Make BALSE great again.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from mangaki.utils.common import RecommendationAlgorithm\n",
    "from mangaki.utils.data import Dataset\n",
    "from mangaki.utils.recommendations import rating_values\n",
    "from mangaki.utils.als import MangakiALS\n",
    "from scipy.sparse import coo_matrix, load_npz\n",
    "from sklearn.model_selection import ShuffleSplit, GroupShuffleSplit\n",
    "from numpy.linalg import cond\n",
    "from collections import defaultdict\n",
    "from sklearn.linear_model import ElasticNet, Ridge, Lasso, LinearRegression, HuberRegressor\n",
    "from sklearn.metrics import jaccard_similarity_score\n",
    "from sklearn.metrics.pairwise import pairwise_distances\n",
    "from sklearn.preprocessing import binarize\n",
    "import scipy.sparse as sp\n",
    "from numpy.matlib import repmat\n",
    "from scipy.sparse.linalg import spsolve\n",
    "from scipy.sparse import kron\n",
    "from scipy.spatial.distance import cdist\n",
    "import numpy as np\n",
    "import logging\n",
    "import gc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "REG_THRESHOLD = 0\n",
    "\n",
    "\n",
    "def relu(x):\n",
    "    return max(-2, min(2, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class MangakiBALSE(RecommendationAlgorithm):\n",
    "    M = None\n",
    "    U = None\n",
    "    VT = None\n",
    "\n",
    "    def __init__(self, NB_COMPONENTS=10, NB_ITERATIONS=10, LAMBDA=0.1, a=0.05, b=0.2):\n",
    "        super().__init__()\n",
    "        self.NB_COMPONENTS = NB_COMPONENTS\n",
    "        self.NB_ITERATIONS = NB_ITERATIONS\n",
    "        self.LAMBDA = LAMBDA\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "\n",
    "    @staticmethod\n",
    "    def load_tags(T=None):\n",
    "        # From file\n",
    "        if T is None:\n",
    "            T = load_npz('../code/data/balse/weighted_tags.npz').toarray()\n",
    "        _, nb_tags = T.shape\n",
    "        \n",
    "        return T, nb_tags\n",
    "\n",
    "    def create_appropriate_model(self, n_samples):\n",
    "        if n_samples <= 3:\n",
    "            return LinearRegression(), False\n",
    "        else:\n",
    "            alpha = self.a + self.b\n",
    "            l1_ratio = self.a / alpha\n",
    "            return ElasticNet(alpha=alpha, positive=True, l1_ratio=l1_ratio), False\n",
    "            # return LassoLars(alpha=0.05)\n",
    "    \n",
    "    @staticmethod\n",
    "    def make_link_matrix(T):\n",
    "        # return pairwise_jaccard_sparse(binarize(T), 0.6)\n",
    "        return pairwise_distances(sp.csr_matrix(binarize(T)), metric='l2', n_jobs=-2)\n",
    "    \n",
    "    def fit_als(self, X, y):\n",
    "        self.als = MangakiALS(self.NB_COMPONENTS, self.NB_ITERATIONS, self.LAMBDA)\n",
    "        self.als.set_parameters(self.nb_users, self.nb_works)\n",
    "        self.als.fit(X, y)\n",
    "        return self.als.predict(X)\n",
    "    \n",
    "    def warm_start_als(self, als, X):\n",
    "        self.als = als\n",
    "        return self.als.predict(X)\n",
    "\n",
    "    def fit(self, X, y, warm_start = None):\n",
    "        self.T, self.nb_tags = self.load_tags()\n",
    "        print('Cond number for T: {:f}'.format(cond(self.T)))\n",
    "        print(self.T.shape)\n",
    "        \n",
    "        if warm_start is None:\n",
    "            y_pred = self.fit_als(X, y)\n",
    "        else:\n",
    "            y_pred = self.warm_start_als(warm_start, X)\n",
    "        \n",
    "        row = X[:, 0]\n",
    "        col = X[:, 1]\n",
    "        data = y - y_pred\n",
    "        \n",
    "        M_res = coo_matrix((data, (row, col)), shape=(self.nb_users, self.nb_works))\n",
    "        print(M_res)\n",
    "        M_res = M_res.tocsr()\n",
    "        \n",
    "        self.encountered_works = X[:, 1]\n",
    "        self.reg = {}\n",
    "        user_ids = sorted(set(row))\n",
    "        self.r2_scores = [0] * len(user_ids)\n",
    "        self.cond_numbers = [0] * len(user_ids)\n",
    "        \n",
    "        for index, user_id in enumerate(user_ids):\n",
    "            indices = M_res[user_id].indices\n",
    "            values = M_res[user_id].data\n",
    "            n_samples = len(indices)\n",
    "            \n",
    "            self.cond_numbers[index] = cond(self.T[indices])\n",
    "            \n",
    "            if user_id not in self.reg:\n",
    "                self.reg[user_id], is_local = self.create_appropriate_model(n_samples)\n",
    "\n",
    "            self.reg[user_id].fit(self.T[indices], values)\n",
    "\n",
    "            score = self.reg[user_id].score(self.T[indices], values)\n",
    "            self.r2_scores[index] = score\n",
    "            if score < REG_THRESHOLD:  # Ignore dangerous regressions.\n",
    "                del self.reg[user_id]\n",
    "\n",
    "            if user_id % 100 == 0:\n",
    "                print(user_id)\n",
    "\n",
    "    def predict(self, X):\n",
    "        # return self.M[X[:, 0].astype(np.int64), X[:, 1].astype(np.int64)] + self.means[X[:, 0].astype(np.int64)]\n",
    "        y_pred = self.als.predict(X)\n",
    "        y_delta_res = []\n",
    "        # R = self.make_link_matrix(X)\n",
    "        mean_error_reconstruction = np.mean(\n",
    "            [self.reg[user_id].predict(self.T[work_id].reshape(1, -1))\n",
    "            for user_id, work_id in X if user_id in self.reg]\n",
    "        )\n",
    "        for user_id, work_id in X:\n",
    "            if user_id not in self.reg:\n",
    "                print(user_id, 'not')\n",
    "                y_delta_res.append(mean_error_reconstruction)\n",
    "            else:\n",
    "                prediction = np.mean(self.reg[user_id].predict(self.T[work_id].reshape(1, -1)))\n",
    "                y_delta_res.append(prediction)\n",
    "\n",
    "        cold_works = np.setdiff1d(X[:, 1], self.encountered_works)\n",
    "        print('{}-Item cold-start. ({} % cold)'.format(\n",
    "            len(cold_works), (len(cold_works)/len(X[:, 1]))*100\n",
    "        ))\n",
    "\n",
    "        return np.clip(y_pred + y_delta_res, -0.5, 4)\n",
    "\n",
    "    def get_shortname(self):\n",
    "        return 'balse-%d' % self.NB_COMPONENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Research:\n",
    "    @staticmethod\n",
    "    def load_dataset(dataset_name):\n",
    "        dataset = Dataset()\n",
    "        dataset.load_csv(\n",
    "            dataset_name,\n",
    "            lambda choice: rating_values[choice]\n",
    "        )\n",
    "        return dataset\n",
    "    \n",
    "    @staticmethod\n",
    "    def make_item_groups(X):\n",
    "        return X[:, 1]\n",
    "\n",
    "    @staticmethod\n",
    "    def make_user_groups(X):\n",
    "        return X[1, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dataset = Research.load_dataset('ratings.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing M: (2264 × 15663)\n",
      "Chrono: fill and center matrix [0q, 6962ms]\n",
      "Shapes (2264, 10) (10, 15663)\n",
      "Chrono: factor matrix [0q, 91591ms]\n",
      "Cond number for T: 2434.048621\n",
      "(15663, 503)\n",
      "  (676, 6392)\t-3.11889999118\n",
      "  (416, 3621)\t1.05088852036\n",
      "  (2199, 13035)\t1.44864612938\n",
      "  (499, 10502)\t0.841165206468\n",
      "  (70, 10424)\t0.406049779022\n",
      "  (2226, 4140)\t-0.722300404786\n",
      "  (624, 226)\t0.266411335123\n",
      "  (1413, 15541)\t-0.77181766783\n",
      "  (1794, 3388)\t-0.375363206757\n",
      "  (1799, 12253)\t0.0795611601991\n",
      "  (1720, 8940)\t-1.74465143779\n",
      "  (1250, 8635)\t0.826562868683\n",
      "  (878, 5036)\t0.499522590695\n",
      "  (764, 3705)\t0.419666350545\n",
      "  (813, 12801)\t0.54943523897\n",
      "  (2225, 3029)\t0.49086855277\n",
      "  (1117, 10157)\t1.54646248713\n",
      "  (1484, 2416)\t1.13560682454\n",
      "  (1186, 9325)\t-0.272378183792\n",
      "  (584, 13234)\t-0.917445599099\n",
      "  (697, 8248)\t-2.76505693364\n",
      "  (2085, 9596)\t1.4593000469\n",
      "  (1506, 4746)\t2.22146894629\n",
      "  (331, 2485)\t-0.152372949151\n",
      "  (373, 15339)\t-0.0357881069387\n",
      "  :\t:\n",
      "  (1808, 2880)\t-1.51976815516\n",
      "  (427, 482)\t-0.87680894976\n",
      "  (971, 14463)\t-0.960135974682\n",
      "  (367, 13905)\t0.968791168643\n",
      "  (2071, 3275)\t-0.509047067439\n",
      "  (1752, 4309)\t-0.656730318569\n",
      "  (2167, 10387)\t-1.10607850413\n",
      "  (425, 2880)\t-0.702120938592\n",
      "  (955, 8790)\t-0.367181877906\n",
      "  (1856, 2418)\t-1.2828069715\n",
      "  (596, 13741)\t-1.16424640388\n",
      "  (337, 12162)\t0.553952997999\n",
      "  (51, 10082)\t1.66372656802\n",
      "  (980, 603)\t0.3545682878\n",
      "  (304, 13826)\t2.68396674228\n",
      "  (122, 3094)\t0.866498939049\n",
      "  (651, 8541)\t-0.0706719081959\n",
      "  (1872, 15247)\t-0.209795004902\n",
      "  (1221, 442)\t0.119596143691\n",
      "  (26, 13524)\t-0.213680972675\n",
      "  (1235, 1487)\t-0.672471562454\n",
      "  (807, 14191)\t1.26975871955\n",
      "  (1886, 11002)\t-0.622123243067\n",
      "  (1795, 11431)\t-0.620154148429\n",
      "  (1373, 1756)\t-0.939951346414\n",
      "0\n",
      "100\n",
      "200\n",
      "400\n",
      "500\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n",
      "1200\n",
      "1300\n",
      "1400\n",
      "1500\n",
      "1600\n",
      "1700\n",
      "1800\n",
      "1900\n",
      "2000\n",
      "2100\n",
      "2200\n",
      "1474 not\n",
      "1654 not\n",
      "1362 not\n",
      "1224 not\n",
      "1617 not\n",
      "219 not\n",
      "131 not\n",
      "1654 not\n",
      "105 not\n",
      "1543 not\n",
      "1116 not\n",
      "219 not\n",
      "870 not\n",
      "2114 not\n",
      "1362 not\n",
      "334 not\n",
      "2018-Item cold-start. (3.1563306483146945 % cold)\n",
      "Was: [ 0.1  2.   0.1 ...,  2.  -0.5 -2. ]\n",
      "Predicted: [ 0.80937445  2.07685959  0.47063416 ...,  0.26437495  0.73166888\n",
      "  1.15903821]\n",
      "RMSE=1.305114\n",
      "Predicted: [ 0.82252959  2.11470033  0.53281125 ...,  0.28993669  0.71184283\n",
      "  1.14954108]\n",
      "RMSE=1.302361\n",
      "BALSE diagnostic:\n",
      "Condition number=nan\n",
      "R^2 score=0.112043\n",
      "Computing M: (2264 × 15663)\n",
      "Chrono: fill and center matrix [0q, 6778ms]\n",
      "Shapes (2264, 10) (10, 15663)\n",
      "Chrono: factor matrix [0q, 62623ms]\n",
      "Cond number for T: 2434.048621\n",
      "(15663, 503)\n",
      "  (676, 6392)\t-2.91777049022\n",
      "  (416, 3621)\t1.10351542684\n",
      "  (2199, 13035)\t1.46375832519\n",
      "  (70, 10424)\t0.5399583156\n",
      "  (624, 226)\t0.291963006677\n",
      "  (1413, 15541)\t-0.769504475651\n",
      "  (1794, 3388)\t-0.403160163759\n",
      "  (835, 15538)\t0.651474630105\n",
      "  (1720, 8940)\t-1.85631095757\n",
      "  (878, 5036)\t0.573805558915\n",
      "  (764, 3705)\t0.398273349932\n",
      "  (813, 12801)\t0.56800896827\n",
      "  (2225, 3029)\t0.50501188219\n",
      "  (1484, 2416)\t1.19581288299\n",
      "  (1186, 9325)\t-0.389061793322\n",
      "  (584, 13234)\t-1.09540011009\n",
      "  (697, 8248)\t-2.40850150591\n",
      "  (917, 8411)\t-0.568141460972\n",
      "  (2085, 9596)\t1.32104319544\n",
      "  (1506, 4746)\t2.10154639042\n",
      "  (331, 2485)\t-0.127534715107\n",
      "  (373, 15339)\t-0.0381514923465\n",
      "  (436, 15104)\t-0.397533967825\n",
      "  (960, 3219)\t-1.28937136878\n",
      "  (1333, 15066)\t-0.512862899167\n",
      "  :\t:\n",
      "  (1867, 4865)\t0.798862277602\n",
      "  (1919, 1259)\t-0.797590916193\n",
      "  (1752, 4309)\t-0.731629289209\n",
      "  (2167, 10387)\t-1.04502995039\n",
      "  (425, 2880)\t-0.255733297577\n",
      "  (955, 8790)\t-0.4357376352\n",
      "  (1179, 15378)\t1.02565413862\n",
      "  (1856, 2418)\t-1.42619482738\n",
      "  (596, 13741)\t-1.16850172139\n",
      "  (337, 12162)\t0.519135413575\n",
      "  (51, 10082)\t1.68382613148\n",
      "  (980, 603)\t0.448145426667\n",
      "  (304, 13826)\t2.76087948489\n",
      "  (122, 3094)\t0.858164119728\n",
      "  (651, 8541)\t-0.0610137916889\n",
      "  (1872, 15247)\t-0.241446032698\n",
      "  (1221, 442)\t-0.0747515471833\n",
      "  (26, 13524)\t-0.229656937443\n",
      "  (1235, 1487)\t-0.661760773839\n",
      "  (807, 14191)\t1.34716523459\n",
      "  (1886, 11002)\t-0.695307973797\n",
      "  (109, 307)\t-0.642815821001\n",
      "  (1344, 4670)\t-2.69525068946\n",
      "  (1795, 11431)\t-0.659920333266\n",
      "  (1373, 1756)\t-0.92550358404\n",
      "0\n",
      "100\n",
      "200\n",
      "400\n",
      "500\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n",
      "1200\n",
      "1300\n",
      "1500\n",
      "1600\n",
      "1700\n",
      "1800\n",
      "1900\n",
      "2000\n",
      "2100\n",
      "2200\n",
      "1400 not\n",
      "2151 not\n",
      "2194 not\n",
      "686 not\n",
      "1598 not\n",
      "1543 not\n",
      "1558 not\n",
      "1043 not\n",
      "2018-Item cold-start. (2.8164689462665735 % cold)\n",
      "Was: [ 0.1  2.  -0.5 ...,  0.1  0.1  0.5]\n",
      "Predicted: [ 1.22731714  0.73304724  0.80490482 ...,  1.12583029  1.31090647\n",
      "  0.84981551]\n",
      "RMSE=1.292699\n",
      "Predicted: [ 1.26093194  0.7638396   0.83663845 ...,  1.23399921  1.30167399\n",
      "  0.80003668]\n",
      "RMSE=1.289833\n",
      "BALSE diagnostic:\n",
      "Condition number=nan\n",
      "R^2 score=0.118293\n",
      "Computing M: (2264 × 15663)\n",
      "Chrono: fill and center matrix [0q, 8868ms]\n",
      "Shapes (2264, 10) (10, 15663)\n",
      "Chrono: factor matrix [0q, 78390ms]\n",
      "Cond number for T: 2434.048621\n",
      "(15663, 503)\n",
      "  (676, 6392)\t-2.99012672524\n",
      "  (1472, 7410)\t-0.86320384127\n",
      "  (2199, 13035)\t1.45623850974\n",
      "  (499, 10502)\t1.00113389898\n",
      "  (70, 10424)\t0.49261292575\n",
      "  (2226, 4140)\t-0.679931437275\n",
      "  (624, 226)\t0.224191491761\n",
      "  (1413, 15541)\t-0.592410888986\n",
      "  (835, 15538)\t0.617895509053\n",
      "  (1799, 12253)\t0.0733215322063\n",
      "  (1720, 8940)\t-1.79497785292\n",
      "  (1250, 8635)\t0.884597927323\n",
      "  (764, 3705)\t0.403857105183\n",
      "  (2225, 3029)\t0.485361790876\n",
      "  (1117, 10157)\t1.47276113777\n",
      "  (1186, 9325)\t-0.462309498154\n",
      "  (697, 8248)\t-2.62929766745\n",
      "  (2085, 9596)\t1.44396551665\n",
      "  (331, 2485)\t-0.102323473345\n",
      "  (373, 15339)\t-0.0837015225395\n",
      "  (436, 15104)\t-0.44117149783\n",
      "  (960, 3219)\t-1.39854857103\n",
      "  (1819, 1756)\t0.230380182957\n",
      "  (1494, 2860)\t-2.3112175687\n",
      "  (1266, 6211)\t-0.914867080088\n",
      "  :\t:\n",
      "  (832, 8402)\t-0.686758641502\n",
      "  (1808, 2880)\t-1.47190497539\n",
      "  (427, 482)\t-0.865994620467\n",
      "  (367, 13905)\t1.03964406483\n",
      "  (2071, 3275)\t-0.58303605517\n",
      "  (1867, 4865)\t0.848082687211\n",
      "  (1919, 1259)\t-0.683735445349\n",
      "  (1752, 4309)\t-0.774639018598\n",
      "  (425, 2880)\t-0.406329753388\n",
      "  (955, 8790)\t-0.479684197776\n",
      "  (1179, 15378)\t0.93712432974\n",
      "  (1856, 2418)\t-1.18709287462\n",
      "  (596, 13741)\t-1.09609312692\n",
      "  (51, 10082)\t1.60954238581\n",
      "  (304, 13826)\t2.7716653237\n",
      "  (122, 3094)\t0.837850605083\n",
      "  (651, 8541)\t-0.0730444522065\n",
      "  (1221, 442)\t0.0679450421906\n",
      "  (26, 13524)\t-0.282620532621\n",
      "  (1235, 1487)\t-0.75574818864\n",
      "  (807, 14191)\t1.36084422087\n",
      "  (1886, 11002)\t-0.666648294268\n",
      "  (109, 307)\t-0.562546096389\n",
      "  (1344, 4670)\t-2.72338404629\n",
      "  (1373, 1756)\t-0.961596080484\n",
      "0\n",
      "100\n",
      "200\n",
      "400\n",
      "500\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n",
      "1200\n",
      "1300\n",
      "1400\n",
      "1500\n",
      "1600\n",
      "1700\n",
      "1800\n",
      "1900\n",
      "2000\n",
      "2100\n",
      "2200\n",
      "1474 not\n",
      "1957 not\n",
      "1362 not\n",
      "490 not\n",
      "2038 not\n",
      "1039 not\n",
      "105 not\n",
      "2005 not\n",
      "1218 not\n",
      "870 not\n",
      "1043 not\n",
      "1362 not\n",
      "334 not\n",
      "1957 not\n",
      "2038 not\n",
      "2018-Item cold-start. (2.9206165424415658 % cold)\n",
      "Was: [ 2.  -0.5  0.5 ...,  2.  -0.5  0.5]\n",
      "Predicted: [ 1.06050435  0.01130692  0.52792872 ...,  1.68199154  0.10474697\n",
      "  1.24893633]\n",
      "RMSE=1.312871\n",
      "Predicted: [ 1.0409652  -0.00756029  0.45357841 ...,  1.71040725  0.04477309\n",
      "  1.27443008]\n",
      "RMSE=1.312253\n",
      "BALSE diagnostic:\n",
      "Condition number=nan\n",
      "R^2 score=0.115210\n",
      "BALSE: RMSE=1.303561, R^2 score=0.116300\n",
      "ALS: RMSE=1.301482\n"
     ]
    }
   ],
   "source": [
    "k_fold = GroupShuffleSplit(n_splits=3)\n",
    "\n",
    "balse_instances = []\n",
    "means = defaultdict(list)\n",
    "item_groups = Research.make_item_groups(dataset.anonymized.X)\n",
    "for i_train, i_test in k_fold.split(dataset.anonymized.X, dataset.anonymized.y, item_groups):\n",
    "    als = MangakiALS(NB_COMPONENTS=10, LAMBDA=0.2)\n",
    "    als.set_parameters(dataset.anonymized.nb_users, dataset.anonymized.nb_works)\n",
    "    als.fit(dataset.anonymized.X[i_train], dataset.anonymized.y[i_train])\n",
    "    \n",
    "    balse = MangakiBALSE(NB_COMPONENTS=10, LAMBDA=0.2)\n",
    "    balse.set_parameters(dataset.anonymized.nb_users, dataset.anonymized.nb_works)\n",
    "    balse.fit(dataset.anonymized.X[i_train], dataset.anonymized.y[i_train], als)\n",
    "    \n",
    "    balse_y_pred = balse.predict(dataset.anonymized.X[i_test])\n",
    "    als_y_pred = als.predict(dataset.anonymized.X[i_test])\n",
    "    \n",
    "    balse_rmse = balse.compute_rmse(balse_y_pred, dataset.anonymized.y[i_test])\n",
    "    als_rmse = als.compute_rmse(als_y_pred, dataset.anonymized.y[i_test])\n",
    "    \n",
    "    print('Was: {}'.format(dataset.anonymized.y[i_test]))\n",
    "    for y_pred, rmse in zip((balse_y_pred, als_y_pred), (balse_rmse, als_rmse)):        \n",
    "        print('Predicted: {}'.format(y_pred))\n",
    "        print('RMSE={:f}'.format(rmse))\n",
    "    \n",
    "    print('BALSE diagnostic:')\n",
    "    print('Condition number={:f}'.format(np.mean(balse.cond_numbers)))\n",
    "    print('R^2 score={:f}'.format(np.mean(balse.r2_scores)))\n",
    "    balse_instances.append(balse)\n",
    "    \n",
    "    means['balse'].append(balse_rmse)\n",
    "    means['als'].append(als_rmse)\n",
    "    \n",
    "    gc.collect()\n",
    "\n",
    "print('BALSE: RMSE={:f}, R^2 score={:f}'.format(np.mean(means['balse']), np.mean([np.mean(instance.r2_scores) for instance in instances])))\n",
    "print('ALS: RMSE={:f}'.format(np.mean(means['als'])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "def plot_pca_of_reg_lins(instance):\n",
    "    coeffs = np.array([reg.coef_ for reg in instance.reg.values()])\n",
    "    pca = PCA(n_components=2)\n",
    "    reduced_coeffs = pca.fit_transform(coeffs)\n",
    "    print ('Explanied variance ratio: {}'.format(pca.explained_variance_ratio_))\n",
    "    \n",
    "    plt.plot(reduced_coeffs[:,0], reduced_coeffs[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explanied variance ratio: [ 0.30236238  0.10136952]\n",
      "Explanied variance ratio: [ 0.22775693  0.12103242]\n",
      "Explanied variance ratio: [ 0.30943899  0.1923255 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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BfrDwBzybZxS46mncRDt3qYJZ02Al7ZHPze2/fDtRilONUVprDlQfILs42yxZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5d71a86b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for instance in instances:\n",
    "    plot_pca_of_reg_lins(instance)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Django Shell-Plus",
   "language": "python",
   "name": "django_extensions"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}