Neural Network 1T.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import csv\n",
    "import os\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nteams = 20\n",
    "nmatches = (nteams-1)*2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data Pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def season_team_map(season_dir):\n",
    "    readme = season_dir + '/README.md'\n",
    "    f = open(readme, 'r')\n",
    "    \n",
    "    s = \"  \"\n",
    "    \n",
    "    # skip to teams\n",
    "    while(s[1] != '1'):\n",
    "        s = f.readline()\n",
    "        if(len(s)<=1):\n",
    "            s = \"  \"\n",
    "\n",
    "    team_map = {}\n",
    "\n",
    "    for i in range(20):\n",
    "        team_map[s[4:].split('  ')[0]] = i\n",
    "        s = f.readline()\n",
    "\n",
    "    f.close()\n",
    "    \n",
    "    return team_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def season_game_mat(season_dir, team_map):\n",
    "    game_mat = np.zeros((nteams, nmatches), dtype=int)\n",
    "    team_index = np.zeros(nteams, dtype=int)\n",
    "\n",
    "    csvfile = ''\n",
    "    \n",
    "    for entry in os.scandir(season_dir):\n",
    "        if '/1-' in entry.path:\n",
    "            csvfile = entry.path\n",
    "            \n",
    "    with open(csvfile) as gf:\n",
    "        reader = csv.reader(gf)\n",
    "        next(reader)\n",
    "        for row in reader:\n",
    "            team1 = team_map[row[1]]\n",
    "            team2 = team_map[row[2]]\n",
    "\n",
    "            score = row[3].split('-')\n",
    "\n",
    "            # 1 for win, 0 for draw, -1 for loss\n",
    "\n",
    "            if(int(score[0]) > int(score[1])):\n",
    "                game_mat[team1, team_index[team1]] = 1\n",
    "                game_mat[team2, team_index[team2]] = -1\n",
    "            elif(int(score[0]) < int(score[1])):\n",
    "                game_mat[team1, team_index[team1]] = -1\n",
    "                game_mat[team2, team_index[team2]] = 1\n",
    "\n",
    "            team_index[team1] += 1\n",
    "            team_index[team2] += 1\n",
    "    \n",
    "    return game_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "country_dirs = []\n",
    "season_dirs = []\n",
    "\n",
    "nseasons = 0\n",
    "team_maps = []\n",
    "game_mats = []\n",
    "\n",
    "for entry in os.scandir('./data'):\n",
    "    if entry.is_dir():\n",
    "        country_dirs.append(entry.path)\n",
    "\n",
    "for cdir in country_dirs:\n",
    "    for entry in os.scandir(cdir):\n",
    "        if entry.is_dir():\n",
    "            season_dir = entry.path\n",
    "            team_maps.append(season_team_map(season_dir))\n",
    "            game_mats.append(season_game_mat(season_dir, team_maps[nseasons]))\n",
    "            nseasons += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eucl_error(outputs, targets):\n",
    "    return np.mean(np.abs(targets - outputs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def disc_error(outputs, targets):\n",
    "    rounded_outputs = np.round(outputs)\n",
    "    err = 0\n",
    "    n = 0\n",
    "    for i in range(len(outputs)):\n",
    "        if(int(rounded_outputs[i]) != int(targets[i])):\n",
    "            err += 1\n",
    "        n += 1\n",
    "    return float(err)/n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ntraining = 45\n",
    "ntesting = nseasons - ntraining\n",
    "\n",
    "training_game_mats = np.reshape(game_mats[:ntraining], (-1, nmatches))\n",
    "testing_game_mats = np.reshape(game_mats[ntraining:], (-1, nmatches))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_trainings = []\n",
    "Y_trainings = []\n",
    "for i in range(1, nmatches):\n",
    "    X_training = []\n",
    "    Y_training = []\n",
    "    for seq in training_game_mats:\n",
    "        for j in range(nmatches-i):\n",
    "            X_training.append(seq[j:j+i])\n",
    "            Y_training.append(seq[j+i])\n",
    "    \n",
    "    X_trainings.append(X_training)\n",
    "    Y_trainings.append(Y_training)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_testings = []\n",
    "Y_testings = []\n",
    "for i in range(1, nmatches):\n",
    "    X_testing = []\n",
    "    Y_testing = []\n",
    "    for seq in testing_game_mats:\n",
    "        for j in range(nmatches-i):\n",
    "            X_testing.append(seq[j:j+i])\n",
    "            Y_testing.append(seq[j+i])\n",
    "            \n",
    "    X_testings.append(X_testing)\n",
    "    Y_testings.append(Y_testing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "layer_sizes = [30, 50, 100, 200]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nns = {}\n",
    "for size in layer_sizes:\n",
    "    key = str(size)+'_neuron_layers'\n",
    "    nns[key] = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Expected 2D array, got 1D array instead:\narray=[ array([-1,  1,  1,  1,  1,  1,  0,  0,  1,  1,  1, -1,  1,  1,  0,  0,  0,\n       -1, -1,  1,  1, -1,  0,  1,  1,  1,  1,  1,  1,  0,  1,  1,  1,  1,\n       -1,  1,  1])\n array([ 1,  1,  1,  1, -1,  1,  1,  1,  1,  1,  0,  1,  1,  0,  1,  0, -1,\n        1,  1, -1,  1,  1,  1,  1,  1, -1,  0, -1,  1, -1, -1,  1, -1,  1,\n        1,  1,  0])\n array([ 1, -1,  1,  1, -1,  1,  1,  0,  0,  1,  1, -1, -1,  0, -1,  0,  1,\n        1,  1,  0,  1,  0,  1,  1,  0,  1,  1,  1,  0,  1, -1,  1, -1,  1,\n        0,  1,  0])\n ...,\n array([-1, -1, -1,  0, -1,  1,  0, -1,  0, -1, -1,  1, -1, -1, -1,  0, -1,\n        1, -1, -1,  0,  0,  0,  1, -1, -1,  0, -1, -1, -1, -1, -1, -1,  1,\n       -1,  1,  1])\n array([-1,  0,  0, -1,  0, -1, -1, -1,  1,  1,  0, -1,  0,  0, -1, -1,  1,\n       -1,  0,  0,  0, -1,  1, -1, -1,  0,  0, -1,  1, -1, -1,  0,  0, -1,\n       -1,  0, -1])\n array([-1,  1,  1,  0,  0, -1, -1, -1, -1,  0,  1, -1, -1, -1,  0, -1, -1,\n       -1, -1, -1,  1,  0, -1,  1, -1,  0, -1,  1, -1, -1,  0, -1, -1, -1,\n       -1, -1, -1])].\nReshape your data either using array.reshape(-1, 1) if your data has a single feature or array.reshape(1, -1) if it contains a single sample.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-19-4f574b0ea725>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m         \u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;34m'_neuron_layers'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m         \u001b[0mnn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mMLPRegressor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhidden_layer_sizes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolver\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'lbfgs'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m         \u001b[0mnn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_trainings\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY_trainings\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m         \u001b[0mnns\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/multilayer_perceptron.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, X, y)\u001b[0m\n\u001b[1;32m    618\u001b[0m         \u001b[0mself\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0mreturns\u001b[0m \u001b[0ma\u001b[0m \u001b[0mtrained\u001b[0m \u001b[0mMLP\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    619\u001b[0m         \"\"\"\n\u001b[0;32m--> 620\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_fit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mincremental\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    621\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    622\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mproperty\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/multilayer_perceptron.py\u001b[0m in \u001b[0;36m_fit\u001b[0;34m(self, X, y, incremental)\u001b[0m\n\u001b[1;32m    329\u001b[0m                              hidden_layer_sizes)\n\u001b[1;32m    330\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 331\u001b[0;31m         \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_validate_input\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mincremental\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    332\u001b[0m         \u001b[0mn_samples\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_features\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    333\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/sklearn/neural_network/multilayer_perceptron.py\u001b[0m in \u001b[0;36m_validate_input\u001b[0;34m(self, X, y, incremental)\u001b[0m\n\u001b[1;32m   1302\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_validate_input\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mincremental\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1303\u001b[0m         X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'],\n\u001b[0;32m-> 1304\u001b[0;31m                          multi_output=True, y_numeric=True)\n\u001b[0m\u001b[1;32m   1305\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1306\u001b[0m             \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcolumn_or_1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwarn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_X_y\u001b[0;34m(X, y, accept_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, multi_output, ensure_min_samples, ensure_min_features, y_numeric, warn_on_dtype, estimator)\u001b[0m\n\u001b[1;32m    571\u001b[0m     X = check_array(X, accept_sparse, dtype, order, copy, force_all_finite,\n\u001b[1;32m    572\u001b[0m                     \u001b[0mensure_2d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mallow_nd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mensure_min_samples\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 573\u001b[0;31m                     ensure_min_features, warn_on_dtype, estimator)\n\u001b[0m\u001b[1;32m    574\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mmulti_output\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    575\u001b[0m         y = check_array(y, 'csr', force_all_finite=True, ensure_2d=False,\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/sklearn/utils/validation.py\u001b[0m in \u001b[0;36mcheck_array\u001b[0;34m(array, accept_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, warn_on_dtype, estimator)\u001b[0m\n\u001b[1;32m    439\u001b[0m                     \u001b[0;34m\"Reshape your data either using array.reshape(-1, 1) if \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    440\u001b[0m                     \u001b[0;34m\"your data has a single feature or array.reshape(1, -1) \"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 441\u001b[0;31m                     \"if it contains a single sample.\".format(array))\n\u001b[0m\u001b[1;32m    442\u001b[0m             \u001b[0marray\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0matleast_2d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    443\u001b[0m             \u001b[0;31m# To ensure that array flags are maintained\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: Expected 2D array, got 1D array instead:\narray=[ array([-1,  1,  1,  1,  1,  1,  0,  0,  1,  1,  1, -1,  1,  1,  0,  0,  0,\n       -1, -1,  1,  1, -1,  0,  1,  1,  1,  1,  1,  1,  0,  1,  1,  1,  1,\n       -1,  1,  1])\n array([ 1,  1,  1,  1, -1,  1,  1,  1,  1,  1,  0,  1,  1,  0,  1,  0, -1,\n        1,  1, -1,  1,  1,  1,  1,  1, -1,  0, -1,  1, -1, -1,  1, -1,  1,\n        1,  1,  0])\n array([ 1, -1,  1,  1, -1,  1,  1,  0,  0,  1,  1, -1, -1,  0, -1,  0,  1,\n        1,  1,  0,  1,  0,  1,  1,  0,  1,  1,  1,  0,  1, -1,  1, -1,  1,\n        0,  1,  0])\n ...,\n array([-1, -1, -1,  0, -1,  1,  0, -1,  0, -1, -1,  1, -1, -1, -1,  0, -1,\n        1, -1, -1,  0,  0,  0,  1, -1, -1,  0, -1, -1, -1, -1, -1, -1,  1,\n       -1,  1,  1])\n array([-1,  0,  0, -1,  0, -1, -1, -1,  1,  1,  0, -1,  0,  0, -1, -1,  1,\n       -1,  0,  0,  0, -1,  1, -1, -1,  0,  0, -1,  1, -1, -1,  0,  0, -1,\n       -1,  0, -1])\n array([-1,  1,  1,  0,  0, -1, -1, -1, -1,  0,  1, -1, -1, -1,  0, -1, -1,\n       -1, -1, -1,  1,  0, -1,  1, -1,  0, -1,  1, -1, -1,  0, -1, -1, -1,\n       -1, -1, -1])].\nReshape your data either using array.reshape(-1, 1) if your data has a single feature or array.reshape(1, -1) if it contains a single sample."
     ]
    }
   ],
   "source": [
    "for i in range(nmatches-1):\n",
    "    for size in layer_sizes:\n",
    "        key = str(size)+'_neuron_layers'       \n",
    "        nn = MLPRegressor(hidden_layer_sizes=(size,2), solver='lbfgs')\n",
    "        nn.fit(X_trainings[i], Y_trainings[i])\n",
    "        nns[key].append(nn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nns['100_neuron_layers'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def score(key):\n",
    "    training_accs = []\n",
    "    training_errs = []\n",
    "\n",
    "    with open('nn_1t_training_scores_' + key + '.csv', 'w') as f:\n",
    "        writer = csv.writer(f)\n",
    "        writer.writerow(['Games before prediction', 'Accuracy', 'Euclidean Error'])\n",
    "        print(\"training\")\n",
    "        for i in range(nmatches-2):\n",
    "            print(i)\n",
    "            outputs = nns[key][i].predict(X_trainings[i])\n",
    "            acc = 1 - disc_error(outputs, np.array(Y_trainings[i]))\n",
    "            eerr = eucl_error(outputs, np.array(Y_trainings[i]))\n",
    "\n",
    "            writer.writerow([i, acc, eerr])\n",
    "            training_accs.append(acc)\n",
    "            training_errs.append(eerr)\n",
    "            \n",
    "    testing_accs = []\n",
    "    testing_errs = []\n",
    "\n",
    "    with open('nn_1t_testing_scores_' + key + '.csv', 'w') as f:\n",
    "        writer = csv.writer(f)\n",
    "        writer.writerow(['Games before prediction', 'Accuracy', 'Euclidean Error'])\n",
    "        print(\"testing\")\n",
    "        for i in range(nmatches-2):\n",
    "            print(i)\n",
    "            outputs = nns[key][i].predict(X_testings[i])\n",
    "            acc = 1 - disc_error(outputs, np.array(Y_testings[i]))\n",
    "            eerr = eucl_error(outputs, np.array(Y_testings[i]))\n",
    "\n",
    "            writer.writerow([i, acc, eerr])\n",
    "            testing_accs.append(acc)\n",
    "            testing_errs.append(eerr)\n",
    "    \n",
    "    training_accs_dict[key] = training_accs\n",
    "    training_errs_dict[key] = training_errs\n",
    "    testing_accs_dict[key] = testing_accs\n",
    "    testing_errs_dict[key] = testing_errs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "training_accs_dict = {}\n",
    "training_errs_dict = {}\n",
    "testing_accs_dict = {}\n",
    "testing_errs_dict = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "for size in layer_sizes:\n",
    "    print(size)\n",
    "    key = str(size)+'_neuron_layers'\n",
    "    score(key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot(y, ylabel, title, imname):\n",
    "    x = range(1,nmatches-1)\n",
    "    yfit = np.poly1d(np.polyfit(x, y, 1))(np.unique(x))\n",
    "    r2 = np.round(r2_score(y, yfit),decimals=2)\n",
    "    mean = np.round(np.mean(y), decimals=2)\n",
    "\n",
    "    plt.scatter(x, y, s = 5)\n",
    "    plt.plot(x, yfit)\n",
    "    plt.axis([0,nmatches,0,1])\n",
    "    plt.text(1, 0.95, 'R^2: ' + str(r2))\n",
    "    plt.text(1, 0.85, 'Mean: ' + str(mean))\n",
    "    plt.xlabel('Games before prediction')\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.title(title)\n",
    "    plt.savefig('nn1tplots/' + imname + '.png')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7jOke5E/NUH2j5iORo0B2Tg7jKmYwrmJGwuWJaxlVKdcy8sumUzJhBmUVs/tc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\nRElBREQiSgoiIhL5/wFIFqJbNusrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a15afe9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UzMwsy0nBzMyynBTMzCyraFKQ1EPSRysVjJmZVVfRpBARzcC5FYrFzMyqrJTq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\ny0nBykbS1pL+T9KL6VAfD0s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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a15d985c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eZl07j+zdg9LiBB+fMIgRRU0H/iH9epKbZY282SCZ3kdVwK8Jxj/qD3wK+DrQ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\nUVIQEZGIkoKIiESUFEREJPL/AV2i12JkLinRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a14df8128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yoLY6VbLrKsG1jc388k8vM3/JKrYf2p/j6kfQFOsqtsambFszn17IouVr2GpQ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\nMzPLOSmYmVnOScHMzHL/H/zyVN68yvzFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2121e7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yYA9wF1DbNN/dtx9sJQ+EgoL0dI2Nzvq3a4OHF0XJAaupCRMD5mSFiQGb7noq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\n2xcR6ckaG523a+sYXtAfs9a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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a211c4160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yjBEDy9oMsjY87K7Z0efiFrNcds0sFsV8oJDcKua/zW6VFHJVXZDNP+euVJG4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a22299be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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770l8WCKSij4qi+0hVMyWsoMA9OnWngvOOCV8ytiRHkI79hzirtkrqahylm0o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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2268df28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GAg+TjJ8PySBnlxY5DjOAn6fvjwSeyW1zFrBNOn0ucEn6vhcwE9gb\n+CTJ6KCVwG7psTs5t+5akqdlFwF7p/N3KNyvIvs5B/hQ+v6y3HGfAfwwfT8B+L+u/q751bEvNx9Z\np5B0HfBBkquHQ0gq4WuV/MpUI7BfrvjjkQ6jIOlF4P50/tPAh9P3RwP7Jy01AGyXXhX8BfiRpF+S\n/NDK4iLhLIqIv6Tv/4skgf0eGAU8kK6zkmRE0EIfBH4TEevS+H4NHEEyntHCiHg0LTcO2B/4S7q+\nGuCvrRyeKZD8XoSk7ZSOjwNMj4h30vcfA0Y39xcA/UmS6ZHAlIhoBF5VMmRCoXHAwxHxcrqdNofU\nkNQfGBARf0xn3QrcmSvSPLDfLJJkaD2Ik4KVy7PAPzRPRMTnJQ0kOcMF+DLJ+EUHkjRjrs99Nj9O\nTVNuuomN39kK4PBcpdnsyrQZZQLwqKSjI+LvBWUKx3YJknFnno2Iw9vZr2JDuDdbV1DugYg4tZ31\ntRZPsfV9ISLuaxFM0rzV3lg1KqHM5mj+ezTiOqTHcZ+ClcsfgN6Szs/N2zb3vj+wNJLO2DNIzsw3\nx/3Ahc0T6RUHkvaJiKcj4nskCWhEkc/uIam58j+V5GcRnwcGNc+XVC1pZJHPPgycKGlbJaPfnkQy\niFyhR4EPSBqWrm9bSfsVKQdJU1XzgHSrI2J1kTL3AecrGdoaSful238YmJT2OezKxiupvL8CH5K0\nd/rZHdL5a4BN+lzS7b+Z6y84A/hjYTnrmZwUrCwiIkju2vmQkh8lf4ykGaL5B0SuB86S9ChJ09G6\n4mtq1UVAbdoROpek0xTgS2mH7VPAO8Dvinz2uXTbc0hG0vxpJD/xejLwvfSzs4H3F34wkp+rvAV4\njGS00xsj4ski5ZaR/BbzlHQ7j1I8QUFSAT8C/Az4bCtlbgTmAk8ouaX2P0nO0n8DzCNpWvspRSrv\nNJZzgV+n+3ZHuuh/gJOaO5oLPnYW8P009jEk/Qr2HuBRUs26kKQZJJ27M9sra9YZfKVgZmYZXymY\nmVnGVwpmZpZxUjAzs4yTgpmZZZwUzMws46RgZmaZ/w/ZRBCmmhBL+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a226e4160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Om+1CYVdLmVhQZ/eRiLynqhc0UX3qZN1HpiZb9hb7z6z+eMs+SsuVDm0TmDDQ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\nFpgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a23350438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HB+HXlq6j0eHV99ZxxI+eY9UnW5okcRvctxebw4BQYPCbM8czfkR/BpTsqLu7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\nmfUAJgMzksrMAM4OX58OPOf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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a23287198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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T0p9vZky6dlTcMQWNOzSNRLqPjol63BY4HZgPKCmIZIFYBehGD+rOax+uocrh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\nowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2472c3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ld89pU+E2twaN6eMVjS20QpsKN9luaxZXS8Aj899m9IX3dvu+7V9bQ12t6JdW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\neQfLNwQGpo93AWakjw8FlgB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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a232772b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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B9gtkxnwskknhZuA48B+grHa+qu5vaZDNYUmhfdt16ARLivwU+EpYte0gALn9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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1bccceb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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INgoK7cDOtos3t6N0S2198g1caTJ0fvTZJn72zAdBhs6SGJ/fuyzy+MUgX09x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\ngoKCiIgkKCiIiEiCgoKIiCT8f3gsYNpm20cxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a24166898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7pBxOPTx+KcvGuJdB0ksiN6+tI7gbWUQy0L6WstyfexkkfSVyn0J74FvACCDy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\nZAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a23287cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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brGvWtbKmpZUzp9/P/GeXM2bbLTjnI3uwLqJQQbatZEuVZV655i3dshZweaXb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\nIJNtNAkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a23176978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for size in layer_sizes:\n",
    "    key = str(size)+'_neuron_layers'\n",
    "    title = ' ' + str(size) + ' Neuron Layers'\n",
    "    plot(training_errs_dict[key], 'Euclidian Error', 'NN 1T Training Euclidean Error' + title, 'nn_training_error_plot_'+key)\n",
    "    plot(testing_errs_dict[key], 'Euclidian Error', 'NN 1T Testing Euclidean Error' + title, 'nn_testing_error_plot_'+key)\n",
    "    plot(training_accs_dict[key], 'Accuracy', 'NN 1T Training Accuracy' + title, 'nn_training_accuracy_plot_'+key)\n",
    "    plot(testing_accs_dict[key], 'Accuracy', 'NN 1T Testing Accuracy' + title, 'nn_testing_accuracy_plot_'+key)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6.00600601e-05,   6.00600601e-05,   6.00600601e-05, ...,\n",
       "         6.00600601e-05,   6.00600601e-05,   6.00600601e-05])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nns['100_neuron_layers'][0].predict(X_trainings[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}