEhgISHh5csf++990REZMiQIRIcHFyyfMyYMZf97jNnzsiIESMkKipKbrjhBhk0aJAsX75cREQeeeQRCQ8Pl5tvvvmycosXL5aYmBiJjo6WoUOHiohIfn6+DBs2TLp37y533XWXhIeHS3p6uoiITJgwQSIjI2XatGmX7evll1+WyMhIiYyMlFdeeaVkedu2bSU7O9vqe9a2bVtp2rSp+Pr6SqtWrWTHjh0iInLnnXeWjFj65ptvpFWrVuLl5SXBwcEyfPhwERH5+uuvJSIiQqKjo6VHjx6ycOFCEZFy38sZM2ZIy5YtL3r/L9SttJycHBk8eLB07NhRBg8eLLm5ueUev0tVdRSTERudghljbgBGiMhdlte3AleKyL2ltvkOeE5EVlte/wI8CrSrqGypfUyi+OyDNm3a9KrqWGyAqV/8RkFh+e9DQy93HhzWWe8vXUd+//33Ko8SUUqVz9rnyhizUURirW1vy05qa430l34Ll7VNZcoWLxSZDcwGiI2NrVa2e3W87TqslFLKWdkyQWQCpee+DgUu7bEraxuvSpRVSillQ7YcxbQB6GSMaW+M8QLGAwsv2WYhcJtlNNNVwHEROVjJssrF2ar5U6n6qDqfJ5udQYjIeWPMvcCPgDswR0R2GGMmW9a/AywGRgEpQD5wR3llbRWrcjw+Pj7k5ubqlN9K1QKx3A/Cx8enSuVs1kltD7GxsXLpeHLlnPSOckrVrrLuKGevTmqlqs3T07NKd75SStU+ne5bKaWUVZoglFJKWaUJQimllFUu1UltjMkGqn4pdbFAIKcWw7EHV6gDaD0ciSvUAVyjHraqQ1sRCbK2wqUSRE0YYxLL6sl3Fq5QB9B6OBJXqAO4Rj3sUQdtYlJKKWWVJgillFJWaYL4n9n2DqAWuEIdQOvhSFyhDuAa9ajzOmgfhFJKKav0DEIppZRVmiCUUkpZ5ZIJwhgzwhiTZIxJMcZMt7LeGGNet6zfaozpWVFZY0wzY8xSY0yy5WdTJ63Hk8aY/caYzZbHKAeuwxxjTJYxZvslZZztWJRVD6c4FsaY1saY5caY340xO4wxD5Qq4zTHooJ61OmxqGE9fIwx640xWyz1eKpUmdo9HmXdi9RZHxRPD54KdKD4xkNbgIhLthkF/EDxneuuAtZVVBZ4AZhueT4deN5J6/EkMM3Rj4Vl3UCgJ7D9kjJOcywqqIdTHAuK7xPf0/LcH9jtpJ+L8upRZ8eiFuphAD/Lc09gHXCVLY6HK55BXAGkiEiaiJwDvgDGXbLNOOAjKbYWaGKMCamg7DjgQ8vzD4FrnbQedakmdUBE4oEjVvbrTMeivHrUpWrXQUQOisgmABE5CfwOtCpVximORQX1qGs1qYeIyCnLNp6Wh5QqU2vHwxUTRCsgo9TrTC7/Iyhrm/LKNpfiu91h+RlcizFbY6t6ANxrOWWdY+MmgZrUoTzOdCwq4lTHwhjTDuhB8X+t4KTHwko9oO6ORaViLG8bY4y7MWYzkAUsFRGbHA9XTBDWbj926VjesrapTNm6Yqt6vA2EATHAQeDl6gZYCTWpgyOxVT2c6lgYY/yAecBUETlRi7FVha3qUZfHosIYK9pGRApFJAYIBa4wxnSr5fgA10wQmUDrUq9DgQOV3Ka8socvNBlYfmbVYszW2KQeInLY8sdVBLxH8amurdSkDuVxpmNRJmc6FsYYT4q/VD8VkW9KbeNUx6KsetTxsSg3xqpsIyLHgBXACMuiWj0erpggNgCdjDHtjTFewHhg4SXbLARus4wSuAo4bjkdK6/sQuB2y/PbgW+dsR4X/ngsrgO2Yzs1qUN5nOlYlMlZjoUxxgDvA7+LyCwrZZziWJRXjzo+FlCzegQZY5pY4m4ADAV2lSpTe8ejJj3cjvqguPd/N8WjBP5uWTYZmCz/GwXwpmX9NiC2vLKW5QHAL0Cy5WczJ63Hx5Ztt1r+mEIcuA6fU3y6X0Dxf1N3OumxKKseTnEsgP4UN21sBTZbHqOc7VhUUI86PRY1rEc08Jsl1u3AP0vts1aPh061oZRSyipXbGJSSilVCzRBKKWUskoThFJKKas0QSillLJKE4RSSimrNEEoVUuMMS2MMV8YY1KNMTuNMYuNMZ3L2X6qMaZhXcaoVFVoglCqFlguwpoPrBCRMBGJAB4HmpdTbCqgCUI5LE0QStWOOKBARN65sEBENgPuxpjvLiwzxrxhjPmLMeZ+oCWw3BizvO7DVapimiCUqh3dgI2V3VhEXqd4Xp04EYmzWVRK1YAmCKWUUlZpglCqduwAellZfp6LP2c+dROOUjWnCUKp2rEM8DbG3H1hgTGmN8W3lowwxngbYxoDQ0qVOUnxrS+VckiaIJSqBVI86+V1wDDLMNcdFN/n+ADwJcUzb35K8SycF8wGftBOauWodDZXpZRSVukZhFJKKas0QSillLJKE4RSSimrNEEopZSyShOEUkopqzRBKKWUskoThFJKKav+P1cc7sDSAsJSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,y = [0],[binary_iou(train_x<=0, train_y)]\n",
    "for p in tqdm(range(0,50)):\n",
    "    x.append(np.percentile(train_x, p))\n",
    "    y.append(binary_iou(train_x<=x[-1], train_y))\n",
    "\n",
    "max_iou = np.max(y)\n",
    "cut = x[np.argmax(y)]\n",
    "plt.plot(x,y, label=f'Max IOU={max_iou:.3f} at cut of {x[np.argmax(y)]:.3E}')\n",
    "plt.ylabel('IOU')\n",
    "plt.xlabel('Cut')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c628079",
   "metadata": {},
   "source": [
    "So, we can get a slight improvement by using a lower threshold than our initial guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4f4eb7ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3220338983050847\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1024 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 1\n",
    "x0, targ = train_x[idx], train_y[idx]\n",
    "print(binary_iou((x0<cut)[None], targ[None]))\n",
    "plot_x0_targ(x0<cut, targ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eee36fb9",
   "metadata": {},
   "source": [
    "## Threshold optimisation - cut per layer\n",
    "\n",
    "We still want to account for the bias in the predictions caused by the depth in z. We can optimise separate thresholds for every layer. To enable this, whilst still accounting for the whole volume, we can start from out previous cut, and then iteratively find layer-wise cuts by only changing our predictions in each layer in turn. Once we have an optimal cut for a given layer, we'll use it when optimising for subsequent layers, ensuring that the maximum IOU always increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8ce413d4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "  0%|          | 0/10 [00:00<?, ?it/s]"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 10%|█         | 1/10 [00:06<01:02,  6.99s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22262779236048602 0.016869102077558637\n"
     ]
    },
    {
     "data": {
      "image/png": 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578tG927H5GGdeCc1m1e/2eF2OaYGOLlHMwDYpqo7VLUQmAOM9m6gqktU9bDn5TIg2rN8r6qu8nydB6QB7TyvP1XV4vJ9jKmIqvLQvPVk5J7g+Rv7EtHEnivjD+69pDOjerbmbws289G6PW6XY6rJyaBpB2R5vc72LDud8cCC8gtFJA7oAyyvoM/tFfXx9JsoIikikpKTk1PFkk1dM3t5Jh+t28uvf9KFAfEt3C7HVFFAgPB/1/WmX2xzfjV3LZm5+W6XZKrByaCp6PhEhQdcRWQoZUHzQLnlTYD3gHtV9Vi5dQ9TdohtdkXbVNWpqpqsqslRUVHnUL7xdxt2H+XPH21iSOco7hrS0e1yzFlq2KBsAs6gAOEPH26w8zV+zMmgyQZivF5HAz/aBxaRJGAaMFpVc72WB1MWMrNVdV65PuOAK4Cb1X76TAXyCoq4+61VtGjUgGdu6E2AnZfxS22aNeT+y7rwdXoOby7LcLscc46cDJqVQIKIxItIA2AMMN+7gYjEAvOAsaqa7rVcgOlAmqo+Xa7PCMr2fK5SVdufNj+iqjw4bz1Zh7/n+Zv60KJxA7dLMtUw7oI4hnSO4v99nEb6fruZ0x85FjSeE/Z3AwspO5k/V1U3isgkEZnkafYIEAG8JCJrRCTFs3wQMBYY5lm+RkRGeda9AIQBizzLX3ZqDMY/zVqeycfr9vKbn3Shf5ydl/F3IsJT1/WiSUgQk99eTUFRidslmbMk9eHIU3JysqakpFTe0Pi95TtyuWX6cgZ3imT6uP52yKwO+WLzfm6fmcLtg+J55Mryd0oYJ4hIqqomV3c7NjOAqTOyDuVz1+xVxLRoxLNj+ljI1DHDurZi3PntmfHdTr7acsDtcsxZsKAxdUJ+YTETXk/xzMjcn2YNbUbmuuihUd3o3KoJv3lnHbnHT7pdjqkiCxpTJ/z1P2mkH8jjhZv6EB/Z2O1yjENCgwN5bkwfjn1fxB/nb3S7HFNFFjTG732dnsOsZZlMGBzPhQl2z1Rd161NU345tBMfrdvL1+l2M7Y/sKAxfu1ofhH3v7uWhJZN+PVPurhdjqklky7uQIeoxvzhgw12FZofsKAxfu2P8zeQe7yQp6/vTWhwoNvlmFoSEhTIX37ag8xD+Tz/xVa3yzGVsKAxfus/6/fywZo93DMsgZ7Rzdwux9SyCzpGck3fdkxdvIOtdiOnT7OgMX7pQF4BD7+/nqToZvxiqM1jVl89PKobjUOCePj9DZSW1v17Av2VBY3xO6rK7+atJ7+whKev70VwoP0Y11cRTUJ4aGRXVuw6xLup2W6XY07DfkON33knNZvP0g5w/4iudGoZ5nY5xmXX9Yuhf1xz/rogze6t8VEWNMavZB3K58//3sTADi247YI4t8sxPiAgQPh/V/fkeEExf/3PZrfLMRWwoDF+o7RU+e27awF46rpeNsWM+UHnVmHccVEH3luVzerMw5V3MLXKgsb4jdeW7GLZjkM8ckUi0c0buV2O8TG/HNqJqLAQ/vzRJntImo+xoDF+Ycu+PP7+yWYu6daS65Kj3S7H+KAmIUH89rIurM48wnurdrtdjvFiQWN8XkFRCVPmrKZpaDCP/yyJsufiGfNj1/aNpl/75jz20Sa7MMCHWNAYn/f3TzazeV8eT12XRGSTELfLMT4sIEB4/JqeHD9ZzPNfbHO7HONhQWN82ldbDvDad7u49YI4Lu7S0u1yjB9IaBXG9ckxzFqWwa6DJ9wux2BBY3zYgbwCfvPOWjq3asKDI7u6XY7xI/ddkkBwYAB/W5DmdikGCxrjo0pLlV/9ay3HTxbzwk19bcJMc1ZaNg3l7mGdWLhxvz2N0wdY0Bif9PLi7Xy77SB/urI7nVvZ3f/m7E24MJ4OkY354/yN9igBl1nQGJ+TmnGY//s0nSuS2nBD/xi3yzF+KiQokD+P7kFGbj6vfL3D7XLqNQsa41OO5hcx+e3VtA0P5a/X9LRLmU21DE6I5IqkNrz41TayDuW7XU69ZUFjfIaq8sB769h/rIDnb+xL09Bgt0sydcDvRnUjQOCP8zfajAEucTRoRGSEiGwRkW0i8mAF628WkXWejyUi0suzPEZEvhSRNBHZKCJTvPq0EJFFIrLV87m5k2MwtWfW8kw+2biP+0d0oXdMuNvlmDqibXhD7r+sK19sPsA79igBVzgWNCISCLwIjAQSgRtFJLFcs53AEFVNAh4DpnqWFwO/VtVuwEDgl159HwQ+V9UE4HPPa+Pn0vYe47GPNnFxlygmDO7gdjmmjrltUBx9Y8N5auEW8guL3S6n3nFyj2YAsE1Vd6hqITAHGO3dQFWXqOqpqVaXAdGe5XtVdZXn6zwgDWjnaTcaeN3z9evATx0cg6kFR78v4u63VhHeMNhmZTaOEBEevrwbB/JOMu2bnW6XU+84GTTtgCyv19n8NywqMh5YUH6hiMQBfYDlnkWtVHUvlAUSUOHt4iIyUURSRCQlJyfnrIs3teP7whImvL6SzEP5PDemj00xYxzTr30LRnRvzctfb+dAXoHb5dQrTgZNRX+WVngmTkSGUhY0D5Rb3gR4D7hXVY+dzTdX1amqmqyqyVFRUWfT1dSSwuJS7pqdSkrGYZ69oQ/nd4xwuyRTxz0wsiuFxaU8+9lWt0upV5wMmmzA+yaIaGBP+UYikgRMA0araq7X8mDKQma2qs7z6rJfRNp42rQB7LZfP1RSqvz6nbV8tSWHv17dk8uT2rhdkqkH4iMbc8vA9vxrZRZb9+e5XU694WTQrAQSRCReRBoAY4D53g1EJBaYB4xV1XSv5QJMB9JU9ely250PjPN8PQ740KH6jYP+/O+N/HvtHh4c2ZUbB8S6XY6pRyYPT6BRcCCPL7DHPtcWx4JGVYuBu4GFlJ3Mn6uqG0VkkohM8jR7BIgAXhKRNSKS4lk+CBgLDPMsXyMiozzrHgcuFZGtwKWe18aPzF6ewetLM7jjwngmDenodjmmnmnRuAG/GNqJzzcfYOn23Mo7mGqT+nADU3JysqakpFTe0DguZdchbnx1GYM6RTJ9XH8C7Qoz44KCohKGPfUVEU1CmH/3IJuB4jREJFVVk6u7HZsZwNSavUe/Z9KsVUQ3b8RzY/pYyBjXhAYHcu+lnVm/+yhf2uzOjrOgMbWioKiESW+m8n1hMVPH9qNZQ5texrjr6j7tiG7ekKcWplNSWveP7LjJgsY4TlV5+P0NrM0+yjM39CbBpv03PiA4MIDfXtaFTXuPMW+VTU3jJAsa47jnPt/Ke6uyufeSBH7SvbXb5Rjzg6t6taVPbDhPLtzCiZM2NY1TLGiMo95ekcmzn23l2n7RTBme4HY5xvwPEeH3lydyIO8kryy2Z9Y4xYLGOObztP08/P56hnSO4m/2bBnjo/q1b84VSW14dfEOjuQXul1OnWRBYxyxKvMwv3xrFT3aNeOlm/sSHGg/asZ3/eLiTnxfVMJbKzLdLqVOst9+U+N25Bxn/MyVtGoayoxb+9M4JMjtkow5o8S2TbmocxRTF+/gaH6R2+XUORY0pkbtO1rAz2esIECE128bYLMxG7/x4IiuHP2+iFcWb3e7lDrHgsbUmMMnChk7fTlH8ot47bb+xEU2drskY6ossW1TLu/ZhteX7OLwCTtXU5MsaEyNOH6ymFtfW0HGoXxe/XkySdH2KGbjfyYPTyC/qIRp39oVaDXJgsZUW0FRCRPfSGHDnmO8eFNfe66M8VudW4Vxec82vPbdLg4cs4ej1RQLGlMtxSWlTH57NUu25/LUdUlcmtjK7ZKMqZbfXtaFopJSXvxym9ul1BkWNOaclZYqD85bz6eb9vOnKxO5uk+02yUZU23tIxpzZa+2vLdqN8dttoAaYUFjzklxSSkPvLeOd1Ozue+Sztw6KN7tkoypMePOj+P4yWJmfrfT7VLqhDMGjYi0KPfRXOz27nqvoKiEu2av4p3UbKYMT2Dy8E5ul2RMjeoVE86lia14+esdHLIr0Kqtsj2aVCDF8zkVWAUcEJHPRCTO2dKMLzpWUMS4GSv4LG0/j17Vnfsu7WxTy5g66YERXcgvLOb5L7a6XYrfO2PQqGq8qnbwfD71EQW8BLxcOyUaX3Hw+ElunLqM1IzDPHtDb8ZdEOd2ScY4plPLMK5PjmHWsgwyc/PdLsevndM5GlWdB7Ss4VqMD8s6lM91Ly9le85xpo1LZnTvdm6XZIzj7ru0M4EBwlOfbnG7FL92TkEjIk3Ota/xP+n787j25SUcOlHI7AkDubiL/Y1h6odWTUMZPzie+Wv3sGH3UbfL8VtnnO1QRH5VweLmwFXAC45UZHzKZ5v28+t31hISFMDcO8+nS2t7OqapX+4c0pG3lmfy+ILNzJpwntvl+KXK9krCyn00AfYBt6jqqw7XZlx0/GQxD7y7jglvpNA2vCHv3XWBhYypl5qGBnP3sAS+3XaQxek5bpfjl864R6Oqj5762nO4TFX1RFU3LiIjgOeAQGCaqj5ebv3NwAOel8eBu1R1rWfdDOAK4ICq9vDq05uyCxFCgWLgF6q6oqo1mcqt2HmIX7+zht2Hv+cXF3dkyiUJhAQFul2WMa65ZWAsr323kycXbuHChEi70vIsVXqeRUTuEpFMIAPIFJEMEflFFfoFAi8CI4FE4EYRSSzXbCcwRFWTgMeAqV7rZgIjKtj0E8CjqtobeMTz2tSAk8Ul/G1BGjdMXYogzL3zfO4f0dVCxtR7IUGBTB6ewPrdR/ks7YDb5fidym7Y/D1wJXCxqkaoagQwFBjpWXcmA4BtqrpDVQuBOcBo7waqukRVD3teLgOivdYtBg5VsF0Fmnq+bgbsqaQOUwVpe48x+oXveOXrHYzpH8OCKReSHNfC7bKM8RnX9GlH+4hGPPtZOqrqdjl+pbI9mrHANar6w5zZnq+vB35eSd92QJbX62zPstMZDyyoZJsA9wJPikgW8BTwUBX6mNMoKVX++dV2rnrhWw4eL2TGrcn87ZokeyqmMeUEBQZwz7AENu45xqeb9rtdjl+p9NCZqv5ormxV/R4oraRrRQcxK/wzQESGUhY0D1S0vpy7gPtUNQa4D5h+mm1OFJEUEUnJybETeOWVlCrrs48yZupS/v7JZi7p1opP77uIYV1t9mVjTuenvdsSH9mYZxalU1pqezVVVdmfrdkiMlxVP/deKCLDgL2V9QVivF5HU8FhLhFJAqYBI1U1t/KSGQdM8Xz9jqfvj6jqVDznfJKTk+v9T8T+YwWszjzCmqwjrM48zPrdR8kvLCEsJIinr+/F1X3a2QlOYyoRFBjA5OGduO9fa1m4cR8je7ZxuyS/UFnQTAY+FJFvKZvrTIH+wCDKnW+pwEogQUTigd3AGOAm7wYiEgvMA8aqanoVa94DDAG+AoYBNhFROd8XlrBhz1FWZx5mTdYR1mQeYc/Rsh3T4EChW5umXNcvmt6x4QzuFEVUWIjLFRvjP67q1Y7nv9jGs59t5bLurQkIsD/QKlPZ5c0bRaQHZQHRnbLDYYuBOys6pFaub7GI3A0spOzy5hme7U3yrH+ZsqvGIoCXPH9NF6tqMoCIvA1cDESKSDbwR1WdDtwBPCciQUABMPGcRl5HlJYqOw6e+GFPZU3WETbvy6PEs1sf3bwhfds3Z3xsc3rHhNO9bVNCg+0qMmPOVWCAMGV4AlPmrGHBhn1cnmR7NZWR+nD1RHJysqakpLhdRo04dKKQNVmHWZN5hNVZR1ibdYRjBWUPZ2oSEkSvmGb0jgmnd0xZsNjeijE1r6RUuezZxQjwyb0XEVhH92pEJPXUH//VUdkUNHlUfAJfKLt5s2kF60wNOVlcQtrevP8eAss6QoZnFtkA8TzfPKktfWLC6R0bTseoJnX2B94YX3Jqr+aet1fz8fq9XNWrrdsl+bTKDp3ZnCO1RFXJOvQ9q7MOew6DHWHTnmMUlpRd3NeqaQi9Y8IZ0z+WPrHh9GzXzC5BNsZFl/dsw/NfbOW5z9K5vGcb+yPvDOx/KpccKyhiXdbR/9lbyfU8yS80OICkduHcOiiO3jHh9IkNp02zhi5XbIzxFhAg3HtJZ34xexX/XruHn/axR2ecjgXNGby6eAcLNvzvVdynO6NV0amu07XNKyhi58ETP/TpGNWYoV1besTDYtQAABDySURBVM6thNOldRjBgfYUBmN83YjurenaOox/fL6VK5LaEGS/txWyoDmD4EA5q8NTFd2HUtHOdKuwEH7aux19YsNJig6nWcPgalRpjHHLqb2aSbNSmb92D9f0ja68Uz1kV50ZY0w1qCqX/+Nb8guL+exXQ+rUXk1NXXVWd/5FjDHGBSLCvZcksCs3n/dX73a7HJ9kQWOMMdV0aWIrurdtyj+/3m5zoFXAgsYYY6pJRJh4UQd25Jzgi832vJryLGiMMaYGjOrZhnbhDXn1mx2VN65nLGiMMaYGBAcGcNugOJbvPMTS7VWZiL7+sKAxxpgacsvA9rRtFsrjn2y2p3B6saAxxpgaEhocyD3DE1ibdYRvth50uxyfYUFjjDE16Jq+7WjTLJQXvtjmdik+w4LGGGNqUEhQIHde1IEVuw6xfIedqwELGmOMqXFjBsQS2aQBL3xpezVgQWOMMTUuNDiQOy7swDdbD7Im64jb5bjOgsYYYxxw88D2hDcK5oUvtrpdiussaIwxxgFNQoK4fVA8n6UdYNOeY26X4yoLGmOMcci4C+IICwnixXp+rsaCxhhjHNKsYTDjLojjPxv2su1AntvluMaCxhhjHHT74HhCgwJ58cvtbpfiGgsaY4xxUIvGDbjpvFjmr91D1qF8t8txhaNBIyIjRGSLiGwTkQcrWH+ziKzzfCwRkV5e62aIyAER2VBBv3s8290oIk84OQZjjKmuCRfGEyAwdXH9nNnZsaARkUDgRWAkkAjcKCKJ5ZrtBIaoahLwGDDVa91MYEQF2x0KjAaSVLU78FTNV2+MMTWnTbOGXNMnmn+lZJGTd9Ltcmqdk3s0A4BtqrpDVQuBOZQFxA9UdYmqHva8XAZEe61bDByqYLt3AY+r6klPO3vKkDHG5905pANFJaXMXLLT7VJqnZNB0w7I8nqd7Vl2OuOBBVXYbmfgQhFZLiJfi0j/ihqJyEQRSRGRlJycnCoXbYwxTugQ1YTLElvz5tIM8gqK3C6nVjkZNFLBsgof0OA5HDYeeKAK2w0CmgMDgd8Cc0XkR99LVaeqarKqJkdFRVW9amOMccikiztyrKCYt1dkul1KrXIyaLKBGK/X0cCe8o1EJAmYBoxW1apMdZoNzNMyK4BSILIG6jXGGEf1jgnn/A4RTP92JyeLS9wup9Y4GTQrgQQRiReRBsAYYL53AxGJBeYBY1U1vYrb/QAY5unfGWgA2BOGjDF+YeKQDuw/dpJPN+53u5Ra41jQqGoxcDewEEgD5qrqRhGZJCKTPM0eASKAl0RkjYiknOovIm8DS4EuIpItIuM9q2YAHTyXPc8Bxqk9M9UY4yeGJETRLrwhc1bWn8NnUh/+j05OTtaUlJTKGxpjTC146attPPHJFj66ZzA92jVzu5zTEpFUVU2u7nZsZgBjjKllN5/XniYhQbxST27gtKAxxpha1qxhMDefF8vH6/aQmVv3p6WxoDHGGBfcNiiewADh1W/q/l6NBY0xxrigdbNQru7TjrkpWeQer9vT0ljQGGOMSyZe1IGTxaW8uSzD7VIcZUFjjDEu6dQyjOFdW/LG0gy+L6y7N3Ba0BhjjIsmXtSBQycKeXdVttulOMaCxhhjXDQgvgW9YsKZ9s0OSkrr5n2NFjTGGOMiEWHihR3IyM1n0aZ9bpfjCAsaY4xx2YgerYlt0YhXFu+gLs7WYkFjjDEuCwwQJlwYz+rMI6RkHK68g5+xoDHGGB9wbb9omjUMZuaSXW6XUuMsaIwxxgc0ahDE9cnRLNywj31HC9wup0ZZ0BhjjI+4ZWB7SlR5q449gdOCxhhjfET7iMZc3DmKt1dkUlhc6nY5NcaCxhhjfMjPL4gjJ+8kn2ysO5c6W9AYY4wPGZIQRfuIRry5dJfbpdQYCxpjjPEhAQHC2IHtWbnrMCm7DrldTo2woDHGGB9z03mxRIWF8OTCLW6XUiMsaIwxxsc0ahDEnRd1YPnOQ2zYfdTtcqrNgsYYY3zQdckxNGoQyGvf7XK7lGqzoDHGGB/UrGEw1/aL5t9r95CT599P4LSgMcYYHzXugjgKS0p5a7l/38DpaNCIyAgR2SIi20TkwQrW3ywi6zwfS0Skl9e6GSJyQEQ2nGbbvxERFZFIJ8dgjDFu6RjVhCGdo5i1PMOvb+B0LGhEJBB4ERgJJAI3ikhiuWY7gSGqmgQ8Bkz1WjcTGHGabccAlwL+HfPGGFOJ2waV3cD5n/V73S7lnDm5RzMA2KaqO1S1EJgDjPZuoKpLVPXUnNjLgGivdYuB011E/gxwP1D3HtxgjDFeLkqIokNkY177bqffPqvGyaBpB2R5vc72LDud8cCCyjYqIlcBu1V1bSXtJopIioik5OTkVKVeY4zxOQEBwq2D4libfZS12f55qbOTQSMVLKswjkVkKGVB88AZNyjSCHgYeKSyb66qU1U1WVWTo6KiqlCuMcb4pqv7tKNBUAAfrN7tdinnxMmgyQZivF5HA3vKNxKRJGAaMFpVcyvZZkcgHlgrIrs821wlIq1rpGJjjPFBYaHBXNKtJfPX7uFkcYnb5Zw1J4NmJZAgIvEi0gAYA8z3biAiscA8YKyqple2QVVdr6otVTVOVeMoC7O+qlp3pjk1xpgKjOkfy6EThXy8zv8uCnAsaFS1GLgbWAikAXNVdaOITBKRSZ5mjwARwEsiskZEUk71F5G3gaVAFxHJFpHxTtVqjDG+7sKESDpGNeZ1P3zUs/jrVQxnIzk5WVNSUipvaIwxPuyNpbt45MONvHfXBfRr39zx7yciqaqaXN3t2MwAxhjjJ37WN5rmjYJ57vOtbpdyVixojDHGTzQOCeKOizqwOD2HtL3H3C6nyixojDHGj9w0IJbQ4AC/OldjQWOMMX4kvFEDru7Tjg/W7OZIfqHb5VSJBY0xxviZcRfEUVBUytyUrMob+wALGmOM8TNdWzflvPgWvLE0g5JS379y2ILGGGP80G2D4sk+/D0LNvj+DZwWNMYY44cuTWxFh8jGvPz1dp+f1dmCxhhj/FBggDDxog5s2H2M77ZVNk2kuyxojDHGT13dtx0tw0J4+evtbpdyRhY0xhjjp0KCArl9cDzfbjvIxj2++6waCxpjjPFjNw6IpVGDQF77bpfbpZyWBY0xxvixZg2D+VnfaOav2UNO3km3y6mQBY0xxvi5WwfFUVhSylvLM90upUIWNMYY4+c6RjXhwoRI3l6RSXFJqdvl/IgFjTHG1AFjB7Zn37ECPks74HYpP2JBY4wxdcCwri1p2yyUWcsy3C7lRyxojDGmDggKDOCm82L5dttBtuccd7uc/2FBY4wxdcQN/WMJDhTeXOpbezUWNMYYU0dEhYUwqmcb3k3NJq+gyO1yfmBBY4wxdchtg+I5frKYd1Oz3S7lBxY0xhhTh/SOCadvbDgzl+zymWfVWNAYY0wdc9ugeDJy8/lys29c6uxo0IjICBHZIiLbROTBCtbfLCLrPB9LRKSX17oZInJARDaU6/OkiGz29HlfRMKdHIMxxvibET1a06ZZKK8t2el2KYCDQSMigcCLwEggEbhRRBLLNdsJDFHVJOAxYKrXupnAiAo2vQjo4emTDjxUw6UbY4xfCw4MYOz57fluWy5b9uW5XY6jezQDgG2qukNVC4E5wGjvBqq6RFUPe14uA6K91i0GDpXfqKp+qqrFFfUxxhhT5sb+sVzUOYrCYvenpAlycNvtgCyv19nAeWdoPx5YcJbf43bgXxWtEJGJwESA2NjYs9ysMcb4t+aNG/DG7QPcLgNwdo9GKlhW4SUQIjKUsqB5oMobF3kYKAZmV7ReVaeqarKqJkdFRVV1s8YYY2qYk3s02UCM1+toYE/5RiKSBEwDRqpqlR58LSLjgCuA4arqG9fvGWOMqZCTezQrgQQRiReRBsAYYL53AxGJBeYBY1U1vSobFZERlO35XKWq+TVcszHGmBrmWNB4TtjfDSwE0oC5qrpRRCaJyCRPs0eACOAlEVkjIimn+ovI28BSoIuIZIvIeM+qF4AwYJGnz8tOjcEYY0z1SX048pScnKwpKSmVNzTGGPMDEUlV1eTqbsdmBjDGGOMoCxpjjDGOsqAxxhjjqHpxjkZEcoBzfRJQJHCwBsvxBTYm31fXxgM2Jn9QfjztVbXaNyLWi6CpDhFJqYmTYb7ExuT76tp4wMbkD5wajx06M8YY4ygLGmOMMY6yoKnc1Mqb+B0bk++ra+MBG5M/cGQ8do7GGGOMo2yPxhhjjKMsaIwxxjiqXgWNiIwQkS0isk1EHqxgvYjIPzzr14lI38r6ikgLEVkkIls9n5vX1njOVJfX+nMZ059EZLdn0tI1IjKqtsZzprq81p9pTDNE5ICIbCjXx5/fp9ONybX36VzHIyIxIvKliKSJyEYRmeLVxy/fo0rG5Je/SyISKiIrRGStZ0yPevU5+/dJVevFBxAIbAc6AA2AtUBiuTajKHvKpwADgeWV9QWeAB70fP0g8Pc6MKY/Ab/xt/fJs+4ioC+woVwfv3yfKhmTK+9TNX/u2gB9PV+HAel14HfpTGPyy98lz+smnq+DgeXAwHN9n+rTHs0AYJuq7lDVQmAOMLpcm9HAG1pmGRAuIm0q6TsaeN3z9evAT50eiBenxuSm6owJVV0MHKpgu/76Pp1pTG455/Go6l5VXQWgqnmUPUKknVcfv3uPKhmTm6ozJlXV4542wZ4P9epzVu9TfQqadkCW1+tsfvzDcLo2Z+rbSlX3Ang+t6zBmivj1JgA7vbsSs+o5UMY1RnTmfjr+1QZN96nGhmPiMQBfSj7axnqwHtUwZjAT3+XRCRQRNYAB4BFqnrO71N9ChqpYFn5a7tP16Yqfd3g1Jj+CXQEegN7gf871wLPQXXG5KucGpNb71O1xyMiTYD3gHtV9VgN1naunBqT3/4uqWqJqvYGooEBItLjXAupT0GTDcR4vY4G9lSxzZn67j91iMPz+UAN1lwZR8akqvs9P2SlwKuU7YLXluqM6Uz89X06LRffp2qNR0SCKfsPebaqzvNq47fv0enGVBd+l1T1CPAVMMKz6Kzfp/oUNCuBBBGJF5EGwBhgfrk284Gfe67EGAgc9ewanqnvfGCc5+txwIdOD8SLI2M69UPkcTWwgdpTnTGdib++T6fl4vt0zuMREQGmA2mq+nQFffzuPTrTmPz1d0lEokQkHEBEGgKXAJu9+pzd+3QuVzP46wdlV1ikU3YlxsOeZZOASfrfKy1e9KxfDySfqa9neQTwObDV87lFHRjTm5626zw/VG38aExvU3aIooiyv9bG14H36XRjcu19OtfxAIMpOzSzDljj+Rjlz+9RJWPyy98lIAlY7al7A/CI1zbP+n2yKWiMMcY4qj4dOjPGGOMCCxpjjDGOsqAxxhjjKAsaY4wxjrKgMcYY4ygLGmMcJiKtRWSOiGwXkU0i8h8R6XyG9veKSKParNEYJ1nQGOMgz8187wNfqWpHVU0Efge0OkO3ewELGlNnWNAY46yhQJGqvnxqgaquAQJF5KNTy0TkBRG5VUQmA22BL0Xky9ov15iaZ0FjjLN6AKlVbayq/6BsrqmhqjrUsaqMqUUWNMYYYxxlQWOMszYC/SpYXsz//v6F1k45xtQ+CxpjnPUFECIid5xaICL9KXvMbqKIhIhIM2C4V588yh4JbEydYEFjjIO0bNbaq4FLPZc3b6TsOfJ7gLmUzY47m7KZck+ZCiywiwFMXWGzNxtjjHGU7dEYY4xxlAWNMcYYR1nQGGOMcZQFjTHGGEdZ0BhjjHGUBY0xxhhHWdAYY4xx1P8HsO74A+gZG7QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 20%|██        | 2/10 [00:14<00:58,  7.31s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22451377860541968 0.016267780676484107\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 30%|███       | 3/10 [00:21<00:51,  7.34s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22498197962630423 0.01264219737611711\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 40%|████      | 4/10 [00:30<00:47,  7.95s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22514045089355295 0.011047122783958911\n"
     ]
    },
    {
     "data": {
      "image/png": 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fnU3vDqm8dE0WTRN1rUYsUnCISK1YuG4Ho16ZRafWzZhw3SBSmyaGXZIERMEhIkdtZcFurhk/k9SmjXl11KmkpzQJuyQJkIJDRI7Kjr3FXPvyLAD+dMOpdGzVLOSKJGj6IicROWLuzs/+Zx7rt+/jzZtPo3vblLBLkjqgPQ4ROWLPfLycDxflc993j+fkrvpOtXih4BCRI/L7T1fwXx8t55KBnbj+jMywy5E6pOAQkRr7bFkBj7+/hAv7duDJ7/fTVeFxRsEhIjWydute7pg4h57tUnny+31J0FXhcUfBISLVVlhcyi2vzaa01HnhqpNpnqTza+KRXnURqRZ3Z8zb81m4bid/uDqLbm2Swy5JQqI9DhGplt9/tpI/z13Pz847jnP7tA+7HAmRgkNEqvTP5ZsPDobfOqRH2OVIyBQcInJY+TsLuXPiHHq0TeHJ7/fVGVSiMQ4RObSS0gi3vzGHvUWlTLxpoAbDBVBwiMhh/PbDZcxctZWnf9iPnu1Twy5H6gkdqhKRSk1bsonnP1nBFYM6M2JARtjlSD2i4BCRb1i/fR93TZrL8R1a8NDFJ4RdjtQzCg4R+ZoD4xolpc7zIwfqW/zkGzTGISJf88zHy5n91TaevWKALvKTSmmPQ0QO+nzFFp6blstlJ2cwrF/HsMuRekrBISIAbNpVyB0T59AtPZmHh2lcQw5Nh6pEhJLSCHe+MZddhcX8adQgkpvorUEOTX8dIsLTHy3j85VbeOqyfvQ+pkXY5Ug9p0NVInHu70vyGTut7HqNS0/W9RpStUCDw8wuMLOlZpZrZmMqWT7SzOZHH9PNrF+5ZePNbJOZLazQ5mEzW2dmc6OP7wbZB5FYtnbrXu56cx4ndNT1GlJ9gQWHmSUAY4GhQB/gCjPrU2G1VcBZ7t4XeBQYV27ZK8AFh9j80+7eP/r4W+1WLhIfDlyvEXFdryE1E+QexyAg191XunsRMBEYXn4Fd5/u7tuikzOAjHLLPgO2BlifSFwbO20Fc9du5z8vOYmu6bpeQ6ovyODoBKwtN50XnXcoo4D3qrnt26KHt8abWevKVjCzm8ws28yyCwoKqrlZkfgwd+12nv37ckYM6MRFfXW9htRMkMFR2U37vdIVzYZQFhz3VmO7vwO6A/2BDcBTla3k7uPcPcvds9q2bVu9ikXiwN6iEu56cy7tU5voeg05IkEGRx7Qudx0BrC+4kpm1hd4ERju7luq2qi757t7qbtHgD9QdkhMRKrpP/53Mau37OGpH/SnZbPEsMuRBijI4JgF9DSzbmaWBFwOTCm/gpl1ASYDV7n7sups1Mw6lJscASw81Loi8nXTlmzitS/WcOOZx3Ja9/Swy5EGKrALAN29xMxuAz4AEoDx7p5jZqOjy18AHgTSgeejX0dZ4u5ZAGb2BnA20MbM8oCH3P0l4Akz60/ZYa/VwM1B9UEklmzZvZ97/mc+vY9J5e7zjgu7HGnAzL3SYYeYkpWV5dnZ2WGXIRIad+fmP83mk6UFTLn9DF0dLtViZrMPfJgvT1eOi8SBt7LzmLoon3vO76XQkKOm4BCJcXPWbOOBdxcy+Ng0Rn2rW9jlSAxQcIjEsK17irj5T7Np16IJY68cSKNGlZ0lL1IzujuuSIxyd+59ez7b9xbzzq2nk57SJOySJEZoj0MkRr0xcy0fLsrn3y/oxQkdW4ZdjsQQBYdIDMrdtJtf/jWHM3u24fozNK4htUvBIRJjikoi/OTNOTRLTOA3l/XTuIbUusOOcZhZWoVZDmz3eLj4Q6SBeurDpSxct5PfX3Uy7Vs0DbsciUFVDY7Ppiwsyn9kSTGzecAN7r46qMJEpOam525m3GcruWJQF84/4Ziwy5EYddjgcPdKD46a2SXACxz6i5ZEpI5t31vETyfNo1t6Mg9cdHzY5UgMO6IxDnefDLSr5VpE5Ai5O/dNXsDm3ft55vIBNE/SmfYSnCMKDjNLOdK2IlL73srO472FG7n7vF6clKFTbyVYVQ2O/7SS2a2BYcBzgVQkIjWyavMeHv5LDqcdm87N/3Zs2OVIHKhqfza1wrQDG4EfufuCYEoSkeoqLo3wk4lzSExoxFM/0Km3UjeqGhx/5MDz6OEpd/c9gVclItXyzEfLmZe3g7FXDqRjq2ZhlyNxospxCjO7xczWAF8Ba8zsKzP7cfClicjhfLFyC2M/yeWykzO4sG+HqhuI1JLDBoeZ/QK4GDjb3dPdPR0YAgyNLhOREOzYV8xPJ82jS1pzHhp2QtjlSJypao/jKuASd195YEb0+Q+Aq4MsTEQq5+7c/84CNu4s5JnLB5DSRKfeSt2q8lCVuxdWMm8fEAmkIhE5rHfmrOOv8zdw13d60r9zq7DLkThUVXDkmdm3K840s3OADcGUJCKHsmbLXh58N4dTMltzy9k9wi5H4lRV+7h3AO+a2T/5132rTgHOAIYHXJuIlFNSWnbXWwOe/mF/EnTqrYTksHsc7p4DnAh8BmQCx0afnxhdJiJ15LlpuXy5Zju/GnEiGa2bh12OxLEqR9WiYxzj66AWETmE+Xnb+e+/5/K9/h0Z3r9T2OVInKvqliO7KDs89Y1FlF0M2CKQqkTkoP0lpdzz1nzapCTxyLATwy5HpMorxyveckRE6thzf89laf4uxl+bRcvmiWGXI6I73IrUZwvydvD8Jyu4dGAG5/RuH3Y5IoCCQ6Te2ltUwp0T59A2pQkPXtQn7HJEDgo0OMzsAjNbama5ZjamkuUjzWx+9DHdzPqVWzbezDaZ2cIKbdLM7EMzWx792TrIPoiE5Zd/WcSqLXt4+of9dYhK6pXAgsPMEoCxwFCgD3CFmVX82LQKOMvd+wKPAuPKLXuFyr+adgzwsbv3BD6OTovElPcWbGDirLWMPqs7p3VPD7scka8Jco9jEJDr7ivdvQiYSIWLBt19urtvi07OADLKLfsM2FrJdocDE6LPJwDfq+3CRcK0Ycc+xkxeQL+Mlvz03OPCLkfkG4IMjk7A2nLTedF5hzIKeK8a223v7hsAoj8r/e5zM7vJzLLNLLugoKCaJYuEqzTi3PXmXIpLIzxz+QASEzQMKfVPkH+Vld0PobJrQjCzIZQFx7219cvdfZy7Z7l7Vtu2bWtrsyKB+v1nK5ixcisPDzuBzDbJYZcjUqkggyMP6FxuOgNYX3ElM+sLvAgMd/ct1dhuvpl1iLbtAGyqhVpFQjdv7XZ+O3UZF/btwGUnZ1TdQCQkQQbHLKCnmXUzsyTgcmBK+RXMrAswGbjK3ZdVc7tTgGuiz68B3q2lekVCs2d/2am37VKb8OvvnYSZbmAo9VdgweHuJcBtwAfAYmCSu+eY2WgzGx1d7UEgHXjezOaaWfaB9mb2BvA50MvM8sxsVHTRY8C5ZrYcODc6LdKgPTwlhzVb9+rUW2kQzL3SYYeYkpWV5dnZ2VWvKBKCv85fz22vz+H2c3pw93m9wi5H5CAzm+3uWRXn65QNkRCt276P+yYvoH/nVtzx7Z5hlyNSLQoOkZCURpy7Js4lEnGeuby/Tr2VBkPfci8Skt99ksvM1Vv57Q/60TVdp95Kw6GPOCIhmLNmG09/tJxh/ToyYoC+mEkaFgWHSB3bVVjMnRPnckyLpvxqxIk69VYaHB2qEqlD7s797ywkb9teJt18Gi2a6tRbaXi0xyFSh17+v9VMmbeeu8/rRVZmWtjliBwRBYdIHZm5aiu//ttizuvTnh+f3T3sckSOmIJDpA7k7yzkx699SZe05vzmB/00riENmsY4RAJWVBLhx699yZ79Jbx+46ka15AGT8EhErBf/20xs7/axn9fMYDj2qeGXY7IUdOhKpEAvTMnj1emr2bUt7pxcb+OYZcjUisUHCIBWbR+J/dNXsCgbmmMGdo77HJEao2CQyQA2/cWMfrV2bRslshzV+orYCW2aIxDpJaVlEa4/Y05bNixj4k3DaZdatOwSxKpVQoOkVr2+PtL+MfyzTx+6Umc3FUX+Uns0f6zSC16Z04ef/jHKq4+rSs/PKVL2OWIBELBIVJLFuTt4N63F3BqtzQeuKhP2OWIBEbBIVIL9uwv4fY3vqRNchLPjxyowXCJaRrjEKkFj/51EV9t3cvEGweTntIk7HJEAqWPRSJH6e3ZeUyctZZbzurOqcemh12OSOAUHCJHYfZXW7lv8gJO757OXeceF3Y5InVCwSFyhPK27eWmP86mU+tmGteQuKK/dJEjsHt/CTdMyKa4NMKL12TRqnlS2CWJ1BkNjovUUCTi3PXmXJZv2s0r151C97YpYZckUqe0xyFSQ7//bCUfLsrnFxcez5k924ZdjkidU3CI1MD0FZt58oMlXNS3A9eenhl2OSKhUHCIVNPSjbsY/afZdGuTzGOX9tXXv0rcCjQ4zOwCM1tqZrlmNqaS5SPNbH70Md3M+lXV1sweNrN1ZjY3+vhukH0QAVi3fR/XjJ9Js6QEJlw/iJQmGh6U+BXYX7+ZJQBjgXOBPGCWmU1x90XlVlsFnOXu28xsKDAOOLUabZ92998EVbtIedv2FHH1S1+wp6iEt0afRkbr5mGXJBKqIPc4BgG57r7S3YuAicDw8iu4+3R33xadnAFkVLetSF3YW1TC9RNmsXbbPl68Oovex7QIuySR0AUZHJ2AteWm86LzDmUU8F41294WPbw13sxaV7YxM7vJzLLNLLugoKDm1UvcKymNcPvrc5i3djvPXt5ftxMRiQoyOCobOfRKVzQbQllw3FuNtr8DugP9gQ3AU5Vt093HuXuWu2e1batTJqVm3J2HpuTw8ZJNPDL8RC44sUPYJYnUG0EGRx7Qudx0BrC+4kpm1hd4ERju7luqauvu+e5e6u4R4A+UHdYSqVUvfLqS175Yw+izunPV4K5hlyNSrwQZHLOAnmbWzcySgMuBKeVXMLMuwGTgKndfVp22Zlb+o98IYGGAfZA49O7cdTz+/hIu7teRfz+/V9jliNQ7gZ1V5e4lZnYb8AGQAIx39xwzGx1d/gLwIJAOPB89J74kenip0rbRTT9hZv0pO3S1Grg5qD5I/Jmxcgv3vDWfQd3S+M1lfWnUSNdqiFRk7pUOO8SUrKwsz87ODrsMqecWrtvBlX+YQdvUJrx9y+m6caHEPTOb7e5ZFefrynERyr5X44pxM0htmsgr1w1SaIgchoJD4t7nK7Zw1UszSU9JYtLo0+icpgv8RA5H902QuDZr9Vauf2UWGa2b8doNp9KuRdOwSxKp9xQcErfmrt3OdS/PokOrprx+42DapjYJuySRBkGHqiQuzc/bztUvfUFachKv36DQEKkJBYfEnf/L3cwV42bQolkir994Kse01OEpkZpQcEhceX/hBq57eRYZrZvz9i2n6063IkdAYxwSN96du4673pxL/86tGH/tKTrlVuQIKTgkLrwzJ4+7J83jlMw0xl97Csn6IiaRI6b/PRLz3p6dx8/+Zx6Du6Xz0rVZNE/Sn73I0dD/IIlZ7s4Ln67k8feXcEaPdF68+hSaJSWEXZZIg6fgkJhUUhrhwSk5vP7FGi7u15Env9+XpokKDZHaoOCQmLN7fwm3vvYlny4r4Mdnd+dn5/XSXW5FapGCQ2LKxh2FXPfKLJbl7+I/LzmJKwZ1CbskkZij4JCYsWj9Tq5/ZRa7CosZf+0pnHWcvjJYJAgKDokJHy3K5ydvziWlSWPeGn06fTq2CLskkZil4JAGraQ0wm+mLuOFT1dwQscWvHhNFh1aNgu7LJGYpuCQBmvTzkJue2MOM1dt5YpBXXjo4j46c0qkDig4pEGavmIzd7wxlz37S/jtD/pxycCMsEsSiRsKDmlQIhHnd5+u4KmpS8lsk8zrN57Kce1Twy5LJK4oOKTB2L63iLvenMu0pQVc3K8j/3nJSaTonlMidU7/66RBmLFyC3dPmsemXYX8cvgJXDW4K2a6qE8kDAoOqdf27C/hifeXMOHzr+iS1py3Rp9O/86twi5LJK4pOKTemr5iM/e+PZ+8bfu47oxM7jm/l+5sK1IP6H+h1Du7Cot5/P0lvDpjDZnpzXnzptMY1C0t7LJEJErBIfWGu/NBzkYempLDpl37uf6Mbtxzfi/dCl2knlFwSL2wfvs+Hnw3h48W53N8hxb8/qosjWWI1FONglypFQkAAAjUSURBVNy4mV1gZkvNLNfMxlSyfKSZzY8+pptZv6ramlmamX1oZsujP1sH2QcJVmnEeemfq/jObz/ln7kF3De0N1NuO0OhIVKPBbbHYWYJwFjgXCAPmGVmU9x9UbnVVgFnufs2MxsKjANOraLtGOBjd38sGihjgHuD6ocEo6gkwp/nrON3n65g1eY9nN2rLY8OP5HOac3DLk1EqhDkoapBQK67rwQws4nAcOBgcLj79HLrzwAyqtF2OHB2dL0JwCcoOBqMwuJS3py1lt9/uoL1Owo5oWMLXvjRyZx/QntdlyHSQAQZHJ2AteWm84BTD7P+KOC9arRt7+4bANx9g5m1q2xjZnYTcBNAly76Mp+w7Sos5tUZa3jpnyvZvLuIrK6t+Y9LTuLs49oqMEQamCCDo7J3A690RbMhlAXHt2ra9lDcfRxlh77IysqqUVupHZGIM2ftdt5bsIFJ2WvZWVjCmT3bcNuQHgzqlqbAEGmgggyOPKBzuekMYH3FlcysL/AiMNTdt1Sjbb6ZdYjubXQANtV65XLESiPOzFVbeX/hBj7IyWfjzkISE4xv927PLWd3p58GvUUavCCDYxbQ08y6AeuAy4Ery69gZl2AycBV7r6smm2nANcAj0V/vhtgH6QaiksjfL5iC+8t3MjUnI1s2VNEk8aNOOu4ttx7Ui/O6d2els0Swy5TRGpJYMHh7iVmdhvwAZAAjHf3HDMbHV3+AvAgkA48Hz1sUeLuWYdqG930Y8AkMxsFrAEuC6oP8k2lEWfHvmK27tnPyoI9fJCTz0eL89mxr5jkpASG9G7H0BM7cHavtiTrzrUiMcncY//wf1ZWlmdnZ4ddRr3j7uwpKmXbniK2lnts23vo6e37iin/J9OiaWO+06c9Q0/swJk92+gb+ERiiJnNdvesivP1kTCGFJVE2L63iC17isrCoNwbftl02Z7C1j3FB5cXlUQq3VbjRkbr5CTSmieRlpxE72Na0Do5kbTkJqQ1T6R1chLHtGjKgC6tSWoc6HWkIlLPKDjqqUjE2VlYfPAT/5bdBz75F1eY/lcw7NpfcsjttWyWSFpyEq2bJ9KpVVNO6tTia8GQlpz0r+mUJFKbNNZZTyJSKQXHYTz78XKmzPvGiWDVcqSHAN1hZ2Ex2/YWUxqpfBtNGjciPbnsDb518yS6pjendfMk0g+8+Zd7tG6eRKvmiSQmaK9ARGqHguMw2qU2odfRfJ/1EXxgN6BFs0TSmpeFQHq5PYHWyYmkJzfR3WJFJFQKjsO4fFAXLh+kq85FRMrT8QsREakRBYeIiNSIgkNERGpEwSEiIjWi4BARkRpRcIiISI0oOEREpEYUHCIiUiNxcXdcMysAvjrC5m2AzbVYTn2j/jVs6l/DV5/72NXd21acGRfBcTTMLLuy2wrHCvWvYVP/Gr6G2EcdqhIRkRpRcIiISI0oOKo2LuwCAqb+NWzqX8PX4PqoMQ4REakR7XGIiEiNKDhERKRG4io4zOwCM1tqZrlmNqaS5WZmz0aXzzezgVW1NbM0M/vQzJZHf7auq/5UFFD/njSzJdH13zGzVnXVn8oE0cdyy39mZm5mbYLux6EE1T8zuz26LMfMnqiLvlQmoL/R/mY2w8zmmlm2mQ2qq/5UdJT9G29mm8xsYYU29eY95iB3j4sHkACsAI4FkoB5QJ8K63wXeI+yb3AdDHxRVVvgCWBM9PkY4PEY6995QOPo88fD6l+QfYwu7wx8QNmFom1iqX/AEOAjoEl0ul2M9W8qMLRc+08aWv+iy/4NGAgsrNCmXrzHlH/E0x7HICDX3Ve6exEwERheYZ3hwB+9zAyglZl1qKLtcGBC9PkE4HtBd+QQAumfu09195Jo+xlARl105hCCeg0Bngb+HQjzbJGg+ncL8Ji77wdw90110ZlKBNU/B1pEn7cE1gfdkUM4mv7h7p8BWyvZbn15jzkonoKjE7C23HRedF511jlc2/buvgEg+rNdLdZcE0H1r7zrKfu0FJZA+mhmw4B17j6vtguuoaBew+OAM83sCzP71MxOqdWqqy+o/v0EeNLM1gK/Ae6rxZpr4mj6dzj15T3moHgKDqtkXsVPl4dapzptwxZo/8zsfqAEeO2Iqqsdtd5HM2sO3A88eJS11YagXsPGQGvKDo3cA0wys8rWD1pQ/bsFuMvdOwN3AS8dcYVH52j616DEU3DkUXYc+4AMvrlLe6h1Dtc2/8CuZvRnWIcBguofZnYNcBEw0qMHWkMSRB+7A92AeWa2Ojr/SzM7plYrr56gXsM8YHL08MhMIELZjfXqWlD9uwaYHH3+FmWHjMJwNP07nPryHvMvYQ+y1NWDsk9dKyl7kzgwcHVChXUu5OsDVzOrags8ydcHrp6Isf5dACwC2sbqa1ih/WrCGxwP6jUcDfwy+vw4yg6VWAz1bzFwdvT5t4HZDe31K7c8k28OjteL95iv1RR2AXX8wn4XWEbZmQ/3R+eNBkZHnxswNrp8AZB1uLbR+enAx8Dy6M+0GOtfbvSNZm708UKsvYYVtr+akIIjwNcwCXgVWAh8CZwTY/37FjCbsjfqL4CTG2j/3gA2AMWU7ZmMis6vN+8xBx665YiIiNRIPI1xiIhILVBwiIhIjSg4RESkRhQcIiJSIwoOERGpEQWHSMDM7Bgzm2hmK8xskZn9zcyOO8z6P4le0S5SLyk4RAIUvbXHO5TdsbW7u/cBfg60P0yznwAKDqm3FBwiwRoCFLv7CwdmuPtcIMHM/npgnpk9Z2bXmtkdQEdgmplNq/tyRaqm4BAJ1omUXdVcLe7+LGX3Lhri7kMCq0rkKCg4RESkRhQcIsHKAU6uZH4JX///17RuyhE5egoOkWD9HWhiZjcemBH9IqUEoI+ZNTGzlpTd1fWAXUBq3ZYpUn0KDpEAedldREcA50ZPx80BHqZsHGMSMJ+yL8eaU67ZOOA9DY5LfaW744qISI1oj0NERGpEwSEiIjWi4BARkRpRcIiISI0oOEREpEYUHCIiUiMKDhERqZH/B4vlaJlcY2AMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 50%|█████     | 5/10 [00:38<00:39,  7.96s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22590213826864067 0.01014724488928914\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 60%|██████    | 6/10 [00:45<00:30,  7.63s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22732045910141488 0.010204158745706082\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 70%|███████   | 7/10 [00:52<00:21,  7.31s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22733701047578334 0.011642923432402313\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 80%|████████  | 8/10 [00:59<00:14,  7.24s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22857837663844033 0.013628254866227507\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      " 90%|█████████ | 9/10 [01:07<00:07,  7.49s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.229045706497467 0.014346392717212438\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10/10 [01:16<00:00,  7.68s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22929202679699653 0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "x,y = [],[]\n",
    "threshes = []\n",
    "class_preds = train_x<cut  # Start from our initial threshold\n",
    "for z in tqdm(range(train_y.shape[1])):\n",
    "    class_preds[:,z] = 0\n",
    "    x.append([0])\n",
    "    y.append([binary_iou(class_preds, train_y)])\n",
    "    for p in range(0,225):\n",
    "        x[-1].append(np.percentile(train_x[:,z], p/10))\n",
    "        class_preds[:,z] = train_x[:,z]<=x[-1][-1]  # Only change predictions in the current z layer\n",
    "        y[-1].append(binary_iou(class_preds, train_y))\n",
    "\n",
    "    plt.plot(x[-1],y[-1], label=f'layer {z}')\n",
    "    plt.ylabel('IOU')\n",
    "    plt.xlabel('Cut')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    threshes.append(x[-1][np.argmax(y[-1])])\n",
    "    print(np.max(y[-1]), threshes[-1])\n",
    "    class_preds[:,z] = train_x[:,z]<=threshes[-1]  # Update our predicitons to use the optimal cut for each layer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e511f51d",
   "metadata": {},
   "source": [
    "We can that the thresholds reflect the X0 depth bias, with lower values being found in the central layers. However there is also something interesting going on with the IOU in some of the layers, and the the threshold for the shallowest layer is zero. Why do you think that is? Maybe taking a look at the data can help."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7b64db53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.016869102077558637,\n",
       " 0.016267780676484107,\n",
       " 0.01264219737611711,\n",
       " 0.011047122783958911,\n",
       " 0.01014724488928914,\n",
       " 0.010204158745706082,\n",
       " 0.011642923432402313,\n",
       " 0.013628254866227507,\n",
       " 0.014346392717212438,\n",
       " 0]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threshes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34b76362",
   "metadata": {},
   "source": [
    "Applying the thresholds is a bit more complicated now, but results in a slightly better IOU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f25a386a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class_preds = np.zeros_like(train_x)\n",
    "for i,t in enumerate(threshes):\n",
    "    class_preds[:,i] = train_x[:,i] <= t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c59ef6cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22929202679699653"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_iou(class_preds, train_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4e8482ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3218390804597701\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x1024 with 22 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 1\n",
    "pred, targ = class_preds[idx], train_y[idx]\n",
    "print(binary_iou(pred[None], targ[None]))\n",
    "plot_x0_targ(pred, targ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d1e6c16",
   "metadata": {},
   "source": [
    "## Validation\n",
    "\n",
    "Given that we optimised the thresholds on the same data we have applied them, we need to get an accurate estimate of our generalised performance to unseen data. For this we can use the validation dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "3c731138",
   "metadata": {},
   "outputs": [],
   "source": [
    "class_preds = np.zeros_like(valid_x)\n",
    "for i,t in enumerate(threshes):\n",
    "    class_preds[:,i] = valid_x[:,i] <= t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "2286d6d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2243626128609209"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_iou(class_preds, valid_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13a37c1f",
   "metadata": {},
   "source": [
    "So a slight drop in IOU, but nothing drastic. Seems we haven't overfitted to the training data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12dcadae",
   "metadata": {},
   "source": [
    "## Submission prep\n",
    "\n",
    "Let's say we are happy with our solution and we want to submit predictions for the test data. We first need to load the data, score it, and then save our predictions to a new file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "60566983",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-34-188d474f73f5>:1: H5pyDeprecationWarning: The default file mode will change to 'r' (read-only) in h5py 3.0. To suppress this warning, pass the mode you need to h5py.File(), or set the global default h5.get_config().default_file_mode, or set the environment variable H5PY_DEFAULT_READONLY=1. Available modes are: 'r', 'r+', 'w', 'w-'/'x', 'a'. See the docs for details.\n",
      "  with h5py.File(DATA/'test.h5') as h5:\n"
     ]
    }
   ],
   "source": [
    "with h5py.File(DATA/'test.h5', 'r') as h5:\n",
    "    test_x = h5['x0'][()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "e369c968",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30036"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(test_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28b52549",
   "metadata": {},
   "source": [
    "We compute our predictions just like we did on the validation data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9f8b71fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "class_preds = np.zeros_like(test_x)\n",
    "for i,t in enumerate(threshes):\n",
    "    class_preds[:,i] = test_x[:,i] <= t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f688fd9",
   "metadata": {},
   "source": [
    "To submit predictions, please save them to a HDF5 file using the function below. The file name should use the format `[your_full_name]_test_preds.h5`. Ypu can also include an option ID number in case you submit multiple times. Your final score, and score for the Friday announcements, will be computed on your submission with the highest ID number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "68ad2036",
   "metadata": {},
   "outputs": [],
   "source": [
    "FULL_NAME_AND_ID = 'MY_FULL_NAME_ID00'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "6408cf91",
   "metadata": {},
   "outputs": [],
   "source": [
    "with h5py.File(f'{FULL_NAME_AND_ID}_test_preds.h5', 'w') as h5:\n",
    "    h5.create_dataset(\"preds\", data=class_preds.astype(\"int\"), dtype=\"int\", compression='lzf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecafd098",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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